Title Page Trace Element Partitioning in Mantle Minerals with Applications to Subsolidus Re-Equilibration and Thermobarometry by Chenguang Sun B.Sc. China University of Geosciences, Beijing, 2007 M.Sc. Brown University, 2010 A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Geological Sciences at Brown University Providence, Rhode Island May 2014 Copyright Page © Copyright 2014 by Chenguang Sun Signature Page This dissertation by Chenguang Sun is accepted in its present form by the Department of Geological Sciences as satisfying the dissertation requirement for the degree of Doctor of Philosophy. Date _____________________ ____________________________ Yan Liang, Advisor Recommended to the Graduate Council Date _____________________ ____________________________ Reid Cooper, Reader Date _____________________ ____________________________ Stephen Parman, Reader Date _____________________ ____________________________ E. Marc Parmentier, Reader Date _____________________ ____________________________ Alberto Saal, Reader Date _____________________ ____________________________ E. Bruce Watson, External Reader Approved by the Graduate Council Date _____________________ ____________________________ Peter M. Weber Dean of the Graduate School iii Curriculum Vitae Chenguang Sun 324 Brook St. Box 1846 Cell: +1 (401) 215-0432 Providence, RI 02912 Email: Chenguang_Sun@brown.edu Chenguang Sun was born on October 2, 1985 in Henan Province, P. R. China. Education Brown University, Providence, RI, U.S. Ph.D., Geological Sciences, 2014 Thesis: Trace element partitioning between mantle minerals and basaltic melts with applications to subsolidus re-equilibration and thermobarometry Advisor: Prof. Yan Liang M.Sc., Geological Sciences, 2010 Thesis: Partitioning behavior of rare-earth elements between diopside and anhydrous silicate melt during adiabatic mantle melting Advisor: Prof. Yan Liang China University of Geosciences, Beijing, China B.Sc., Geology, 2007 Thesis: Geochronology and geochemistry of Sailipu ultrapotassic volcanic rocks, Southern Tibet Advisor: Prof. Zhidan Zhao Research Interests My research interests are in the areas of experimental petrology, mantle geochemistry, mantle melting, magma fractionation, diffusion and application of experimental and modeling results to understanding of geological observations. My current research focuses on ! Trace element partitioning in major rock-forming minerals ! Development and applications of REE based two-mineral geothermobarometry ! Mantle melting and melt migration ! Evolution of the lunar magma ocean Publications 9. Sun C, Liang Y. 2014. An assessment of subsolidus re-equilibration on REE distribution among mantle minerals, olivine, orthopyroxene, clinopyroxene, and garnet in peridotites. Chemical Geology, 372: 80-91. Doi: 10.1016/j.chemgeo.2014.02.014. 8. Dygert N, Liang Y, Sun C, Hess P. 2014. An experimental study of trace element partitioning between augite and Fe-rich basalts. Geochimica et Cosmochimica Acta. Doi: 10.1016/j.gca.2014.01.042. 7. Sun C, Liang Y. 2013. The importance of crystal chemistry on REE partitioning between mantle minerals (garnet, clinopyroxene, orthopyroxene and olivine) and basaltic melts. Chemical Geology, 358: 23-36. Doi:10.1016/j.chemgeo.2013.08.045 iv 6. Liang Y, Sun C, Yao L. 2013. A REE-in-two-pyroxene thermometer for mafic and ultramafic rocks. Geochimica et Cosmochimica Acta, 102: 246-260. Doi: 10.1016/j.gca.2012.10.035 5. Sun C, Liang Y. 2013. Distribution of REE and HFSE between low-Ca pyroxene and lunar picritic melts around multiple saturation points. Geochimica et Cosmochimica Acta, 119: 340-358. Doi: 10.1016/j.gca.2013.05.036 4. Yao L, Sun C, Liang Y. 2012. A parameterized model for REE distribution between low- Ca pyroxene and basaltic melts with applications to REE partitioning in low-Ca pyroxene along a mantle adiabat and during pyroxenite-derived melt and peridotite interaction. Contributions to Mineralogy and Petrology, 164: 261-280. Doi: 10.1007/s00410-012-0737- 5 3. Sun C, Liang Y. 2012. Distribution of REE between clinopyroxene and basaltic melt along a mantle adiabat: effects of major element composition, water, and temperature. Contributions to Mineralogy and Petrology, 163: 807-823. Doi: 10.1007/s00410-011-0700- x 2. Zhao Z, Mo X, Dilek Y, Niu Y, DePaolo DJ, Robinson P, Zhu D, Sun C, Dong G, Zhou S, Luo Z, Hou Z. 2009. Geochemical and Sr-Nd-Pb-O isotopic compositions of the post- collisional ultrapotassic magmatism in SW Tibet: Petrogenesis and implications for India intra-continental subduction beneath southern Tibet. Lithos, 113: 109-212. Doi: 10.1016/j.lithos.2009.02.004 1. Yang Z, Luo Z, Zhang H, Zhang Y, Huang F, Sun C, Dai J. 2009. Petrogenesis and Geological Implications of the Tianheyong Cenozoic Basalts, Inner Mongolia China. Earth Science Frontiers, 16(2): 090-106. Doi: 10.1016/S1872-5791(08)60083-4 • Zhu DC, Mo XX, Zhao ZD, Xu JF, Zhou CY, Sun CG, Wang LQ, Chen HH, Dong GC, Zhou S. 2008. Zircon U-Pb geochronology of Zenong group volcanic rocks in Coqen area of the Gangdese, Tibet and tectonic significance. Acta Petrologica Sinica, 24 (3): 401-412 (in Chinese with English abstract) • Sun CG, Zhao ZD, Mo XX, Zhu DC, Dong GC, Zhou S, Chen HH, Xie LW, Yang YH, Sun JF, Yu F. 2008. Enriched mantle source and petrogenesis of Sailipu ultrapotassic rocks in southwestern Tibetan Plateau: constraints from zircon U-Pb geochronology and Hf isotopic compositions. Acta Petrologica Sinica, 24 (2): 249-264 (in Chinese with English abstract) • Zhao ZD, Mo XX, Sun CG, Zhu DC, Niu YL, Dong GC, Zhou S, Dong X, Liu YS. 2008. Mantle xenoliths in southern Tibet: geochemistry and constraints for the nature of the mantle. Acta Petrologica Sinica, 24 (2): 193-202 (in Chinese with English abstract) • Sun CG, Zhao ZD, Mo XX, Zhu DC, Dong GC, Zhou S, Dong X and Xie GG. 2007. Geochemistry and origin of the Miocene Sailipu ultrapotassic rocks in western Lhasa block, Tibetan Plateau. Acta Petrologica Sinica, 23 (11): 2715-2726 (in Chinese with English abstract) Manuscripts in preparation 1. Sun C, Liang Y. A REE-in-garnet-clinopyroxene thermobarometer for garnet peridotites, eclogites, and garnet pyroxenites 2. Sun C, Liang Y. A REE-in-plagioclase-clinopyroxene thermometer for mafic and ultramafic rocks v 3. Sun C, Graff M, Liang Y. Distribution of REE between anorthite and lunar basaltic melts: a parameterized model with applications to parent magma compositions of lunar ferroan anorthosites 4. Sun C, Liang Y. A critical reappraisal of the solubilities of rutile, ilmenite, and armalcolite in molten silicates: Effects of temperature, pressure, water, and melt composition. 5. Sun C, Liang Y. Parameterized models for HFSE partitioning between pyroxene and basaltic melt and between orthopyroxene and clinopyroxene. Conference Abstracts/Presentations 19. Sun C, Liang Y. 2014. Crystallization temperatures of lunar FANs revealed by a new REE- in-plagioclase-clinopyroxene thermometer. Goldschmidt, abstract. 18. Sun C, Liang Y, Ashwal L, and VanTongeren J. 2013. Temperature variations along stratigraphic height across the Bushveld complex with implications for magma chamber processes in layered intrusions. GSA Annual Meeting in Denver: 125th Anniversary of GSA 17. Sun C, Yao L, Liang Y. 2013. Thermobarometers based on REE partitioning between mantle minerals. GSA Annual Meeting in Denver: 125th Anniversary of GSA. 16. Sun C, Liang Y. 2013. Distribution of REE between garnet and clinopyroxene: a new thermobarometry for garnet peridotites and eclogites. Fall AGU, V51B-2649. 15. Liang Y, Sun C, Ashwal L, VanTongeren J. 2013. Spatial variations in temperature across the Bushveld layered intrusion revealed by REE-in-plagioclase-pyroxene thermometers with implications for magma chamber processes. Fall AGU, V54B-07. 14. Sun C, Liang Y. 2013. A REE-in-plagioclase-clinopyroxene thermometer for mafic and ultramafic rocks from the Earth, Moon, and other planetary bodies. 44th Lunar and Planetary Science Conference, abstract# 1627. 13. Sun C, Liang Y, Hess P. 2013. A parameterized thermodynamic model for ilmenite solubility in silicate melts. 44th Lunar and Planetary Science Conference, abstract# 2295. 12. Graff M, Sun C, Liang Y. 2013. Internally consistent REE partitioning models for anorthite and low-Calcium pyroxene: a reappraisal of subsolidus reequilibration with applications to parent magma compositions of lunar ferroan anorthosites. 44th Lunar and Planetary Science Conference, abstract# 1641. 11. Sun C, Liang Y, Yao L. 2012. A REE-in-two-pyroxene thermometer and a REE-in-garnet- cpx thermometer for mafic and ultramafic rocks. Fall AGU, V33C-2888. 10. Sun C, Liang Y. 2012. Trace element partitioning between low-calcium pyroxene and lunar picritic glass melts at multiple-saturation points with applications to melting and melt migration in a heterogeneous lunar cumulate mantle. 43rd Lunar and Planetary Science Conference, #1952. 9. Liang Y, Yao L, Sun C, Hess P. 2012. A REE-in-two-pyroxene thermometer for mafic and ultramafic rocks from the Earth, Moon (FANs and Mg-suite rocks), and other planetary bodies: promises and challenges. 43rd Lunar and Planetary Science Conference, #1987. 8. Sun C, Liang Y. 2011. Simple models for trace element fractionation during melting, melt transport and melt-rock reaction in a chemically and lithologically heterogeneous mantle. Fall AGU, V23B-2569. vi 7. Yao L, Sun C, Liang Y. 2011. Self-consistent models for REE partitioning among high-Ca pyroxene, low-Ca pyroxene, and basaltic melts with applications to REE distribution during adiabatic mantle melting and pyroxenite-derived melt and mantle interaction. Fall AGU, V23B-2570. 6. Sun C, Yao L, Liang Y. 2011. Some speculations on the distribution of REE between orthopyroxene and lunar picritic glass melts at multiple-saturation points. 42nd Lunar and Planetary Science Conference, #2009. 5. Sun C, Liang Y. 2010. Distribution of REE between clinopyroxene and basaltic melt along a mantle adiabat: Effects of major element composition, water, and temperature. Fall AGU, V23B-2399. 4. Yao L, Dygert N, Peterson M, Sun C, Wetzel D, Liang Y. 2010. A “bundle of columns” model for trace element fractionation during melting and melt migration in a vertically upwelling, chemically and lithologically heterogeneous mantle, Fall AGU, V11A-2258. 3. Sun C, Liang Y. 2010. The distribution of REE between diopside and basaltic melt along a mantle adiabat: A coupled major and trace element study. Geochimica et Cosmochimica Acta, 74, A1006. 2. Sun CG, Zhu DC, Zhao ZD, Mo XX, Dong GC. 2007. Geochemistry of the Sailipu ultrapotassic rocks in western Lhasa block: origin and tectonic implications. 22nd HKT (Himalayas-Karakoram-Tibet) Workshop (Hong Kong), Abstract volume, 90. 1. Zhao ZD, Mo XX, Sun CG, Dong GC, Zhou S, Zhu DC. 2007. Mantle-derived xenoliths from the Sailipu ultrapotassic rocks in western Lhasa block: constraints on the nature of the mantle. 22nd HKT (Himalayas-Karakoram-Tibet) Workshop (Hong Kong), Abstract volume, pp.117. Honors/Awards ! Devonshire Postdoctoral Scholar, Woods Hole Oceanographic Institution, 2014 ! Student Travel Grant, GSA Annual Meeting, 2013 ! Dissertation Fellowship, Brown University, Spring 2013 ! Outstanding Student Paper Award, VGP section, AGU Fall Meeting, 2012 ! Outstanding Graduate Student Paper Award, China Univ. of Geosciences, Beijing, 2007 ! Outstanding Undergraduate Senior Thesis Award, China Univ. of Geosciences, Beijing, 2007 ! Outstanding Student Paper Award, National Annual Symposium on Petrology and Geodynamics, Wuhan, China, 2007 Professional Experience ! Research/Teaching Assistant, Brown University, August 2008 to present ! Research Assistant, China Univ. of Geosciences, Beijing, August 2006 to June 2008 Teaching Experience ! Mentor: Undergraduate senior research, Co-advising Michelle Graff with Prof. Yan Liang, Brown University, August 2012 to May 2013 ! Teaching Assistant: Mineralogy Lab (9 students), Brown University, Fall 2011 vii ! Instructor: Field Geology (30 students), China Univ. of Geosciences, Beijing, China, July 2008 Field Experience ! Field Assistant to Prof. Zhidan Zhao, Tibet, China, August 2006 ! Geology field camp, Zhoukoudian, Beijing, China, July 2005 ! Geology field camp, Beidahe, Hebei, China, July 2004 Skills ! Piston cylinder, petrographic microscopy, electron microprobe, LA-ICP-MS, SIMS, thin section ! Proficient in Matlab, Microsoft Office, and Adobe Illustrator/Photoshop; intermediate skills in COMSOL, VB/VBA, and Fortran; knowledge of C Services ! Graduate student representative, Department of Geological Sciences, Brown University, Fall 2011 ! Organizer of Geochemistry/Mineralogy/Petrology seminar, Brown University, Fall 2010 ! Reviewer for Geochimica et Cosmochimica Acta, Bulletin of Volcanology Invited Seminars ! Geophysical Sciences Colloquium, University of Chicago, April 2014 ! Department of Geology and Geophysics, WHOI, January 2014 ! Solid Earth Seminar, Boston University, March 2013 Professional Associations ! American Geophysical Union (AGU) ! Mineralogical Society of America (MSA) ! The Geochemical Society (GS) ! The Geological Society of America (GSA) viii Abstract Olivine, orthopyroxene, clinopyroxene, garnet and plagioclase are major rock-forming minerals in the Earth mantle and other planetary bodies. The partitioning of trace elements into these minerals is fundamental to understanding of the magmatic and subsolidus processes in the Earth and other planetary bodies. In Chapters 1, 2, 3, and 6, I present a new generation of lattice strain models for rare earth elements (REEs) partitioning between mantle minerals (clinopyroxene, orthopyroxene, garnet, olivine, and plagioclase) and basaltic melts that were calibrated against experimentally determined partitioning data. Application of these models to mantle melting and magma fractionation processes demonstrate: (1) temperature, pressure and mineral composition dominate REE partitioning between mantle minerals and basaltic melts; (2) the competing effects of temperature and composition lead to constant REE partition coefficients in pyroxene during adiabatic mantle melting; (3) the combining effects of temperature and composition result in significant variations in mineral-melt REE partition coefficients during solidification of a large magma body. In Chapter 4, I have developed generalized models for REE partitioning between coexisting mantle minerals. These models reveal that subsolidus re-equilibration can significantly redistribute REEs among minerals in peridotites. Without proper correction for subsolidus re- equilibration, the extents of melting for abyssal peridotites based on REE abundances in clinopyroxene can be significantly over-estimated. In Chapters 5 and 6, I present two new thermobarometers, a REE-in-garnet-clinopyroxene thermobarometer, and a REE-in-plagioclase-clinopyroxene thermometer, for mafic and ultramafic rocks. These thermobarometers are based on the temperature and pressure dependent REE partitioning between two coexisting minerals. The REE-based thermobarometers are unique because they can fully make use of all REEs as a group to constrain robust temperatures and pressures simultaneously. Due to the slower diffusion rates of REEs in minerals, the REE-based thermometers generally record higher closure temperatures than major element-based ix thermometers for samples that experienced cooling, but provide former equilibrium temperatures for samples that underwent heating. The REE-based thermobarometers can shed new light on thermal evolutions of mafic and ultramafic rocks from different tectonic environments. x Acknowledgements First, I would like to thank my PhD advisor, Yan Liang, for his guidance and continuous support along the long journey towards my PhD degree. I am sincerely grateful that he opened me the doors to experimental petrology and geochemical kinetics and provided me with a great opportunity to pursue a wide range of problems. Liang has also been a good friend. Having dinner with Liang’s family on Chinese New Year in my first year made me feel warmly welcomed. I would also like to thank Alberto Saal, Marc Parmentier, Reid Cooper, Steve Parman, and Bruce Watson for their support and serving on my committee. Paul Hess was always there to talk about some scientific problem, and inspired me to think deeply about many problems on the Moon. I wish to thank Bruce Watson for taking his time on my PhD defense committee and for his encouragement. I would like to thank Lijing Yao and Nick Dygert for working together in the lab and for discussing preliminary ideas. I also want to thank Qinglan Peng for her help and support during my first year at Brown. I would like to thank Colin Jackson, Amanda Getsinger, Mary Peterson, Tabb Prissel, Kei Shimizu, Diane Wetzel, and many other graduate students for making the basement like a family. Ruby Ho, Li Gao, and Yun Wang are thanked for their help and support during the past years at Brown. I am deeply indebted to my parents for teaching me the value of hard work and for their love and support through my 6 more years of school. I also want to thank my mother-in-law for her help especially in the last month of my thesis. Finally, I am eternally grateful to my wife and best friend, Lijing Yao, for putting up with me during the difficult time, for her encouragement and belief in me whenever I have doubt about myself. Without her, I would never achieve all that I have during the past seven years. The arrival of our newborn son, Lucus, was the greatest thing in the past six years, and brought a lot of busy but delightful time at the end of my thesis. This thesis is dedicated to my wife, Lijing, and my son, Lucus! xi Table of Contents Title&Page& i& Copyright&Page& ii& Signature&Page& iii& Curriculum&Vitae& iv& Abstract& ix& Acknowledgements& xi& Table&of&Contents& xii& List&of&Tables& xvi& List&of&Illustrations& xvii& Chapter 1:1& Distribution+of+REE+between+Clinopyroxene+and+Basaltic+Melt+along+a+ Mantle+Adiabat:+Effects+of+Major+Element+Composition,+Water,+and+ Temperature+ 1& Abstract& 2& 1.&Introduction& 3& 2.&Method& 7& 2.1.&Data&compilation&and&criteria& 7& 2.2.&Parameterization&procedures& 8& 3.&Results& 11& 4.&Discussion& 12& 4.1.&Model&sensitivity&to&analytic&uncertainty&and&model&limitations& 13& 4.2.&Effects&of&melt&structure&and&pressure&on&REE&partitioning& 15& 4.3.&The&effects&of&temperature&and&cpx&composition&on&REE&partitioning& 15& 4.4.&Competing&or&enhancing&effects&of&temperature&and&cpx&composition& 18& 4.5.&The&effect&of&H2O&on&REE&partitioning& 19& 5.&Implications&for&Adiabatic&Mantle&Melting& 19& 5.1.&REE&partitioning&in&cpx&along&the&mantle&adiabat& 20& 5.2.&The&effect&of&varying&partition&coefficients&on&REE&fractionation& 23& 5.3.&The&effect&of&water&on&REE&fractionation& 24& 6.&Conclusions& 26& Acknowledgements& 27& References& 27& Figure&Captions& 34& Figures& 40& Tables& 60& Supplementary&Material& 63& Chapter 2:2& Distribution+of+REE+and+HFSE+between+LowHCa+Pyroxene+and+Lunar+ Picritic+Melts+around+Multiple+Saturation+Points+ 65& Abstract& 66& 1.&Introduction& 67& 2.&An&Experimental&Study&of&Trace&Element&Partitioning&between&LowTCa&Pyroxene&and& Lunar&Picritic&Melts& 70& 2.1.&Experimental&methods& 70& 2.2.&Analytical&methods& 71& xii 2.3.&Experimental&results& 72& 3.&Models&for&Trace&Element&Partitioning& 75& 3.1.&Lattice&strain&model& 75& 3.2.&REE&partitioning&between&lowTCa&pyroxene&and&lunar&basaltic&melts& 77& 3.3.&A¶meterized&model&for&Ti,&Hf,&and&Zr&partitioning&in&lowTCa&pyroxene& 80& 3.3.1.&Data&compilation& 81& 3.3.2.&Parameterization&method& 82& 3.3.3.&Model&result& 83& 4.&Lunar&Applications& 84& 4.1.&REE&and&HFSE&partitioning&in&lowTCa&pyroxene&at&multipleTsaturation&points& 84& 4.2.&Trace&element&partitioning&in&lowTCa&pyroxene&during&crystallization&of&the&lunar& magma&ocean& 87& 5.&Summary&and&Conclusions& 88& Acknowledgements& 89& References& 90& Figure&Captions& 98& Figures& 103& Tables& 116& Chapter 3:3& The+Importance+of+Crystal+Chemistry+on+REE+Partitioning+between+ Mantle+Minerals+(Garnet,+Clinopyroxene,+Orthopyroxene,+and+Olivine)+ and+Basaltic+Melts+ 124& Abstract& 125& 1.&Introduction& 126& 2.&Review&of&Previous&Partitioning&Models& 130& 2.1.&Garnet&models& 130& 2.2.&Olivine&models& 133& 3.&Methods& 135& 3.1.&Data&compilation& 135& 3.2.&Parameterization&strategies&and&methods& 136& 4.&Results& 141& 5.&Discussion& 142& 5.1.&Garnet&model& 142& 5.2.&Olivine&model& 144& 5.3.&Sources&of&uncertainties&and&model&limitations& 146& 5.4.&Model&validation&using&field&data& 147& 6.&Crystal&Chemistry&Controls&on&REE&Partitioning& 149& 7.&Summary&and&Conclusions& 152& Acknowledgements& 152& References& 153& Figure&Captions& 160& Figures& 164& Tables& 204& Chapter 4:4& An+Assessment+of+Subsolidus+ReHEquilibration+on+REE+Distribution+ among+Mantle+Minerals+Olivine,+Orthopyroxene,+Clinopyroxene,+and+ Garnet+in+Peridotites+ 205& Abstract& 206& xiii 1.&Introduction& 207& 2.&MineralTMineral&REE&Partitioning&Models& 208& 2.1.&The&lattice&strain&model& 208& 2.2.&MineralTmelt&REE&partitioning&models& 211& 2.3.&MineralTmineral&REE&partitioning&models& 212& 2.4.&Model&validation& 213& 3.!PTTTX&Dependent&REE&Partitioning&among&Mantle&Minerals& 214& 4.&Implications&for&Subsolidus&ReTEquilibration& 216& 5.&Application&to&Mantle&Melting& 219& 6.&Summary&and&Further&Discussion& 223& Acknowledgements& 224& References& 224& Figure&Captions& 229& Figures& 233& Tables& 245& Supplementary&Material& 248& Chapter 5:5& A+REEHinHGarnetHClinopyroxene+Thermobarometer+for+Eclogites,+ Granulites+and+Garnet+Peridotites+ 251& Abstract& 252& 1.&Introduction& 253& 2.&Developing&a&REETinTGarnetTClinopyroxene&Thermobarometer& 255& 2.1.&Theoretical&basis& 255& 2.2.&GarnetTclinopyroxene&REE&partitioning&model& 257& 2.3.&A&REETinTgarnetTclinopyroxene&thermobarometer& 261& 3.&Validation&of&the&REETinTGarnetTClinopyroxene&Thermobarometer& 263& 3.1.&Experimental&test& 263& 3.2.&Field&test& 266& 4.&Geological&Applications& 269& 4.1.&Physical&meaning&of&calculated&temperature&and&pressure& 270& 4.2.&Granulites,&eclogites&and&peridotites&from&cooling&tectonic&settings& 272& 4.3.&Eclogites,&garnet&pyroxenites&and&peridotites&from&thermally&perturbed&settings & 273& 5.&Summary&and&Further&Discussion& 275& Acknowledgements& 278& References& 278& Figure&Captions& 286& Figures& 291& Chapter 6:6& A+REEHinHPlagioclaseHClinopyroxene+Thermometer+for+Mafic+and+ Ultramafic+Rocks+ 344& Abstract& 345& 1.&Introduction& 346& 2.&Developing&a&REETinTPlagioclaseTClinopyroxene&Thermometer& 347& 2.1.&A&plagioclaseTmelt&REE&partitioning&model& 348& 2.2.&A&REETinTplagioclaseTclinopyroxene&thermometer& 352& 3.&Geological&Applications& 355& xiv 3.1.&Applications&to&planetary&materials& 355& 3.2.&Applications&to&the&Bushveld&layered&intrusions& 357& Acknowledgements& 358& References& 359& Figure&Captions& 364& Figures& 366& Supplementary&Material& 377& ! Appendix A: A Parameterized Lattice Strain Model for Ti, Hf, and Zr Partitioning between Clinopyroxene and Basaltic Melt 384 xv List of Tables Table 1-1 Data sources and experimental run conditions 60& Table 1-2 Derived D0, r0 and E from partitioning experiments 61& Table 1-3 Recommended cpx-melt partition coefficients for anhydrous melting in spinel lherzolite region 62& Table 2-1 Nominal major element compositions of starting materials 116& Table 2-2 Compositions of experimental run products 117& Table 2-3 Experimental conditions and run products 118& Table 2-4 Orthopyroxene-melt partition coefficients 121& Table 2-5 List of lattice strain parameters for individual experiments 122& Table 2-6 Recommended REE and HFSE partition coefficients between orthopyroxene and lunar melts 123& Table 3-1 Data sources and experimental run conditions 204& Table 4-1 Melting parameters obtained by the nonlinear least squares inversion method for abyssal peridotites from the Central Indian Ridge 245& Table 4-S1 Mineral compositions and proportions in four representative mantle peridotites 246& Table 6-S1 Trace element composition of clinopyroxene and plagioclase from the Lower Main Zone of the Bushveld Complex 378& xvi List of Illustrations Figure 1-1: Mineral modal proportions and degrees of melting (F) as a function of pressure during adiabatic melting of a garnet lherzolite 40& Figure 1-2 Comparison of experimentally determined clinopyroxene-melt REE partition coefficients and those predicted by the model of Wood and Blundy (1997, 2002) 41& Figure 1-3 Nonlinear correlations among the lattice strain parameters 42& Figure 1-4 Comparison of experimentally determined clinopyroxene-melt REE partition coefficients and those predicted by the model from this study 43& Figure 1-5 Uncertainties of predicted partition coefficients derived from the uncertainties in temperature and composition 44& Figure 1-6 Comparison of experimentally determined and model predicted REE partition coefficients in clinopyroxene relevant to melting of mafic pyroxenite 45& Figure 1-7 Schematic diagrams showing temperature and compositional effects on clinopyroxene-melt REE partitioning 46& Figure 1-8 Partition coefficients of Ce and Yb from Gaetani and Grove (1995) as a function of AlT and MgM2 contents in clinopyroxene 47& Figure 1-9 Schematic diagrams showing the competing effects and enhancing effects between clinopyroxene composition and temperature 48& Figure 1-10 Variations of clinopyroxene-melt REE partition coefficients during adiabatic mantle melting 49& Figure 1-11 REE fractionation during anhydrous adiabatic mantle melting 50& Figure 1-12 REE fractionation during hydrous adiabatic mantle melting 51 Figure 1-S1 Comparisons of measured clinopyroxene-melt partitioning data and those predicted by different models for individual experiments 57& Figure 1-S2 Comparison between experimentally measured partition coefficients and model derived values calculated by refitting the model of Wood and Blundy (1997, 2002) 58& Figure 1-S3 Comparison between experimentally measured partition coefficients and model derived values calculated by our model 59& Figure 1-S4 D0 as a function of temperature, pressure, AlT and MgM2 in pyroxene, NBO/T of bulk melt and H2O content in the melt 52 Figure 2-1 Melt compositions from low-Ca pyroxene partitioning experiments 103& Figure 2-2 Low-Ca pyroxene compositions from partitioning experiments and multiple saturation experiments 104& Figure 2-3 Back-scattered electron images of representative experimental products of runs A15GG210 and A15Red219 105& Figure 2-4 Spider diagram showing low-Ca pyroxene-melt trace element partition coefficients measured in this study and those from the literature 106& Figure 2-5 Onuma diagrams showing the measured partition coefficients between low-Ca pyroxene and lunar picritic melts from this study 107& Figure 2-6 Onuma diagrams comparing measured REE and Y partition coefficients in low-Ca pyroxene with model predictions 108& Figure 2-7 Comparison between predicted Ti, Hf and Zr partition coefficients in low-Ca pyroxene and experimentally measured values 109& Figure 2-8 Estimated partition coefficients of low-Ca pyroxene from multiple saturation experiments 110& Figure 2-9 Variations of REE and HFSE partition coefficients in low-Ca pyroxene during crystallization of the lunar magma ocean 111 Figure 2-S1 Variations of melt Ti in molar fraction per six-oxygen as a function of melt TiO2 contents in weight fraction from the compiled experiments 112& Figure 2-S2 Correlation between Ti molar fraction in the melt per six-oxygen and melt TiO2 xvii contents in weight fraction from the lunar basaltic melts 113& Figure 2-S3 Ti, Hf and Zr partition coefficients in low-Ca pyroxene as a function of pyroxene composition 114& Figure 2-S4 Calculated REE and HFSE partition coefficients in low-Ca pyroxene for the lunar glasses 115 Figure 3-1 REE, Y and Sc partition coefficients in garnet and olivine as a function of their ionic radii 164& Figure 3-2 Comparisons between experimentally determined garnet-melt REE and Y partition coefficients and those predicted by previous models 165& Figure 3-3 Comparisons between experimentally determined olivine-melt REE, Y and Sc partition coefficients and those predicted by previous models 166& Figure 3-4 Composition of garnet from compiled anhydrous and hydrous partitioning experiments 167& Figure 3-5 Comparisons between predicted partition coefficients by this study and experimentally determined values for garnet-melt and olivine-melt 168& Figure 3-6 Plots of garnet-melt Lu partition coefficients as functions of temperature, pressure, and Ca in garnet 169& Figure 3-7 Plots of olivine-melt Sc partition coefficients as functions of temperature, pressure, and forsterite and Al2O3 content in olivine 170& Figure 3-8 Comparisons of predicted and measured garnet- and olivine-clinopyroxene REE and Y partition coefficients from eclogites and peridotites 171 Figure 3-S1 Comparisons of experimentally determined garnet-melt REE and Y partition coefficients and those predicted by previous models 172& Figure 3-S2 Comparisons of measured garnet-melt partitioning data and those predicted by different models for individual experiments 173& Figure 3-S3 Comparisons of measured olivine-melt partitioning data and those predicted by this study for individual experiments 182& Figure 3-S4 Comparisons of experimental olivine-melt partitioning data and those predicted by parameterized lattice strain models based on Al or Si in melt 202& Figure 3-S5 Limitations of the garnet-melt REE partitioning models 203 Figure 4-1 Comparisons of predicted and measured orthopyroxene–clinopyroxene REE partition coefficients for well-equilibrated peridotites 233& Figure 4-2 Compositions of pyroxenes and garnets used in the calibration of our mineral-melt REE partitioning models 234& Figure 4-3 Comparisons of model-derived and measured REE partition coefficients between coexisting minerals from well-equilibrated spinel peridotites or eclogites 235& Figure 4-4 Onuma diagrams showing the temperature, pressure and composition dependent REE partition coefficients among olivine, clinopyroxene and garnet 236& Figure 4-5 Effects of temperature, pressure and composition on REE partitioning among olivine, orthopyroxene and garnet 237& Figure 4-6 Re-distribution of REEs among clinopyroxene, orthopyroxene and olivine in a spinel lherzolite and a spinel harzburgite at selected temperatures 238& Figure 4-7 Re-distribution of REEs among clinopyroxene, garnet, and orthopyroxene in a garnet lherzolite and a garnet harzburgite at selected temperatures 239& Figure 4-8 Variations of Yb and Sm/Yb in clinopyroxene from abyssal peridotites 240& Figure 4-9 Corrected REE concentrations in clinopyroxene from an abyssal peridotite (ANTP89- 15) along the Central Indian Ridge 241 Figure 4-S1 Corrected REE abundances in clinopyroxene from abyssal peridotites 242& Figure 4-S2 Olivine-clinopyroxene and olivine-garnet REE partition coefficients as a function of ionic radii 243& Figure 4-S3 Comparisons of olivine models based on different ionic radii 244 xviii Figure 5-1 Temperature variations as functions of pressure derived from garnet-clinopyroxene Fe-Mg thermometers 291& Figure 5-2 Compositions of clinopyroxenes and garnets used in the calibration of our minera- melt partitioning models 292& Figure 5-3 Comparisons of model-derived and measured garnet-clinopyroxene REE and Y partition coefficients from partitioning experiments and well-equilibrated mantle eclogite xenoliths 293& Figure 5-4 Inversions of temperatures and pressures using the REE-in-garnet-clinopyroxene thermobarometer 294& Figure 5-5 Comparisons of the temperatures and pressures derived from the REE-in-garnet- clinopyroxene thermobarometer and those from the experimental runs 295& Figure 5-6 Comparisons of the calculated temperatures by the garnet-clinopyroxene Fe-Mg thermometers and the experimental temperatures 296& Figure 5-7 Comparisons of the estimated pressures and the experimental pressures 297& Figure 5-8 Calculated temperatures and pressures for eclogites and granulites with quartz, graphite and diamond 298& Figure 5-9 Comparisons of the temperatures derived from the REE-based thermobarometer and the Fe-Mg thermometers for well-equilibrated mantle eclogite xenoliths 299& Figure 5-10 Diffusive re-equilibration times for REE in garnet + clinopyroxene aggregates 300& Figure 5-11 Calculated temperatures and pressures for garnet and clinopyroxene-bearing rocks from cooling and thermally perturbed tectonic settings 301& Figure 5-12 Uncertainties in the temperatures and pressures arising from analytical errors of REEs in garnet and clinopyroxene 302 Figure 5-S1 Inversion of the temperature and pressure for an eclogite with REEs in disequilibrium 303& Figure 5-S2 Inversions of temperature and pressure for individual partitioning experiments 304& Figure 5-S3 Inversions of temperature and pressure for individual field samples 309& Figure 5-S4 The differences in temperatures calculated using the REE-in-garnet-clinopyroxene thermometers with ordering versus random distribution of Fe2+-Mg2+ in clinopyroxene for well-equilibrated mantle eclogite xenoliths. 342& Figure 5-S5 Plots of temperatures vs. pressures derived from Monte Carlo simulations 343 Figure 6-1 Comparisons between experimentally determined plagioclase-melt REE+Y partition coefficients and those predicted by previous models 366& Figure 6-2 Comparisons between experimentally determined plagioclase-melt REE+Y partition coefficients and those predicted by the previous model and this model 367& Figure 6-3 Onuma diagrams showing the temperature, pressure and composition dependent plagioclase-clinopyroxene REE partition coefficients 368& Figure 6-4 An example of the temperature inversion 369& Figure 6-5 Comparisons between the REE-base and An-based thermometers 370& Figure 6-6 Calculated temperatures for different planetary materials 371& Figure 6-7 Composite initial Sr isotope ratios, temperatures, and An along the stratigraphic height in the Bshveld Complex 372& Figure 6-S1 Comparisons of measured plagioclase-melt REE partitioning data and those predicted by this study for individual experiments 373& Figure 6-S2 Comparisons of measured plagioclase-melt partitioning data and those predicted by a new generalized lattice strain model for individual experiments 376& xix CHAPTER 1 1 Distribution of REE between Clinopyroxene and Basaltic Melt along a Mantle Adiabat: Effects of Major Element Composition, Water, and Temperature Chenguang Sun and Yan Liang Department of Geological Sciences, Brown University Providence, RI 02912, USA Published in Contributions to Mineralogy and Petrology, 163, 807-823, 2012 1 Abstract The distribution of rare earth elements (REEs) between clinopyroxene (cpx) and basaltic melt is important in deciphering the processes of mantle melting. REE and Y partition coefficients from a given cpx-melt partitioning experiment can be quantitatively described by the lattice strain model. We analyzed published REE and Y partitioning data between cpx and basaltic melts using the nonlinear regression method, and parameterized key partitioning parameters in the lattice strain model (D0, r0 and E) as functions of pressure, temperature and compositions of cpx and melt. D0 is found to positively correlate with Al in tetrahedral site (AlT) and Mg in the M2 site (MgM2) of cpx, and negatively correlate with temperature and water content in the melt. r0 is negatively correlated with Al in M1 site (AlM1) and MgM2 in cpx. E is positively correlated with r0. During adiabatic melting of spinel lherzolite, temperature, AlT, and MgM2 in cpx all decrease systematically as a function of pressure or degree of melting. The competing effects between temperature and cpx composition result in very small variations in REE partition coefficients along a mantle adiabat. A higher potential temperature (1400°C) gives rise to REE partition coefficients slightly lower than those at a lower potential temperature (1300°C) because the temperature effect overwhelms the compositional effect. A set of constant REE partition coefficients therefore may be used to accurately model REE fractionation during partial melting of spinel lherzolite along a mantle adiabat. As cpx has low Al and Mg abundances at high temperature during melting in the garnet stability field, REEs are more incompatible in cpx. Heavy REE depletion in the melt may imply deep melting of a hydrous garnet lherzolite. Water-dependent cpx partition coefficients need to be considered for modeling low-degree hydrous melting. 2 1. Introduction Mantle upwelling beneath mid-ocean ridges results in decompression melting, which is generally thought as an adiabatic process (e.g., McKenzie and Bickle 1988; Langmuir et al. 1992; Asimow et al. 2001). Once the upwelling mantle reaches the solidus, melting takes place with changing melting reactions at different pressure, and clinopyroxene (cpx) is the only phase that is always consumed to produce melt (e.g., Walter 2003 and references therein). Fig. 1 shows an example of the distribution of residual mineral abundances and melt fraction in an upwelling mantle column during near-fractional melting of an anhydrous garnet lherzolite along a mantle adiabat at potential temperature 1400ºC, calculated using the thermodynamic program pMELTS (Ghiorso et al. 2002). Melting occurs predominately in the spinel lherzolite region. Several models have been developed to quantify the fractionation of trace elements during partial melting and melt segregation, and significantly improved our understanding of mantle melting and melt transport processes (e.g., Gast 1968; Shaw 1970, 2000; McKenzie 1985; Iwamori 1994; Zou 1998; Liang 2008; Liang and Peng 2010). One of the most important assumptions used in the development of simple melting models is constant mineral-melt partition coefficient (D) for a trace element of interest during melting and melt segregation. In general, the trace element partition coefficient between mineral and melt is a function of pressure (P), temperature (T), and compositions of mineral and melt (X) (e.g., Wood and Blundy 2003 and references therein). The heavy rare earth elements (HREE), for example, may become compatible in cpx on the spinel lherzolite solidus (Blundy et al. 1998). Zou (2000) generalized the non-modal dynamic melting model by considering linear variations of D as a function of degree of melting (F). He suggested that significant effects of varying D on the HREE might be expected during mantle melting. During adiabatic mantle melting, both pressure and temperature decrease with varying mineral and melt compositions, and consequently P-T-X dependence of D could lead to markedly different melt composition and estimations of F, compared with that of constant partition 3 coefficients. To accurately determine the extent of melting experienced by residual mantle, it is necessary to take P-T-X dependent D into consideration when modeling mantle melting. A key parameter in understanding the fractionation of trace elements during adiabatic mantle melting is the cpx-melt partition coefficients because cpx has stronger affinity for incompatible elements than orthopyroxene (opx) and olivine and therefore determines incompatible element abundances in the melt during partial melting of spinel lherzolite. Recent partitioning studies (e.g., Witt-Eickschen and O’Neill 2005; Lee et al. 2007) suggest that distributions of trace elements between mantle minerals (olivine, cpx, opx, spinel) can be used to determine mineral-melt partition coefficients provided cpx-melt partition coefficients are known. As trivalent cations, rare earth elements (REE) and Y have ionic radii (0.977 Å to 1.16 Å, VIII- fold coordination, Shannon 1976) similar to those of Ca2+ and Na+ (1.12 Å and 1.18 Å, respectively, VIII-fold coordination, Shannon 1976) in cpx. These trivalent cations enter the M2 site of cpx by substituting for Ca2+ or Na+. For instance, REE and Y could replace Ca2+ in M2 site while charge balanced by Al3+ replacing Si4+ in tetrahedral site, or Na+ replacing Ca2+ in M2 site (e.g., Gaetani and Grove 1995; Wood and Blundy 1997). Importantly, cpx-melt REE partition coefficients from a given cpx-melt partitioning experiment at equilibrium vary systematically as a function of their ionic radii, which can be quantitatively described by the lattice strain model (Brice 1975; Blundy and Wood 1994; Wood and Blundy 1997): ⎡ −4π EN A ⎛ r0 3⎞ ⎤ ( ) 1 ( ) 2 D diopside-melt = D0 exp ⎢ ⎜ r0 − rj − r0 − rj ⎟ ⎥ (1) ⎣ RT ⎝ 2 ⎠⎦ j 3 where D0 is the mineral-melt partition coefficient for the strain-free substitution; r0 is the optimum radius for the lattice site; rj is the ionic radius of the element of interest; E is the effective Young’s modulus for the lattice site; R is the gas constant; and NA is Avogadro constant. T is temperature in K. The effective Young’s modulus E controls the tightness of the parabola and D0 determines the peak of the parabola with corresponding ideal lattice size r0. 4 On the basis of the lattice strain model and available experimental partitioning data published before 1997, Wood and Blundy (1997) proposed a predictive model for REE partitioning between cpx and anhydrous silicate melt. They suggest E is a simple linear M1 combination of temperature and pressure, and find Al content in the M1 site ( X Al ) and Ca M2 content on the M2 site ( XCa ) of cpx are sufficient to describe the derived values of r0 from nonlinear regression. To estimate D0, they construct a thermodynamic model for a hypothetic end-member REE pyroxene (REEMgAlSiO6). Assuming the effect of H2O on the activity of REEMgAlSiO6 is the same as CaMgSi2O6, Wood and Blundy (2002) further extend their original model to the hydrous system. However, partitioning experiments indicate that tetrahedrally coordinated Al in cpx (AlT) and NBO/T of bulk melt significantly affect cpx-melt D values for REE (e.g., Lundstrom et al. 1998; Hill et al. 2000; Gaetani 2004; see also Fig. 10 in Lo Cascio et al. 2008 for a recent compilation) and these parameters are not included in the models of Wood and Blundy (1997, 2002). REE partitioning data in cpx demonstrate that Wood and Blundy’s models can provide predictions for partitioning data to within a factor of two to three of the measured values (see Fig. 2). Nonetheless, discrepancies and poor correlations between the predicted and the measured partition coefficients (especially those published after 1997) suggest the need of an update or revision of their models (Fig. 2). Another potential difficulty in the parameterization of cpx-melt partition coefficients for the REE is the strong trade-off between E and r0 during regression analysis of the nonlinear lattice strain model. The REE partitioning data can be fitted equally well using a range of E and r0 so long as the exponent in Eq. (1) remains the same. To demonstrate this, we perform a Monte Carlo simulation in which we use Eq. (1) to invert the model parameters D0, E, and r0 from 1000 sets of synthetic cpx-melt partition coefficients (see the caption to Fig. 3 for details). Figs. 3a and 3b compare the inverted model parameters (crosses) with the expected values (pentagram). As shown in Fig. 3b, there is a strong positive correlation between E and r0, rendering their 5 simultaneous determination non-unique. However, correlations between the inverted D0 and r0 (Fig. 3a) or D0 and E (not shown) are rather poor, suggesting that D0 can be determined with confidence. To get round the strong correlation between E and r0, Wood and Blundy (1997) assumed E is a linear function of temperature and pressure (their Eq. 14) and inverted D0 and r0 from the published partitioning data using the lattice strain model. For partitioning of trivalent cations REE and Y, the effective Young’s modulus may also depend on cpx composition. Since the exact P-T-X relationship is not known for the effective Young’s modulus, it may be more straightforward to consider E as a function of r0 which in turn is a function of composition, temperature and pressure. The importance of REE in unraveling mantle melting processes requires a more general formulation that can be used to better predict REE partition coefficients between cpx and basaltic melt during mantle melting. In this study, we invert D0 and r0 from a set of published REE and Y partitioning data while assuming E varies linearly as a function of r0. Our data set includes 43 published cpx-basaltic melt partitioning experiments and is selected on the basis of major element compositions, attainment of chemical equilibrium, and method of chemical analysis. As an independent check, we show that our new parameterization can also reproduce REE and Y partition coefficients determined by electron microprobe. Finally, as an application, we apply our new parameterization to adiabatic mantle melting through pMELTS and pHMELTS (Ghiorso et al. 2002; Asimow et al. 2004), and investigate the variations of cpx-melt partition coefficients along the mantle adiabat for several mantle sources at two potential temperatures and under both anhydrous and hydrous conditions. 6 2. Method 2.1. Data compilation and criteria REE and Y partitioning data for cpx in basaltic melts were obtained from partitioning experiments published in the past two decades and conducted either by melting of peridotite or crystallization of basalt, in which peridotite and basalt could be natural or synthetic materials. Partitioning data of pigeonite (Salters et al. 2002; Salters and Longhi 1999; van Westrenen et al. 2000; Tuff and Gibson 2007) were excluded, as pigeonite is low-Ca pyroxene and may have REE partitioning more similar to opx. Only partitioning data between cpx and basaltic melt (SiO2 < 57 wt%) were considered. Partitioning experiments were chosen on the basis of several criteria. Clinopyroxene from partitioning experiments showing obvious concentric zoning, heterogeneity between core and rim, sector zoning in major elements, or with inclusions (e.g., Hart and Dunn 1993; Skulski et al. 1994) suggest significant kinetic effect (Watson and Liang 1995). Short duration experiments (e.g., experiments less than 7 hours from Schmidt et al. 1999, Blundy and Dalton 2000, and Johnson 1998) may not be sufficient to establish equilibrium for cpx because of slow diffusion rate of REE in the crystal (van Orman et al. 2001) and fast crystal growth rate. Some partitioning experiments were not evaluated for equilibrium, and had cpx reported from each experiment having large variations in major and trace element compositions (Gallahan and Nielsen 1992). These partitioning experiments were excluded in the present study, though some of the experiments that we excluded (Gallahan and Nielsen 1992) constituted the majority of the database used in the models of Wood and Blundy (1997, 2002). Since the low oxygen fugacity imposed by the graphite capsule in some experiments produced high Eu2+/Eu3+ ratio in the melt (Hauri et al. 1994; McDade et al. 2003a; Blundy et al. 1998; Gaetani et al. 2003), cpx exhibited negative anomalies of Eu partition coefficients (DEu). In order to obtain smooth parabolas with less uncertainty, DEu in cpx from these experiments were excluded. 7 Table 1 lists the filtered partitioning studies that are used to calibrate our model described below. These partitioning data can be divided into three groups based on the analytical method for measuring REE and Y abundances: data analyzed by electron microprobe (EMP), ion probe, and laser ablation inductively coupled plasma mass spectroscopy (LA-ICP-MS). Inter-laboratory biases may exist in partitioning data analyzed by different methods in different laboratories, which introduces additional errors and uncertainties to the empirical model. Nevertheless, because ion probe and LA-ICP-MS progressively improved the precision and accuracy of trace element analyses, our parameterization focuses on data analyzed by ion probe or LA-ICP-MS (a total of 43 partitioning experiments and 344 data), whereas EMP data are used as independent tests for the goodness of fit for the potential model. 2.2. Parameterization procedures To develop a parameterized model for REE and Y partitioning between cpx and basaltic melt, we conduced multi-variable nonlinear least squares regressions (Seber and Wild 1989) using the 344 filtered data in studies listed in Table 1. Given the number of potential parameters involved, we carried out our analysis in two steps. First, we use Eq. (1) to fit REE and Y partition coefficients from individual experiment, in which four or more elements are available, to obtain D0, r0 and E by nonlinear least squares method (Seber and Wild 1989). Ionic radii of REE and Y are taken from Shannon (1976, VIII- fold coordination). We find that there is a strong correlation between the derived E and r0, and no obvious correlation between D0 and E or r0. The correlations among D0, E and r0 are consistent with the Monte Carlo simulation shown in Fig. 3. Given the strong intrinsic trade-off between E and r0 in Eq. (1), we assume that E is a linear function of r0, in which coefficients were determined by adopting linear regression for derived E and r0 from each partitioning experiment. This correlation will not affect the reliability of our parameterization to predict REE and Y partition coefficients by interpolation, although we have not found a better way to resolve this 8 problem. As D0 is the partition coefficient for strain-free substitution of the M2 site, we assume that D0 has the simple form a1 ⎛ P⎞ ln D0 = a0 + + f ⎜ X, ⎟ (2) RT ⎝ T⎠ where a0 and a1 are constants to be determined, and f is a function of composition X and P/T. The derived r0 is also assumed P-T-X dependent. Here, the composition X could be cations on different lattice sites of cpx (per six oxygen), mole fractions of the cation in the melt, the melt structure parameter NBO/T calculated from melt composition, or the mole fraction of H2O in the melt melt ( X H2O ). Cpx formulae are calculated by assuming a random distribution of Fe2+ and Mg2+ over the M1 and M2 sites (Wood and Banno 1973) and that all iron is present as ferrous iron. melt NBO/T of the bulk melt is calculated following the expression of Mysen et al. (1985). And X H2O is calculated using the method from Wood and Blundy (2002). To find the first order or primary factors that affect D0 and r0, we first carried out stepwise multiple linear regressions exploring the dependence of D0 and r0 as functions of P, T and X. The coefficients of determination (R2) were calculated for different linear combinations of P, T and X between predicted and derived values of D0 and r0 to test the goodness of fit. More parameters used in the fit generate a set of predictions with a lower degree of freedom. If a parameter cannot significantly improve the fit, it is considered unimportant. To obtain the best fit with possibly the highest degree of freedom, only the intensive parameters are acceptable in this study. Through an extensive search of various permutations of the composition variables, we find that Mg content in T melt M2 site ( X Mg ) and Al content in tetrahedral site ( X Al ) in cpx, X H2O and T are the primary M2 M2 M1 variables determining D0, and X Mg and Al content in M1 site ( X Al ) in cpx are the main factors affecting r0. Expressions for D0, r0, and E, therefore, take the linear forms, a1 ln D0 = a0 + + a2 X AlT + a3 X Mg M2 + a4 X Hmelt 2O (3) RT 9 r0 = a5 + a6 X AlM 1 + a7 X Mg M2 (4) E = a8 + a9 r0 (5) where a0, a1, …, a9 are constant coefficients determined by stepwise multiple linear regression analyses of the lattice strain parameters (D0, r0 and E). We also explored several nonlinear combinations of the composition variables and found them to be unimportant, at least for the filtered data examined in this study. To better constraint the cpx/melt partitioning model for REE and Y, we substitute Eqs. (3)- (5) back into Eq. (1) and use the lattice strain model and all of our filtered partition coefficients (a total of 344 data) to invert for the 10 fitting parameters a0, a1, …, a9 simultaneously through a global nonlinear least squares analysis (e.g., Seber and Wild 1989). The advantages of a simultaneous inversion are two folds. (1) Partitioning experiments with 3 or less elements can now be included in the global inversion. (2) Uncertainties for the fitting parameters can be properly assessed. To carry out the global inversion, we use the coefficients from the stepwise multiple linear regressions as the initial guess in the nonlinear least squares analysis and minimize the chi-square as defined below ( ) N χ = ∑ ln D j − ln D jm 2 2 , (6) j=1 m where Dj is defined by Eq. (1) for element j; D j is the measured cpx-melt partition coefficient for element j; N (= 344) is the total number of measured partitioning data used in this study. Logarithmic normalized partition coefficient is used in our chi-square calculation because the absolute values of D are different from one element to another and systematic variations in REE abundances and partition coefficients are usually examined in normalized semi-log spider diagrams. Although convenient in nonlinear regression analysis, the absolute values of the chi- square defined in Eq. (6) depends on the number of data points used in the inversion and hence is 10 not statistically meaningful. To better assess the goodness of fit, we also calculate the Pearson’s chi-square after the inversion using the expression χ =∑ 2 N (D − D ) j m 2 j , (7) P j=1 Dj A better predictive model should provide partition coefficients closer to measured values, and then produce smaller χ P . The results are shown in Fig. 4 and discussed below. 2 3. Results Our selected 43 partitioning experiments cover a wide range of pressure (1 bar to 4 GPa), temperature (1042 to 1470°C), and water content in the melt (0-17.35wt%). These experiments produced melt and cpx with wide ranges in compositions (e.g., melt SiO2: 42.1-56.8wt%, and cpx Al2O3: 3.19-15.6wt%; Table 1) and partition coefficients (e.g., DYb: 0.22-1.43). The derived D0 (0.28-4.25), r0 (0.93-1.07Å) and E (107-525GPa) from these experiments are listed in Table 2 and used in the stepwise multiple linear regressions. For comparison, partitioning data analyzed by EMP are also listed in Tables 1 and 2. Results of the global or simultaneous fit of the 344 partitioning data from the 43 experiments (Table 1) are 7.19 ( ±0.73) × 10 4 ln D0 = −7.14 ( ±0.53) + + 4.37 ( ±0.47 ) X AlT RT +1.98 ( ±0.36 ) X Mg M2 − 0.91( ±0.19 ) X Hmelt 2O (8) r0 = 1.066 ( ±0.007 ) − 0.104 ( ±0.035 ) X AlM 1 − 0.212 ( ±0.033) X Mg M2 (9) E = ⎡⎣ 2.27 ( ±0.44 ) r0 − 2.00 ( ±0.44 ) ⎤⎦ × 10 3 (10) where R = 8.3145 J mol-1K-1, and numbers in parentheses are 2 errors. It is important to note T M2 that D0 positively correlates with X Al and X Mg in cpx, negatively correlates with T and water M1 M2 content in the melt. r0 has negative correlations with X Al and X Mg in cpx, whereas E increases 11 with the increase of r0. As D0 determines the peak value of parabola defined by Eq. (1), we may T make the first-order observation that REE partition coefficients increase with the increase of X Al M2 and X Mg in cpx but decreases with increasing T and water content in the melt. For convenience, we provide an Excel worksheet online (http://dx.doi.org/10.1007/s00410-011-0700-x) that can be used to calculate REE partition coefficients in cpx for a given cpx and melt composition and temperature. 4. Discussion Equations (1, 8-10) provide a general empirical model for REE and Y partitioning between cpx and basaltic melt. Fig. 4 shows the excellent agreement between the predicted REE and Y partition coefficients using Eqs. (1, 8-10) and the observed values (See comparisons for individual experiments in Fig. S1). A much smaller χ P value (7.33) for 344 data suggests the 2 consistency between partitioning experiments (analyzed by ion probe or LA-ICP-MS) and the model prediction. Small 2σ errors from model prediction also indicated good predictions of partition coefficients (Fig. 4). Small discrepancies between observed and predicted partition coefficients for ion probe and LA-ICP-MS analysis may be due to several reasons, such as inter- laboratory biases in compiled partitioning data, disequilibrium in cpx from compiled partitioning experiments, and/or deficiencies of our empirical model, or some combination of the three. The small χ P value (7.33) indicates the significant improvement of our model over the 2 model of Wood and Blundy (1997, 2002); the latter has a χ P value of 113.47 (cf. Figs. 2 and 4). 2 To further compare with the model of Wood and Blundy, we updated their model by a global or simultaneous inversion of the 344 partitioning data used to calibrated our model and found a χ P 2 value of 26.37 for their formulation, which, though improved, is still considerably larger than the value obtained in our new model. (For a graphic comparison, see Fig. S2) 12 For reasons outlined in the section “Data compilation and criteria”, we excluded EMP data in our regression analyses. As an independent test of our new parameterization, partitioning data from EMP analysis are compared with our model-derived values in Fig. 4 (blue squares). The apparent discrepancies for some partitioning data from EMP analysis presumably represent analytical limitations. To further check the validity and consistency of the primary variables identified in Eqs. (8-10), we carried out a global inversion using all the measurements (EMP, ion probe and LA-ICP-MS; a total of 527 data) listed in Table 1 (Regression coefficients and a comparison with the measured data are given in the supplementary material). As expected, we observe a slight improvement in the fits to the EMP data ( χ P is decreased from 11.60 to 9.63), 2 but a decrease in the goodness of fit to the ion probe and LA-ICP-MS data ( χ P is increased from 2 7.33 to 10.64, see also Fig. S3). In general, addition of 183 EMP data in the calibration does not change the first order parameters of our model, nor does it improve the model prediction. Our preferred model for REE and Y partitioning between cpx and basaltic melts, therefore, are Eqs. (1, 8-10), calibrated by the high precision data (ion probe and LA-ICP-MS). 4.1. Model sensitivity to analytic uncertainty and model limitations From Eqs. (1, 8-10), it is apparent that REE and Y partition coefficients can be described by 10 variables, each with its own associated uncertainty. In order to estimate the uncertainties of our calculated partition coefficients, we perform two Monte Carlo simulations by assigning T M1 M2 variables (T, X Al , X Al and X Mg in cpx) reported in the anhydrous partitioning experiments of Blundy et al. (1998) and McDade et al. (2003a) as the input values, respectively. Normally distributed random noises representing uncertainties are added to the input values to generate 1000 sets of partition coefficients. Although uncertainties in T or cpx composition can be different in terms of different types of thermocouple or analytical methods, for simplicity T is 13 M1 M2 assumed to have 10°C uncertainty, and cpx compositions (, X Al and X Mg ) are assumed to have 10% uncertainties. Given the 1000 sets of synthetic partition coefficients, we use our model (Eqs. (1), (8)-(10)) to calculate REE and Y partition coefficients for each group of variables. The mean values of this population are taken as predicted partition coefficients, and the standard deviations on these partition coefficients are taken as the uncertainties that result from assumed analytic uncertainties. As shown in Fig. 5, predicted values have uncertainties of 9-22% and 5-12% for the two cpx compositions, respectively, due to assumed analytical uncertainties. However, some limitations need to be considered for applications of this model. As REE and Y partition coefficients in low-Ca pyroxene, such as pigeonite (e.g., Salters and Longhi 1999; van Westrenen et al. 2000; Salters et al. 2002; Tuff and Gibson 2007), are excluded in the parameterization, their predicted values are generally overestimated by a factor of two. This suggests that factors controlling REE partitioning in low-Ca pyroxene are different from those in high-Ca pyroxene. In addition, our new model cannot provide good predictions for partition experiments by melting of silica-rich starting materials, which produce more polymerized melts than basalts (e.g., Huang et al. 2006; Barth et al. 2002). Reasonable predictions can be obtained for partitioning experiments involving melting of pyroxenite and eclogite of mafic compositions (Pertermann and Hirschmann 2002; Pertermann et al. 2004; Elkins et al. 2008), though small but systematic deviations are noticeable (Fig. 6). The discrepancies between predictions and observations from those partitioning experiments presumably stem from the polymerization of melt (e.g., NBO/T < 0.5 in melts from Pertermann and Hirschmann 2002 and Pertermann et al. 2004). These predictions may be significantly improved if our parameterization accounts for partitioning data from mafic melts derived from pyroxenite and eclogite, and NBO/T in the base function of D0. To what extent this model can be applied to low-Ca pyroxene and to melting of eclogite and pyroxenite needs further investigation, but is beyond the scope of this study. 14 4.2. Effects of melt structure and pressure on REE partitioning Our empirical model does not include effects of melt structure and pressure. Gaetani (2004) suggests that melt structure has significant influence on trace element partitioning in cpx at NBO/T value less than 0.49. However, the results of stepwise regressions and global fit indicate that inclusion of NBO/T does not lead to any significant improvement in the regression analysis. Furthermore, a plot of D0 against NBO/T does not show any obvious trend for NBO/T > 0.49 (see Fig. S4e). A possible explanation of this result is that NBO/T in most of the experimental melts used in our parameterization are greater than 0.49 (Table 1, see also Fig. S4e). Even though the derived D0 roughly shows a negative correlation with P (see Fig. S4b), the prediction is not improved by adding P into the multiple linear regressions and the global fit. As hydrous partitioning data have great contribution to the apparent trend between D0 and P (Fig. S4), it is possible that P dependence for D0, as suggested by Gaetani et al. (2003), may include the H2O effect that shows an obvious trend with D0 (see Fig. S4f). To constrain the possible P effect on partition coefficients, we perform the multiple linear regressions, without P, for D0, r0 and E at lower P (< 1.7GPa) under anhydrous condition. After obtaining the coefficients for the functions of D0, r0 and E by the global fit, we extrapolate this model to anhydrous partitioning experiments at higher P (> 1.7GPa), and find excellent agreements between predicted and observed partition coefficients, which suggest minor P effect on REE and Y partitioning in cpx. Therefore, given available partitioning experiments, P and NBO/T may be unimportant for REE and Y partitioning between cpx and basaltic melt. Alternatively, P or NBO/T may affect major compositions of cpx, such as Al and Mg, which in turn influence REE and Y partitioning in cpx. 4.3. The effects of temperature and cpx composition on REE partitioning Wood and Blundy (1997) suggested that REE partition coefficients decrease with the increase of temperature due to the positive entropy of fusion of silicate minerals. McDade et al. 15 (2003a) argued that strain-free partition coefficients, D0, could be compared at different T by removing crystal chemistry effects. They found ln(D0) increases linearly with 1/T. This is confirmed by our new parameterization (Eq. 8). Since r0 and E are independent of T in our model, the effect of decreasing temperature at a constant composition is to shift the parabola downwards while keeping its shape and relative position in the Onuma diagram (Fig. 7a). As demonstrated in T M2 melt this study, D0 also depends strongly on composition ( X Al and X Mg in cpx, and X H 2 O ; Eq. 8). It has been observed that cpx compositions have great influence on REE and Y partitioning in cpx, especially the Al2O3 content (e.g., Gaetani and Grove 1995; Lundstrom et al. 1998; Hill et al. 2000; Lo Cascio et al. 2008). The Al effect on REE partitioning is attributed to the charge balancing substitution of Si in tetrahedral site during the substitution of Ca2+ in the M2 site by REE3+. This is in good agreement with our model, as D0 is positive correlated with Al in tetrahedral site (AlT) (Eq. 8). The mean M2-O distance in Ca-Tschermakite (2.461 Å, X Al = 1 , M1 Cameron and Papike 1981) is smaller than that in diopside (2.498 Å, X Al = 0 ). This may help to M1 explain the negative correlation between Al and r0 (Eq. 9). Since Mg in M2 site (MgM2) has smaller ionic radius than Ca, MgM2 shows an inverse correlation with r0 (Eq. 9). However, the Mg effect on D0 may not be easily observed due to the combined effects of T and X. To further investigate the compositional effect, we examined 6 partitioning experiments from Gaetani and Grove (1995) that were run at 1 bar and very similar temperatures (1240- T 1249°C, anhydrous). These experiments produced cpx with different X Al (0.042-0.206) and M2 X Mg (0.019-0.219), and had Ce and Yb analyzed by EMP. As previously shown by Gaetani and T Grove (1995), both DCe and DYb have positive correlations with X Al in cpx (Fig. 8a). In contrast, M2 DCe and DYb show negative correlations with X Mg in cpx (Fig. 8b). In order to better understand T M2 this phenomenon, we plot X Al against X Mg in Fig. 8c, which indicates a negative correlation 16 T M2 between X Al and X Mg . As this inverse correlation yields two opposing effects on partition T M2 coefficients, a greater impact from X Al results in the apparent inverse correlation between X Mg and partition coefficients (Fig. 8b). Although there are few partitioning data available to investigate the effect of cpx composition on REE and Y partitioning at fixed temperature, our empirical model is consistent with existing experimental results that REE partition coefficients strongly depend on Al in cpx. At a given temperature, under anhydrous condition, our empirical model (Eqs. 1, 8-10) shows that increasing Al and Mg in cpx would increase D0, but decrease r0 and E. The parabolic pattern of partition coefficients will move upwards and shift towards left, hence becoming more open in the Onuma diagram (Fig. 7b). Consequently, partition coefficients of HREE, which are on the left side of the parabola, increase with the increase of Al and Mg in cpx. However, partition coefficients of light and middle REE (LREE and MREE), which are on the right side of the parabola, decrease slightly as the parabola shifts to the left, but increases as the parabola becomes more open. These opposing effects suggest that r0 and E have minor effects on the partitioning of LREE and MREE in cpx. In spite of this completing effect, partition coefficients of LREE and MREE still increase as the result of increasing D0 (Fig. 7b). On the other hand, the decrease of Al and Mg should lead to a decrease in D0 and an increase in r0 and E, and therefore the parabolic pattern moves downwards and shifts to the right, and hence becoming tighter (Fig. 7b). Even though r0 and E have an insignificant impact on LREE and MREE because of the opposing effects, all REE would have partition coefficients decreased with decreasing D0. Thus, D0, influenced by cpx composition at a given T, dominates the variations in REE and Y T partitioning in cpx. In addition, the larger coefficient of X Al in Eq. (8) indicates the greater T M2 influence of X Al on partitioning than that of X Mg in cpx. 17 4.4. Competing or enhancing effects of temperature and cpx composition During partial melting or crystallization, compositions of cpx and coexisting melt change systematically as a function of temperature and pressure. Our empirical model can be used to understand the combined effects of temperature, Al and Mg in cpx. For purpose of illustration, we T M2 consider REE partitioning under anhydrous condition. The coefficients of X Al , X Mg and T in Eq. T M2 (8) show that partition coefficients positively correlate with X Al and X Mg in cpx, and negatively T M2 correlate with T, as stated above. Depending on how X Al and X Mg in cpx vary as a function of temperature, one expects either a competing effect or an enhancing effect between composition T M2 and temperature. The former arises when X Al and X Mg in cpx show positive correlations with T M2 temperature (Fig. 9a), whereas the latter happens when X Al and X Mg in cpx show negative correlations with temperature (Fig. 9b). For the first possibility, it is necessary to consider the relative effects between temperature and cpx composition. If magnitudes of these two effects are comparable to each other and hence cancel out, we would expect a set of nearly constant partition coefficients. However, temperature would become the dominant factor if changes in Al and Mg are small over a large range of temperature, and vice versa. For the second possibility, REE partition coefficients may even become compatible in cpx rich in Al at low temperature. For instance, as reported by Blundy et al. (1998), HREE are compatible (DLu = 1.45) in cpx near the solidus of a fertile spinel lherzolite at 1.5GPa. This is because the partitioning experiment was run at relatively lower temperature (1250°C), and the starting composition is highly enriched in Al2O3 (21.03 wt%). Since adiabatic mantle melting is accompanied by decreasing temperature and varying cpx composition, identifying the competing or enhancing effect is critical to understanding REE and Y fractionation during mantle melting. We will discuss the implications of these observations in a later section. 18 4.5. The effect of H2O on REE partitioning Studies of H2O in mid-ocean ridge basalts (MORBs) suggest that depleted MORB mantle (DMM) contains 50 to 200 ppm H2O (e.g., Saal et al. 2002; Simon et al. 2002). Partitioning experiments under hydrous conditions demonstrated that a higher H2O content in the melt would decrease REE partitioning in cpx (Green et al. 2000; Gaetani et al. 2003), even though it is still not clear how H2O in the melt influences partition coefficients. By evaluating the network modifiers for the melt, Gaetani et al. (2003) attributed the decrease of partition coefficients to the de-polymerizing effect of H2O on the structure of the silicate melt, whereas Wood and Blundy (2002), based on the thermodynamic model of cpx, suggested that addition of H2O decreases partition coefficients by reducing the activity and activity coefficient of the component in the melt. In general, addition of H2O to the mantle source lowers the mantle solidus, resulting in greater depth of initial melting and hence higher pressure and temperature than melting of an otherwise anhydrous mantle. During mantle melting, temperature and even cpx composition could be influenced by H2O, all of which determines the possible variation in partition coefficients. The negative coefficient of H2O in Eq. (8) indicates the inverse correlation between H2O in the melt and REE and Y partition coefficients in cpx (Fig. 7a), which is consistent with experimental observations. Even if detailed partitioning experiments on adiabatic mantle melting are not available, our empirical model allows us to assess the combined effects of temperature, T M2 cpx composition ( X Al and X Mg ) and H2O in the melt on REE and Y partitioning in cpx along a mantle adiabat. 5. Implications for Adiabatic Mantle Melting Our predictive model indicates that REE and Y partition coefficients strongly depend on temperature, cpx composition (Al and Mg) and H2O in the melt. Temperature and cpx composition have opposing effect on REE and Y partitioning in cpx, giving rise to the competing 19 effect. Addition of H2O could also impact melting temperature and cpx composition. An important question then is how REE and Y partition coefficients vary during adiabatic mantle melting. In this section we explore the effects of starting mantle composition (DMM vs. enriched mantle), H2O content, and potential temperature (TP) on the partitioning of REE and Y during adiabatic mantle melting. Compositions of residual melt and cpx are calculated using pMELTS or pHMELTS (Ghiorso et al. 2002; Asimow et al. 2004). 5.1. REE partitioning in cpx along the mantle adiabat Herzberg et al. (2007) evaluated the primary magma compositions of MORBs and various ocean island basalts, and obtained mantle potential temperatures ranging from 1280°C to 1400°C. As illustrative examples, we consider REE and Y partitioning during adiabatic mantle melting along two potential temperatures (1300°C and 1400°C). We use the anhydrous DMM of Workman and Hart (2005) as our starting composition and pMELTS (Ghiorso et al. 2002) to calculate cpx and melt compositions during near-fractional melting while assuming 0.5% melts retained at each melting step. For the 1300°C potential temperature, melting takes place in the T M1 M2 spinel lherzolite field and X Al , X Al and X Mg in cpx decrease with the decrease of temperature (Fig. 10a). For the 1400°C potential temperature, melting starts in the garnet stability field where Al in cpx are relatively low at high temperature and negatively correlate with temperature. The extent of melting is 0.75% in the garnet stability field, followed by 18.51% of additional melting in the spinel stability field. Within the spinel lherzolite regime at 1400°C potential temperature, Al in cpx always shows a positive correlation with temperature, whereas Mg in cpx switches to a positive correlation with temperature in spinel lherzolite regime. Mg contents of cpx in the higher potential temperature case are greater than those in the lower potential temperature case, while Al contents in cpx show similar ranges for these two potential temperatures (Fig. 10a). In general, the competing effects of temperature and cpx composition control REE and Y partitioning 20 behaviors in cpx when melting takes place in the spinel lherzolite field. Given cpx composition and corresponding melting temperature from pMELTS calculations, the model derived cpx partition coefficients are nearly constant during melting of spinel lherzolite along the 1300°C potential temperature (Fig. 10b). Cpx from the higher potential temperature case have smaller partition coefficients at the beginning of melting because of the enhancing effect between cpx T M2 composition (lower X Al and X Mg ) and temperature (higher melting temperature). When melting occurs in the spinel lherzolite field even for different potential temperatures, the variations in REE and Y partition coefficients are within a factor of two. However, melting at higher potential temperature generally produces cpx with slightly smaller partition coefficients. In order to evaluate REE and Y partitioning behavior during melting of a hydrous mantle, we carried out a pHMELTS calculation (Ghiorso et al. 2002; Asimow et al. 2004) assuming near- fractional melting of a damped lherzolite (DMM with 200 ppm H2O) at the potential temperature of 1300°C. As addition of H2O decreases the solidus of mantle peridotite, melting starts deeper in the garnet stability field where the temperature and H2O content in the melt are higher, whereas the AlT, AlM1 and MgM2 abundances in cpx are lower than those in the case of melting of an otherwise anhydrous mantle (cf. dashed vs. solid lines in Fig. 10c). Consequently, at the beginning of hydrous melting, REE and Y are expected to be more incompatible than the dry case (Fig. 10d). Temperature and H2O content in the melt both decrease with the increase extent of melting, and as a result partition coefficients increase dramatically until the mantle source becomes dry. At that point, the competing effect between temperature and cpx composition determines the small variations in partition coefficients. This example indicates that REE and Y are more incompatible in the hydrous melting regime, and have nearly constant partition coefficients in the anhydrous melting region. A similar exercise can be performed using pMELTS to evaluate REE and Y partitioning behaviors during melting of different mantle compositions, such as DMM, primitive mantle (PM, 21 Sun and McDonough 1989) and enriched mantle (EM), at potential temperature of 1300°C and under anhydrous condition. For purpose of demonstration, we assume that the EM is a mixture of 90% DMM and 10% N-MORB, in which N-MORB composition is taken from Hofmann (1988). The three mantle compositions all start to melt in the spinel lherzolite field, and generate similar T M1 M2 T M1 M2 ranges in X Al , X Al and X Mg in cpx, in which X Al , X Al and X Mg all decrease with the decrease of temperature (Figs. 10e and 10f, for diagram clarity only cases for EM and DMM are shown because the case for PM has cpx composition and REE partition coefficients in between the cases for DMM and EM). As a result of competing effect, cpx partition coefficients vary within a factor of two for melting of the three mantle compositions, even though the fertile mantle has slightly larger partition coefficients. To further constrain the variation of partition coefficients for different melting models, we also consider batch melting and calculate partition coefficients using Eqs. (1), (8)-(10). We find that the effect of different melting models (batch or fractional) is negligible for the variation of partition coefficients along the mantle adiabat. The partition coefficients derived from pMELTS calculation and our empirical model (Eqs. 1, 8-10) indicate that at a given potential temperature REE and Y partition coefficients in cpx are nearly constant in the spinel lherzolite regime under anhydrous condition, and become slightly more incompatible at higher potential temperature. Constant REE and Y partition coefficients, therefore, can be used to model adiabatic mantle melting at a given potential temperature in the spinel lherzolite melting region under anhydrous condition. Table 3 presents our recommended cpx-melt partition coefficients based on the averaged values derived from anhydrous melting in spinel lherzolite regime for a given mantle composition and at a given potential temperature. The preceding discussion is based on the result of pMELTS or pHMELTS calculations in which the thermodynamic model of cpx is highly simplified (i.e. a regular solution model, Ghiorso et al. 2002; Asimow et al. 2004). Clinopyroxene 22 may have larger variations in Al and Mg contents during adiabatic melting, resulting in greater variations in REE and Y partition coefficients along a mantle adiabat. 5.2. The effect of varying partition coefficients on REE fractionation To assess the differences between variable and constant partition coefficients, we examine La, Nd, and Yb variations in cpx during partial melting of dry DMM at Tp = 1300°C. For non- modal steady-state melting in an upwelling mantle column with spatially variable crystal-melt partition coefficients, we can use the following mass conservation equation to calculate the m abundance of a trace element in interstitial melt ( C f ) coexisting with the residual solid (Liang and Peng 2010), dC mf ⎡ dk ⎤ ⎡⎣ km + (1− km − R ) F ⎤⎦ = ⎢( km − 1) + ( F − 1) m ⎥ C mf (11) dF ⎣ dF ⎦ where km is the bulk solid-melt partition coefficient for the element of interest; F is the degree of melting; R is a dimensionless melt suction rate, defined as the amount of melt extracted from the residual solid relative to that produced by melting. Eq. (11) recovers the batch melting and fractional melting models when R = 0 and R = 1 , respectively (e.g., Iwamori 1994; Liang and Peng 2010). The last term in the square brackets on the right hand side of Eq. (11) accounts for the spatially variable partition coefficient. Given the interstitial melt composition, the abundance m of a trace element in the aggregated matrix melt ( C f ) can be calculated using the simple expression, Csm 0 − ⎡⎣ km + (1− km − R ) F ⎤⎦ C mf C = m (12) RF f where Csm0 is the starting mantle composition. To integrate Eq. (11), we first interpolate cpx/melt REE partition coefficients calculated using Eqs. (1), (8)-(10) and pMELTS along the 1300°C adiabat as a function of F for both batch melting and near fractional melting. We then integrate 23 Eq. (11) numerically for R = 0 (batch melting) and R = 0.9 (near-fractional melting), respectively. Details of model setup are given in the caption to Fig. 11. Fig. 11 compares the abundances of La, Nd, and Yb in the aggregated melt and residual cpx as a function of F. To highlight the effect of variable partition coefficient, we normalize the trace element abundances in the melt and cpx by the respective values derived from the case of constant partition coefficients at Tp = 1300°C (Table 3). For both batch melting and near- fractional melting, compositions of the aggregated melt and residual cpx generated by varying partition coefficients are very close to those derived from constant partition coefficients (Fig. 11). The differences become even smaller from LREE to HREE. Hence the small variation of cpx partition coefficients has negligible effect on REE fractionation during anhydrous melting in spinel lherzolite regime. 5.3. The effect of water on REE fractionation Water has a significant effect on REE and Y partitioning in cpx during hydrous melting, even though water is mostly subtracted from the mantle source at the beginning of melting. Asimow and Langmuir (2003) suggest that water effect on melt composition is significant due to the low-productivity, small-degree melting in the hydrous melting regime. To illustrate the water effect on REE fractionation, we calculate REE abundances in aggregated melt and residual cpx following the aforementioned procedures for partial melting of a hydrous mantle (DMM with 200 ppm H2O, Tp = 1300°C). In order to highlight the water effect, REE abundances are normalized by values derived from the same condition using constant cpx partition coefficients. The constant cpx partition coefficients are averaged values from anhydrous melting of DMM at Tp = 1300°C. For both melting models (batch or near-fractional melting), aggregated melt under hydrous condition is more enriched in LREE at the beginning of melting than those under anhydrous condition (by 5~18%, Figs. 12a-12c). These discrepancies can be explained by low compatibility 24 of REE in cpx as a result of high water content in the melt and high melting temperature. Since the amount of water in the instantaneous melt decreases with the decrease of melting temperature along the mantle adiabat, REE become more compatible in cpx, and therefore the differences in LREE in the melt between varying and constant cpx partition coefficients nearly disappear at greater extent of melting (e.g., F = 6% for La). As water induces incipient melting in the garnet stability field, garnet would have a secondary effect on REE fractionation. Because of great compatibility of heavy REE in garnet, the differences in heavy REE (e.g., Yb), however, are small at the onset of melting and increase with water subtraction or garnet consumption (Fig. 12c). After water or garnet totally disappears, the differences in heavy REE would approach zero. When the extent of melting is greater than 10%, the effect of water and/or water-induced garnet on REE abundances in aggregated melt may be negligible. Hence, we can expect a higher ratio of La/Yb in aggregated melt during hydrous melting. Heavy REE depletion in the melt could indicate the garnet signature in mantle source, and/or deep melting of a hydrous mantle. The extent of melting under hydrous condition would be underestimated by using constant partition coefficients from anhydrous melting, whereas the degree of melting can be better estimated for greater extents of melting (F > 10%). Residual cpx derive from water-dependent cpx partition coefficients are more depleted in REE than those from constant cpx partition coefficients (Figs. 12d-12f). At the onset of hydrous melting, due to the low compatibility of REE residual cpx are more depleted in LREE (e.g., La) compared to those from constant partition coefficients. REE fractionation in residual cpx is the product of instantaneous melt and REE partitioning in cpx. For near-fractional melting LREE depletion in instantaneous melt increases dramatically with the extent of melting, whereas for batch melting it is weaker because of the auto-enrichment effect (Liang 2008; Liang and Peng 2010). Even though REE partition coefficients in cpx increase with the decrease of water in the melt, LREE depletion in residual cpx increases for near-fractional melting as LREE depletion in the melt may have greater influence than water-dependent cpx partition coefficients. For batch 25 melting, LREE depletion in residual cpx becomes insignificant for large extent of melting (>10%) due to water-dependent partition coefficients and the auto-enrichment effect. However, the strong depletion of HREE in residual cpx suggests that the presence of garnet could have great impact on HREE fractionation in residual cpx through the instantaneous melt (Fig. 12f). The garnet influence would diminish with garnet out for both batch and near-fractional melting. By investigating REE abundances in residual cpx, we find that water effect on REE partitioning in cpx may be neglected as the extent of melting approaches 10% for batch melting, but it would enhance LREE depletion in cpx for near-fractional melting (by 38% for La, Fig. 12d). Therefore, the extent of melting might be overestimated from the REE abundance in residual cpx produced by near-fractional hydrous melting. 6. Conclusions We present a new predictive model for REE and Y partitioning between cpx and basaltic melt obtained by least squares analysis of published partitioning data using the lattice strain model (Brice 1975; Blundy and Wood 1994). Our model suggests that variations in partition coefficients result mostly from temperature, Al and Mg contents in cpx and water content in the melt. Using cpx compositions derived from pMELTS and pHMELTS (Ghiorso et al. 2002; Asimow et al. 2004), we examined the REE and Y partitioning in cpx during adiabatic melting of three mantle compositions for two potential temperatures and under anhydrous or hydrous conditions. Our study reveals strong competing effect between temperature and cpx composition such a set of constant partition coefficients is adequate for modeling REE and Y partitioning between cpx and basaltic melt during adiabatic melting of an anhydrous spinel lherzolite at a given potential temperature. Addition of water in the mantle source could induce and enhance the garnet signature for small-degree melting. Water effect becomes negligible in aggregated melt for large extent of melting (>10%), but is significant for LREE fractionation in residual cpx produced by near-fractional melting. The extent of melting may be overestimated by residual cpx without 26 taking into account of the water effect. 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Treatise Geochem 2:395-424 Wood BJ, Trigila R (2001) Experimental determination of aluminour clinopyroxene-melt partition coefficients for potassic liquids, with application to the evolution of the Roman province potassic magmas. Chem Geol 172:213-223 Workman RK, Hart SR (2005) Major and trace element composition of the depleted MORB mantle (DMM). Earth Planet Sci Lett 231:53-72 Zou H (1998) Trace element fractionation during modal and nonmodal dynamic melting and open-system melting: a mathematical treatment. Geochim Cosmochim Acta 62:1937-1945 Zou H (2000) Modeling of trace element fractionation during non-modal dynamic melting with linear variations in mineral/melt distribution coefficients. Geochim Cosmochim Acta 64:1095-1102 33 Figure Captions Figure 1-1. Variations in mineral modal proportions and degree of melting (F) as a function of pressure during adiabatic melting of a garnet lherzolite. Phase proportions are calculated using pMELTS (Ghiorso et al. 2002) assuming near-fractional melting of the depleted MORB mantle (DMM; Workman and Hart 2005) at potential temperature 1400ºC. For clarity, modal abundance of olivine is scaled down by a factor of two. Abbreviations sp, gar, ol, cpx and opx represent spinel, garnet, olivine, clinopyroxene and orthopyroxene, respectively. Shaded region on the bottom indicates the garnet stability field. Figure 1-2. Observed versus predicted partition coefficients of REE and Y, in which observed partition coefficients are obtained from partitioning experiments (see Table 1 for complete references), and predicted partition coefficients are calculated using the partitioning model of Wood and Blundy (1997, 2002). Error bars for observed values are from reported standard derivation of partitioning experiments. EMP represents data analyzed by electron microprobe, whereas IP-ICP includes data analyzed by ion probe or LA-ICP-MS. Dashed lines represent 2:1 and 1:2 lines, and the solid line represents 1:1 line. To assess the goodness of fit of their model prediction, we calculate χ P (Eq. 7) for partitioning data analyzed by ion probe or LA-ICP-MS ( 2 χ P2 = 113.47) and EMP ( χ P2 = 7.80). Figure 1-3. Nonlinear correlations among the lattice strain parameters obtained by Monte Carlo simulation. Inverted D0 versus r0 (a) and E versus r0 (b) from the simulation. The pentagrams represent the initial inputs of D0, r0 and E (D0 = 1.46, r0 = 0.98 Å, E = 268 GPa), derived from the partitioning experiment by Blundy et al. (1998), and small crosses represent the derived values. The procedure for Monte Carlo simulation is as follows. First, the initial inputs are used to generate a set of hypothetical REE and Y partition coefficients by Eq. (1). We then generate a 34 group of partition coefficients by randomly perturbing the initial values, assuming 10% 1σ error and normal distribution. After generating 1000 sets of synthetic partition coefficients, we then use the nonlinear least squares regression method (Seber and Wild 1989) and minimize χ2 (Eq. 6) to obtain D0, r0 and E from each group of partition coefficients. Figure 1-4. Comparison between experimentally measured partition coefficients (observe D) and model derived values (predicted D). The observed values are obtained from partitioning experiments (see Table 1 for complete references), and the predicted values are calculated by Eqs. (1), (8)-(10). Error bars for observed values are from reported standard derivation of partitioning experiments, and error bars for predicted values represent 2 errors of model prediction. Symbols without error bar represent either no errors reported or smaller (than symbol size) errors. EMP represents data analyzed by electron microprobe, whereas IP-ICP includes data analyzed by ion probe or LA-ICP-MS. Dashed lines represent 2:1 and 1:2 lines, and the solid line represents 1:1 line. Our model generates much smaller χ P (= 7.33) for IP-ICP data than that ( χ P = 113.47; 2 2 cf. Fig. 2) from Wood and Blundy (1997, 2002), indicating the significant improvement of our model. Figure 1-5. Uncertainties of predicted partition coefficients arise from the uncertainties in temperature and composition. Circles represent the predicted values by Eqs. (1), (8)-(10) for given T and cpx compositions of Blundy et al. (1998) and McDade et al. (2003a), solid curves represent the averaged partition coefficients from Monte Carlo simulation, and dashed curves represent the standard deviation from assumed uncertainties of the variables. See text for more details. 35 Figure 1-6. Comparison between the observed and predicted partition coefficients of REE and Y in cpx relevant to melting of mafic pyroxenite. Observed data are from partitioning experiments involving melting of mafic pyroxenite (Elkins et al. 2008) and eclogite (Pertermann and Hirschmann 2002; Pertermann et al. 2004). Error bars for observed values come from reported standard derivation of partitioning experiments, and error bars for predicted values represent 2 errors of model prediction. Symbols without error bar represent no errors reported or small errors. Dashed lines represent 2:1 and 1:2 lines, and the solid line represents 1:1 line. Our model generates a χ P value of 1.60 for those partitioning data. 2 Figure 1-7. Schematic diagrams showing temperature and water effect on REE partitioning (a) and the compositional effect on REE partitioning (b) between cpx and basaltic melt. Figure 1-8. Variation of partition coefficients of Ce and Yb from Gaetani and Grove (1995) as a function of AlT (a) and MgM2 (b) contents in cpx, and the relationship between AlT and MgM2 contents in cpx (c). Solid lines are from linear regressions. Figure 1-9. Schematic diagrams showing the competing effects (a) and enhancing effects (b) between cpx composition and temperature on REE partitioning between cpx and basaltic melt. Figure 1-10. Variations of AlT, AlM1 and MgM2 contents in cpx as a function of temperature from pMELTS and pHMELTS (a, c, e, Ghiorso et al. 2002; Asimow et al. 2004) and corresponding REE partition coefficients (b, d, f) for different cases. a and b show the case of near-fractional melting of a dry DMM (Workman and Hart 2005) at potential temperature 1300°C and 1400°C. c and d show the case of near-fractional melting of DMM at potential temperature 1300°C under hydrous condition (200 ppm H2O). e and f show the case of near-fractional melting of a dry 36 enriched mantle source (EM = 90% DMM + 10% N-MORB, N-MORB from Hofmann 1988) at potential temperature 1300°C. For comparison, we also show the case of anhydrous melting of DMM at potential temperature 1300°C in c, d, e and f. The vertical lines in a and c labeled “gar- out” mark the garnet disappearance. The positive correlation between cpx composition and temperature in spinel lherzolite region suggests the competing effect on partitioning, whereas lower Al and Mg contents in cpx at the beginning of melting of a hotter or wet mantle implies smaller partition coefficients in cpx. The gray areas in b, d and f represent experimental partition coefficients from Table 1. Figure 1-11. Effects of temperature and composition dependent cpx-melt partitioning on REE fractionation during batch (blue lines) or near-fractional (red lines) melting of DMM (Workman and Hart 2005) along the Tp = 1300°C adiabat. We use Eqs. (11)-(12) to calculate aggregated melt composition, and residual cpx composition. For comparison, La, Nd, and Yb abundances in the aggregated melt and residual cpx are normalized by the respective values calculated using the constant cpx-melt partition coefficients listed in Table 3. REE partition coefficients in cpx are calculated by Eqs. (1), (8)-(10) with cpx composition from pMELTS. To calculate km in Eq. (11), we use olivine-, opx-, spinel- and garnet-melt partition coefficients from Kelemen et al. (2003), and phase proportion of each mineral from pMELTS. For near-fractional melting, melt suction R is zero (batch melting) before the extent of melting reaches the threshold, which is the prescribed fmin (0.5%) in pMELTS. Hence, near-fractional melting and batch melting are overlapped for the extent of melting less than 0.5%. Figure 1-12. Effects of temperature, cpx composition, and water dependent cpx-melt partitioning on REE fractionation during batch (blue lines) or near-fractional (red lines) melting of a damped DMM (Workman and Hart 2005, plus 200 ppm water) along the Tp = 1300°C adiabat. For comparison, La, Nd, and Yb abundances in the aggregated melt and residual cpx are normalized 37 by the respective values calculated using the constant cpx-melt partition coefficients listed in Table 3 (See the caption of Fig. 11 for more details). Figure 1-S1 Comparisons of measured clinopyroxene-melt partitioning data (circles) and those predicted by models from this study (red lines) and Wood and Blundy (1997, 2002; gray lines) for individual experiments. Markers with light blue color represent partitioning data excluded in our model calibration. H2O is the water content in the melt. Figure 1-S2. Comparison between experimentally measured partition coefficients (observe D) and model derived values (predicted D). The observed values are obtained from partitioning experiments (see Table 1 for complete references), and the predicted values are calculated by refitting the model of Wood and Blundy (1997, 2002). EMP represents data analyzed by electron microprobe, whereas IP-ICP includes data analyzed by ion probe or LA-ICP-MS. Dashed lines represent 2:1 and 1:2 lines, and the solid line represents 1:1 line. We refit 10 coefficients in Wood and Blundy’s (W&B) model by a global or simultaneous inversion of the 344 high quality partitioning data, which are also used to calibrate our model. Other four coefficients related to water effect are kept as same constant values as those in W&B’s original model during the global inversion, since they were not obtained directly from partitioning data in W&B’s model. Even though the updated W&B model provides a larger χ P (= 9.26) for EMP data than that ( χ P = 2 2 7.80) from their original model, the updated W&B model generates a much smaller χ P (= 26.37) 2 for IP-ICP data than that from their original model ( χ P = 113.47; cf. Fig. 2), indicating the 2 improvement after the global inversion. However, the updated W&B’s model still has a considerably larger χ P for IP-ICP data than that from our new model ( χ P = 7.33; cf. Fig. 4), 2 2 which further supports the improvement of our model formulation. 38 Figure 1-S3. Comparison between experimentally measured partition coefficients (observe D) and model derived values (predicted D). The observed values are obtained from partitioning experiments (see Table 1 for complete references), and the predicted values are calculated by Eqs. (1, S1-S3). EMP represents data analyzed by electron microprobe, whereas IP-ICP includes data analyzed by ion probe or LA-ICP-MS. Dashed lines represent 2:1 and 1:2 lines, and the solid line represents 1:1 line. This model generates a larger χ P (= 10.64) for IP-ICP data than that ( χ P = 2 2 (= 9.63) for EMP data than that ( χ P = 2 7.33; cf. Fig. 4) from Eqs. (1, 8-10), and a smaller 11.60) from Eqs. (1, 8-10). Figure 1-S4. Variation of D0 as a function of temperature (a), pressure (b), AlT content in cpx (c), MgM2 content in cpx (d), NBO/T of bulk melt (e) and H2O content in the melt (f) from partitioning experiments analyzed by ion probe or LA-ICP-MS (see Table 1 for complete references). NBO/T of the bulk melt is calculated following the expression of Mysen et al. melt (1985). X H2O is calculated using the method from Wood and Blundy (2002). 39 Figures Figure 1-1 40 Figure 1-2 41 Figure 1-3 42 Figure 1-4 43 Figure 1-5 44 Figure 1-6 45 Figure 1-7 46 Figure 1-8 47 Figure 1-9 48 Figure 1-10 49 Figure 1-11 50 Figure 1-12 51 Figure 1-S1 Supplementary Fig. 1-S1a This study 0 Yb Ho Gd Eu 10 Yb Er Ho Sm Eu Lu Lu Dy Nd Y Gd Sm Pr Nd Gd Pr Sm Nd Ce Ce La 10 La P = 0.0001 GPa La P = 0.1 GPa P = 0.1 GPa o o o C C C H O = 0 wt% H O = 0 wt% H O = 0 wt% Duration = 88 h Duration = 88 h 10 Dy Partition Coefficient 0 10 Ho Tb Sm Lu Er Yb Er Eu Y Yb Er Nd Yb Pr Lu Sm Y Sm Ce Nd Nd La 10 Ce P = 0.1 GPa P = 1.5 GPa P = 1.9 GPa Ce o o o C C C H O = 0 wt% H O = 0 wt% H O = 0 wt% Duration = 88 h 10 Y Dy Sm Ho Nd 0 10 Pr Yb Lu Lu Y Ce Y Er Sm La Er Sm Nd Nd Ce 10 Ce P = 1.5 GPa o o C C T = 1070oC H O = 0 wt% H O = 0 wt% H O = 1 wt% 10 0.9 1 1.1 0.9 1 1.1 0.9 1 1.1 52 Supplementary Fig. 1-S1b Y Sm Dy Nd Y Sm Ho Pr Dy Y Dy Nd Ho Sm 0 Ce Ho Pr 10 Nd La Ce Pr La Ce La 10 o o C C T = 1140oC H O = 1 wt% H O = 1 wt% H O = 0 wt% Duration = 48 h Duration = 48 h Duration = 48 h 10 Yb Er Lu Partition Coefficient 0 Y 10 Yb Er Yb Y Sm Dy Dy Y Er Eu Nd Sm Sm Eu Nd Eu Nd Ce Ce Ce 10 La La La o o o C C C H O = 0 wt% H O = 1 wt% H Duration = 47 h 10 This study 0 10 Er Lu Er Dy Y Yb Yb Lu Dy Y Eu Sm Sm Eu Sm Eu Nd Nd Nd Ce Ce Ce 10 La o o La o T = 1185 C C C La H O = 6 wt% H O = 0 wt% H O = 0 wt% Duration = 48 h 10 1 1.1 1 1.1 1 1.1 53 Supplementary Fig. 1-S1c 0 10 Yb Dy Eu Lu Y Lu Gd Dy Er Sm Sm Yb Lu Sm Y Nd Nd 10 Pr Run#1787 P = 1.7 GPa Ce P = 3 GPa Pr Ce P = 3 GPa T = 1405oC La T = 1400oC o C Ce H O = 0 wt% H O = 0 wt% H O = 11 wt% La La Hauri et al. (1994) 10 Yb Partition Coefficient 0 10 Lu Eu Gd Sm Ho Dy Ho Nd Eu Lu Tb Yb Yb Pr Gd Sm Nd Ce Nd 10 Run#1807 Pr Run#1956 P = 4 GPa Ce P = 3.5 GPa T = 1080oC La Ce H O = 6 wt% T = 1160oC La T = 1180oC H O = 17 wt% H O = 16 wt% La 10 0 10 Yb Ho Ho Ho Lu Tb Lu Tb Lu Tb Y Yb Y Sm Yb Y Sm Sm Nd Nd Nd Run#R80 Run#1949 Run#1948 10 P = 3 GPa Ce Ce Ce T = 1170oC T = 1160oC T = 1160oC H O = 10 wt% H O = 10 wt% La H O = 8 wt% La La 10 0.9 1 1.1 0.9 1 1.1 0.9 1 1.1 Ionic Radius (Å) 54 Supplementary Fig. 1-S1d 0 10 Ho Yb Ho Ho Lu Tb Lu Tb Tb Yb Sm Sm Y Lu Yb Sm Nd Nd Run#R78 Nd Run#R77 Ce 10 La Ce T = 1100oC Ce T = 1100oC o C La H H H La 10 0 10 Ho Yb Tb Yb Dy Y Lu Y Sm Dy Sm Nd Y Yb Sm Nd Nd Run#R79 Ce Run#E7 10 Ce o La o o C C La C Ce La H H H 10 0 10 Lu Y Y Y Yb Dy Dy Sm Yb Sm Nd Nd Run#E8 Run#E9 10 Ce Ce T = 1391oC o C o C H La H H La 10 1 1 1 55 Supplementary Fig. 1-S1e 0 10 Lu Y Y Lu Y Lu Sm Dy Sm Nd Nd Run#R4 10 Ce T = 1340oC La T = 1340oC o C H O = 0 wt% H O = 0 wt% La H O = 0 wt% 10 Partition Coefficient 0 10 Y Y Lu Lu Sm Lu Dy Y Sm Nd Nd Ce La 10 Ce T = 1340oC C o o C H O = 0 wt% H O = 0 wt% La H O = 0 wt% 10 1 1 0 10 Er Y Eu Lu Yb Sm Nd Run#MW1 10 Ce o C H La 10 1 56 Figure 1-S2 Predicted D (Wood&Blundy) EMP 0 10 10 0 10 10 Observed D 57 Figure 1-S3 EMP Predicted D (Sun&Liang) 0 10 10 0 10 10 Observed D 58 Figure 1-S4 (a) (b) 0 0 0 0 D D 10 10 6 6.5 7 7.5 1 2 3 4 10000/T (/K) P (GPa) (c) (d) D0 D0 0 0 10 10 0.1 0.2 0.3 0.4 0 0.1 0.2 0.3 0.4 XTAl XM2 Mg (e) (f) Hydrous Anhydrous D0 0 0 0 D 10 10 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 melt NBO/T XH O (mol%) 2 59 Tables Table 1-1 Data sources and experimental run conditions Melt H2Ob Melt SiO2 Cpx Al2O3 Reference na P (GPa) T (°C) Duration (hr) NBO/T (wt%) (wt%) (wt%) Ion probe analysis Hauri et al. (1994) 2 1.7-2.5 1405-1430 22-69 0 48.26-48.40 9.16-13.23 0.579-0.697 Blundy et al. (1998) 1 1.5 1255 47 0 50.17 10.47 0.414 Johnson (1998) 11 2.0-3.0 1325-1470 16.8-120 0 50.10-54.40 7.11-10.80 0.499-0.694 Lundstrom et al. (1998) 1 0.0001 1275 24 0 49.50 4.80 0.920 Salters et al. (2002) 1 1.5 1410 23 0 46.50 9.90 0.823 Salters and Longhi (1999) 3 1.2-1.9 1360-1455 - 0 44.50-46.00 8.20-11.40 0.832-0.925 Green et al. (2000) 3 2.0-4.0 1080-1200 22.5-48 6.44-17.35 48.12-56.79 5.72-10.22 0.338-0.892 Hill et al. (2000) 3 0.1 1218 88 0 42.09-52.67 4.74-14.80 0.693-1.070 Wood and Trigila (2001) 4 0.0001-0.2 1042-1070 48 0-1.3 50.42-54.01 7.51-12.15 0.251-0.438 Klemme et al. (2002) 1 3.0 1400 70 0 56.70 15.60 0.178 Gaetani et al. (2003) 3 1.2-1.6 1185-1370 24-26 0.98-6.26 46.80-48.40 7.10-8.70 0.671-0.902 McDade et al. (2003a) 1 1.5 1325 48 0 47.60 9.44 0.720 McDade et al. (2003b) 1 1.3 1245 49 1.64 48.90 7.50 0.816 Total range 35 0.0001-4.0 1042-1470 16.8-120 0-17.35 42.09-56.79 3.19-15.60 0.178-1.070 LA-ICP-MS analysis Adam and Green (2006) 8 1.0-3.5 1050-1180 47 5.8-16.3 44.94-49.58 3.19-6.88 0.724-0.984 EMP analysis Hack et al. (1994) 46 1.2-2.0 1200-1450 23-92 0 47.04-53.20 5.30-14.26 0.383-0.816 Gaetani and Grove (1995) 9 0.0001 1234-1265 24-264 0 43.40-54.50 1.50-10.90 0.709-1.140 Gaetani (2004) 12 1.5 1285-1345 120 0 41.89-53.88 9.95-12.30 0.402-0.759 Total range 67 0.0001-2 1200-1450 23-264 0 41.89-54.50 1.50-14.26 0.383-1.140 a n represents the numbers of experiments. b H2O are analyzed by Fourier transform infrared spectroscopy (FTIR) except for those from Green et al. (2000) and Adam and Green (2006) calculated by mass balance. Zero values represent nominally anhydrous system. Total major oxides in the melt are normalized to 100% for those with water. 60 Table 1-2 Derived D0, r0 and E from partitioning experiments Reference D0 r0 (Å) E (GPa) Ion probe analysis Hauri et al. (1994) 0.442-0.728 1.010-1.020 318-441 Blundy et al. (1998) 1.462 0.982 268 Johnson (1998) 0.357-0.465 0.958-1.022 107-364 Lundstrom et al. (1998) 0.286 1.049 375 Salters et al. (2002) 0.773 0.930 150 Salters and Longhi (1999) 0.461-0.740 0.992-1.002 229-325 Green et al. (2000) 0.279-1.125 1.004-1.036 293-414 Hill et al. (2000) 0.785-1.055 1.023-1.035 332-347 Wood and Trigila (2001) 1.682-4.254 1.048-1.068 364-525 Klemme et al. (2002) 0.633 0.992 342 Gaetani et al. (2003) 0.597-0.731 0.964-1.005 178-233 McDade et al. (2003a) 0.777 1.003 307 McDade et al. (2003b) 0.593 1.015 365 Total range 0.279-4.254 0.930-1.068 107-525 LA-ICP-MS analysis Adam and Green (2006) 0.338-0.558 1.001-1.028 166-351 EMP analysis Hack et al. (1994) - - - Gaetani and Grove (1995) - - - Gaetani (2004) 0.511-1.375 0.969-1.004 234-320 Total range 0.511-1.375 0.969-1.004 234-320 61 Table 1-3 Recommended cpx-melt partition coefficients for anhydrous melting in spinel lherzolite DMMa PMb EMc TP 1300°C 1400°C 1300°C 1300°C La 0.0550 0.0528 0.0574 0.0586 Ce 0.0876 0.0784 0.0914 0.0934 Pr 0.1318 0.1116 0.1377 0.1408 Nd 0.1878 0.1524 0.1963 0.2008 Sm 0.3083 0.2400 0.3224 0.3300 Eu 0.3638 0.2815 0.3802 0.3893 Gd 0.4169 0.3231 0.4357 0.4461 Tb 0.4645 0.3630 0.4851 0.4968 Dy 0.5034 0.3993 0.5255 0.5382 Y 0.5219 0.4192 0.5446 0.5578 Ho 0.5294 0.4283 0.5523 0.5657 Er 0.5437 0.4500 0.5668 0.5806 Tm 0.5482 0.4650 0.5711 0.5852 Yb 0.5453 0.4743 0.5677 0.5819 Lu 0.5373 0.4791 0.5592 0.5733 a DMM is the depleted mantle of mid-ocean ridge basalt from Workman and Hart (2005). b PM is the primitive mantle from Sun and McDonough (1989). c EM is assumed to be composed of 90% DMM added 10% N-MORB in major element compositions, and N-MORB are from Hofmann (1988). 62 Supplementary Material S1. A parameterization including EMP data Here we include all the measurements (EMP, ion probe, LA-ICP-MS; a total of 527 data) from Table 1, and follow the same parameterization procedures described in the main text to obtain a new parameterized model for REE and Y partitioning between cpx and basaltic melts, 6.94 ( ±0.70 ) × 10 4 ln D0 = −6.75 ( ±0.53) + + 3.59 ( ±0.44 ) X AlT RT +1.47 ( ±0.35 ) X Mg M2 − 0.97 ( ±0.18 ) X Hmelt 2O (S1) r0 = 1.064 ( ±0.008 ) − 0.097 ( ±0.034 ) X AlM 1 − 0.177 ( ±0.035 ) X Mg M2 (S2) E = ⎡⎣1.85 ( ±0.56 ) r0 − 1.57 ( ±0.56 ) ⎤⎦ × 10 3 (S3) where definition of the various symbols are the same as those used in Eqs. (8)-(10). Equations (S1)-(S3) show the same composition dependent function forms for the lattice strain parameters (D0, r0 and E) as in Eqs. (8)-(10), with coefficients taking on slightly different numerical values. This suggests again that Al, Mg contents in cpx and water content in the melt are the primary factors controlling REE partitioning in cpx. Equations (S1)-(S3) can generally predict partition coefficients close to measured data (Fig. S3), and provide a small χ P2 value (10.64) for the 344 high precision data (ion probe and LA- ICP-MS) and a small χ P2 value (9.63) for 183 EMP data. The χ P2 value for EMP data is less than that from Eqs. (8)-(10) ( χ P2 = 11.60 ), suggesting the better fit to the EMP data. However, the χ P2 value (10.64) for high precision data is larger than that (7.33, Fig. 4) from Eqs. (8)-(10). In general, addition of 183 EMP data in the calibration does not change the structure of our model, nor does it improve the model prediction. Thus, our 63 preferred model is Eqs. (1), (8)-(10), calibrated with the high precision data (ion probe and LA-ICP-MS). 64 CHAPTER 2 2 Distribution of REE and HFSE between Low-Ca Pyroxene and Lunar Picritic Melts around Multiple Saturation Points Chenguang Sun and Yan Liang Department of Geological Sciences, Brown University Providence, RI 02912, USA Published in Geochimica et Cosmochimica Acta, 119, 340-358, 2013 65 Abstract The abundances and distribution of incompatible trace elements in low-Ca pyroxene are important to the interpretation of the thermal and chemical evolution of the lunar magma ocean and cumulate mantle. We conducted high pressure (2 GPa) and high temperature (1340-1450 °C) experiments to constrain trace elements partitioning between low-Ca pyroxene and a wide range of lunar picritic melt compositions (TiO2 = 1.6-16.6 wt%) under reducing conditions imposed by graphite-lined molybdenum capsules. We show that addition of TiO2 in the melt decreases rare earth element (REE) and Y partition coefficients in low-Ca pyroxene and quantified this effect through a parameterized lattice strain model. Together with published high quality partitioning data of tetravalent high field strength elements (HFSEs) in the literature, we also developed a parameterized lattice strain model for Ti, Hf and Zr partitioning in low-Ca pyroxene. Partition coefficients of REE and HFSE are positively correlated with Al and Ca abundances in low-Ca pyroxene and negatively correlated with temperature. HFSE partition coefficients show an inverse correlation with Fe content in low-Ca pyroxene. As examples of lunar applications, we estimated REE and HFSE partition coefficients in low-Ca pyroxene close to the multiple saturation points of lunar picritic melts, and found small variations of these partition coefficients in low-Ca pyroxene from individual lunar picritic melts. Constant REE and HFSE partition coefficients can be used in melting models exploring the petrogenesis of individual picritic melts. On the other hand, large variations in estimated REE and HFSE partition coefficients for low-Ca pyroxene are expected during lunar magma ocean crystallization, underscoring the significance of temperature-composition dependent REE and HFSE partition coefficients for understanding lunar magma ocean evolution. 66 1. Introduction The canonical lunar formation and evolution model involves a giant impact, a magma ocean, and cumulate overturn (e.g., Stevenson, 1987; Hess and Parmentier, 1995; Papike et al., 1998; Shearer et al., 2006; Wieczorek et al., 2006; Elkins-Tanton et al., 2011). According to the cumulate overturn model, mare basalts were produced by decompression melting of the overturned lunar cumulate mantle (Shearer et al., 2006 and references therein). Mare basalts and picritic glass beads collected during the Apollo missions have a large range of TiO2 abundances (0.22-17.01 wt%) and show systematic relations between TiO2 and other major element compositions (Fig. 1). Low- and high-Ti mare basalts have distinct Hf-Nd isotope signatures, suggesting the presence of at least three chemical end-members in the lunar mantle (KREEP, high-Ti, and low-Ti cumulates; e.g., Nyquist and Shih, 1992; Beard et al., 1998). Extensive geochemical studies have indicated the involvement of ilmenite in the generation of the high-Ti basalts (e.g., Delano, 1986; Nyquist and Shih, 1992; Beard et al., 1998; Shearer et al., 2006; Liu et al., 2010). Addition of ilmenite in the lunar mantle may result from overturn of ilmenite- bearing late cumulate after solidification of the lunar magma ocean (LMO) (Hess and Parmentier, 1995; de Vries et al., 2010). However, ilmenite has not been observed at the multiple-saturation points of pristine mare glasses. Instead, molten picritic glasses are multiply saturated with olivine and low-Ca pyroxene at pressures of 1.3-2.4 GPa and temperatures of 1435-1560°C, which suggests that the mantle sources of mare basalts and picritic glasses primarily consist of olivine and low-Ca pyroxene (e.g., Green et al., 1975; Delano, 1980; Wagner and Grove, 1997; Elkins et al., 2000; Elkins-Tanton et al., 2003). This is also consistent with models of LMO crystallization and overturn of lunar cumulate mantle (e.g., Snyder et al., 1992; Hess and Parmentier, 1995; Elkins-Tanton et al., 2011). Due to its relatively high affinity for incompatible trace elements and high abundance in the lunar mantle, low-Ca pyroxene contributes significantly to trace element fractionation during 67 LMO crystallization and subsequent melting of lunar cumulate mantle. Trace element partition coefficients between low-Ca pyroxene and lunar pristine melt are therefore important parameters in the interpretation of the magmatic evolution of the Moon. To date, there are only a few studies that examined the partitioning of trace elements between low-Ca pyroxene and lunar basaltic melts (e.g., Weill and McKay, 1975; McKay et al., 1991; van Kan Parker et al., 2011; Yao et al., 2012). Weill and McKay (1975) reported trace element partition coefficients between orthopyroxene (opx) and KREEP melts, and McKay et al. (1991) reported rare earth element (REE) partition coefficients between pigeonite and lunar mare basaltic melt. In both cases, trace element abundances in coexisting pyroxene and melt were analyzed by electron microprobe. Recently, van Kan Parker et al. (2011) performed partitioning experiments for low-Ca pyroxene and melts produced from a hybrid lunar mantle source (magma ocean cumulate hybrid or MOCH of Singletary and Grove, 2008). Figs. 1 and 2 show that the major element compositions of coexisting melt and low-Ca pyroxene in the experimental charges of van Kan Parker et al. (2011) generally deviate from trends defined by lunar picritic glass compositions and low-Ca pyroxene compositions from multiple saturation experiments. The Al2O3 and CaO abundances in their pyroxenes, for example, fall on the lower end of the trends defined by low-Ca pyroxenes from multiple saturation experiments (Figs. 2c and 2d). As has been demonstrated previously and further confirmed by additional partitioning experiments reported in this study, both Al and Ca in pyroxene are important in determining the partitioning of REE and high-field strength elements (HFSE) in low-Ca pyroxene. Thus, partitioning data reported in van Kan Parker et al. (2011) might not be used sensu stricto in modeling petrogenesis of mare basalts. Nonetheless, these data are useful in expanding the limited database for trace element partitioning between low-Ca pyroxene and lunar relevant melts. Trace element partition coefficients between minerals and melts are functions of pressure (P), temperature (T), and compositions (X) of the mineral and melt (Blundy and Wood, 1994; Wood and Blundy, 2003). As different lunar picritic melts may have distinct cumulate mantle 68 sources and melting conditions, melts and residual minerals (e.g., low-Ca pyroxene) show large variations in major element compositions (Figs. 1 and 2). Thus, the P-T-X dependence of trace element partitioning in low-Ca pyroxene may lead to markedly different interpretations of melting processes in the lunar mantle. To assess the variations of REE partition coefficients (DREE) in low-Ca pyroxene during magma genesis, Yao et al. (2012) developed a parameterized lattice strain model for REE and Y partitioning between low-Ca pyroxene and basaltic melts. Although lunar relevant partitioning data [including those reported in van Kan Parker et al. (2011) and this study] were included as part of their database, their study focused mainly on melting in the Earth’s upper mantle. The effect of melt TiO2 abundance on REE partitioning in low-Ca pyroxene, for example, was not determined as it is of little relevance to the Earth. In this study, we report results from an experimental study of trace element partitioning between low-Ca pyroxene and lunar picritic melts for a wide range of TiO2 content in melt (TiO2 = 1.6-16.6 wt%) and at a pressure of 2 GPa and temperatures of 1340 to 1450°C. We show that REE partition coefficients for low-Ca pyroxene are inversely correlated with TiO2 abundance in the melt. We expand the model of Yao et al. (2012) by considering the effect of melt TiO2 and also develop a new parameterized lattice strain model for Ti, Zr, and Hf partitioning between low-Ca pyroxene and basaltic melt. As examples of lunar application, we demonstrate how the resulting parameterized lattice strain models can be used to select the appropriate REE and HFSE partition coefficients for low-Ca pyroxene during melting of a cumulate lunar mantle and solidification of the LMO. 69 2. An Experimental Study of Trace Element Partitioning between Low-Ca Pyroxene and Lunar Picritic Melts 2.1. Experimental methods Starting materials were prepared by mixing appropriate amounts of high purity oxides and carbonates, homogenized by grinding in a corundum or agate mortar under ethanol. The starting mixtures A15Red and YG-1d were decarbonated at 1000°C for 12 h, and conditioned at 900°C for 3.5 h with the oxygen fugacity controlled near the iron-wüstite (IW) buffer by flowing mixtures of CO2 and H2 gases. The starting mixtures A15GG and A15YG were obtained by mixing proper amounts of oxide mixtures of A15 red glass with A15 green and yellow glasses that were synthesized by Morgan et al. (2006) and were preconditioned at the IW buffer. The oxide starting materials were then doped with small amounts (~ 2wt% in total) of a trace element oxide cocktail (La2O3, CeO2, Pr6O11, Nd2O3, Sm2O3, Eu2O3, Gd2O3, Dy2O3, Ho2O3, Y2O3, Yb2O3, Lu2O3, ZrO2, HfO2, Nb2O5, Ta2O5, WO3). The trace element mixture was also conditioned at 900°C for 3.5 h with oxygen fugacity controlled near IW, and added into the starting mixtures at the level of ~1000 ppm for each trace element. The doped materials were subsequently reground under ethanol in a corundum mortar, and dried in air under heat lamp. The total grinding times were 5 to 12 hours for each starting material. All the starting materials were stored in a 110°C vacuum oven before use. The nominal element compositions of the starting materials are listed in Table 1. Experiments were conducted using a 19.05 mm piston-cylinder apparatus at Brown University. The furnace assembly consists of a molybdenum capsule in an MgO sleeve sandwiched between two crushable MgO spacers in a graphite, Pyrex® and salt sleeve. The molybdenum capsule (6.5 mm OD and 5 mm long) was lined with a graphite sleeve (4 mm OD, 2 mm ID). Two ends of the graphite sleeve were packed with graphite powder so that actual sample length is 2.5 to 3 mm. To improve the chance of growing large, homogeneous crystals, a thin 70 layer of natural opx powder (< 0.5 mm thickness) from a spinel lherzolite xenolith from Kilbourne Hole, NM (KBH-1 used in Morgan and Liang, 2005) was placed on the top or bottom of the starting materials of runs A15YG, A15Red and YG-1d. The furnace assembly was dried in a 200°C vacuum oven for at least overnight and then stored in a 110°C vacuum oven. Partitioning experiments were carried out at 2 GPa and 1340-1450°C for 48 to 50 h. To assure the growth of large crystals, we performed step cooling and isothermal experiments. The runs were first cold pressurized to a pressure of ~1.9 GPa, and then heated to target temperatures at 75 °C/min. The pressure was then raised to 2 GPa. To run step cooling experiments, we first raised the temperature 50-75 °C higher than the target temperature (Table 2) for 0.1 or 2 h. We then lowered the temperature at 0.5 or 1 °C/min to the run temperature. Experiments were terminated by shutting off the power while maintaining pressure at approximately 2 GPa. Run products were sectioned along the cylindrical axis of the capsule, mounted in epoxy, and polished with Al2O3 to 1 µm finish. Experimental run conditions and run products are summarized in Table 2. Temperature was measured using a W97Re3-W75Re25 thermocouple and controlled by a Eurotherm 818 or 2408 controller with no correction made for the measured electromotive force. Pressure was measured using a Heise pressure gauge without a friction correction. 2.2. Analytical methods Major element compositions of experimental products of runs A15GG210, A15YG217, and A15Red219 were determined using a Cameca SX100 electron microprobe (EMP) at Brown University. Minerals and quenched melts in those charges were analyzed with a 20 kV accelerating potential and a 25 nA beam current. The counting times were 10-30 s for peak and 10-15 s for background. The run products of YG-1d-1, YG-1d-4 and A15Red-1 were analyzed using a JEOL 733 Superprobe at the Massachusetts Institute of Technology with a 15 kV accelerating potential and a 10 nA beam current for both minerals and quenched melts. The 71 counting times for background and peak are 20 s and 40 s, respectively. A focused beam was used for all the mineral analyses, and a defocused beam (20 µm) for all the glass analyses. Natural and synthetic mineral standards were used for calibration. All raw data were reduced using a ZAF matrix correction procedure. Major element compositions of run products are listed in Table 3. Trace elements in glasses and crystals were analyzed in situ using a Thermo X-Series 2 quadrupole ICP-MS in conjunction with a New Wave UP 213 nm Nd-YAG laser-ablation system at the University of Rhode Island. Samples were ablated with 20 to 80 µm diameter beams using output energy of 0.3 mJ and at a frequency of 10 Hz. For each spot, counting times were 30 s for background and 60 s for acquisition of laser ablation. For both opx and glasses, we calibrated the analyses by the internal standard MgO from EMP analyses and multiple external standards, NIST610 (Pearce et al., 1997), BCR2g, BHVO2g, BIR1g (Kelley et al., 2003), GOR132, StHls, T1, ML3B and KL2 (Jochum et al., 2006). Electron microprobe analyses of MgO content were chosen from points close to the spots analyzed by the laser ablation-inductively coupled plasma- mass spectrometry (LA-ICP-MS). The detection limit for each analysis was estimated at 3 times the standard deviation of the background. 2.3. Experimental results Experimental run products are listed in Table 2. All runs produced opx as well as large pools of quenched melt. An oxide mineral was also present in the high-Ti runs A15Red219 and A15Red-1. The quenched melts generally show dendritic quench texture (Fig. 3). Orthopyroxenes are euhedral and show no sign of resorption. Generally, small crystals (~ 10 to 60 µm in size) accumulated in the lower parts of capsules and large ones (~ 80 to 400 µm) at the top of the capsules. Their size varies from run to run, and these two groups of crystal sizes are not present in all runs. All experiments produced crystals large enough (> 50 µm) for LA-ICP-MS analysis. With the exception of opx in run A15YG217, most large crystals are homogeneous without 72 zoning or inclusions (Fig. 3a). One large crystal from run A15Red219 contains a few small melt inclusions (< 5 µm), and care was taken to avoid them during in situ analysis (Fig. 3b). Most crystals from run A15YG217 are uniform in size (~ 100 µm) and show centric zoning with wide rims. Their wide rims were analyzed and used to calculate partition coefficients. Major and trace element compositions of melt and opx from experiments are reported in Table 3. Small standard deviations suggest homogeneous melt compositions in each run. The totals of microprobe analyses are slightly low in the melts (97.21-99.6 wt%) due to the high abundances of trace elements (a total of 1-2 wt%). The melts are generally within the major element compositional trends of lunar glasses (Fig. 1), and show large variations in SiO2, TiO2 contents, and Mg# (48-56 compared with 45-73 for lunar picritic glasses). The melts from runs A15Red219 and A15Red-1 show elevated CaO contents and are slightly off the lunar glass trend (Fig. 1b), which is due to different proportions of opx added to the charges. The opx rims from run A15YG219 show relatively small standard deviations in major and trace element compositions, suggesting local chemical equilibrium between crystal rims and melt was approached. Orthopyroxenes from all runs are within the low-Ca pyroxene range of multiple saturation experiments for lunar basalts (Fig. 2), and show large variations in SiO2, Al2O3 and TiO2 contents but limited variations in CaO contents and Mg# (Fig. 2). In general, the opx from runs A15YG217, A15Red219, YG-1d-1, YG-1d-4 and A15Red-1 have higher TiO2 contents and lower Mg# than the seed opx crystals, indicating those opx precipitated from the melts. A number of undoped trace elements (P, Sc, V, Co, Ni, Cu, Zn, Sr, and Mo) are present at detectable levels with small standard deviations (Table 3). They were likely derived from dissolved opx seeds that we used to facilitate opx growth and/or from impurities in the doped oxides. The partition coefficient (D) of an element (i) is calculated according to its concentration opx melt by weight in opx ( Ci ) and coexisting melt ( Ci ): 73 Ciopx Diopx-melt = (1) Cimelt Orthopyroxene-melt partition coefficients for trace elements and Ti are reported in Table 4 and plotted together with literature data in Fig. 4. Our D values show small variations and are generally within the range of measured partitioning data for low-Ca pyroxene reported in the literature, although a few exceptions are noted. Niobium and Ta partition coefficients are lower than literature values by a factor of 2 to 3. Tungsten partition coefficients are comparable to the only published datum (0.0002) from Adam and Green (2006), except for that from run A15YG213 that is higher than others by a factor of five. Phosphorus partition coefficients are greater than the literature range by a factor of 2 to 6. Partition coefficients of copper (0.059-0.063) fall in the very lower end of the range defined by the literature data (2.8 from Adam and Green, 2006; 0.22 from Klemme et al., 2006; 0.15-0.82 from Fellows and Canil, 2012; and 0.043-0.055 from Yao et al., 2012). Nonetheless, our measured DCu are similar to those observed in the opx- basaltic andesite partitioning experiments of Yao et al. (2012) that used a very similar experimental setup. The reducing condition imposed by the graphite-lined molybdenum capsule may render most, if not all, copper as Cu+ in our experimental charges (see Yao et al., 2012 for additional discussion). We show that the lattice strain model further supports this in section 3.1 (Fig. 5). Finally, compared with those from van Kan Parker et al. (2011), our data show higher D values for Zr, Hf, Sc, V, mid- and heavy-REE (MREE and HREE), but lower D values for Nb, Ta, and light-REE (LREE). As discussed below, these discrepancies can be attributed, in part, to differences in melt and opx compositions, and run conditions (Figs. 1-2). 74 3. Models for Trace Element Partitioning 3.1. Lattice strain model Partition coefficients of isovalent cations ( ) from a given mineral-melt partitioning experiment depend on their ionic radii (ri) (Onuma et al., 1968), and can be quantitatively described by the lattice strain model (Brice, 1975; Blundy and Wood, 1994): ⎡ −4π EN A ⎛ r0 1 3⎞ ⎤ ( ) ( ) 2 Di = D0 exp ⎢ ⎜ r0 − ri − r0 − ri ⎟ ⎥ (2) ⎢⎣ RT ⎝ 2 3 ⎠ ⎥⎦ where r0 is the optimum radius for the lattice site; D0 is the mineral-melt partition coefficient for the strain-free substitution; E is the effective Young’s modulus for the lattice site; R is the gas constant; NA is Avogadro constant; and T is temperature. D0 determines the peak of the parabola with corresponding ideal element radius r0, and E controls the tightness of the parabola. Pyroxene has two different octahedrally coordinated M sites, a smaller M1 site and a larger M2 site. Previous partitioning studies for opx have suggested that REE and Y enter the M2 site whereas Ti, Zr, Hf, Nb, Ta, Sc, Cr, Al and Co prefer the M1 site (e.g., Frei et al., 2009). Here we apply a non-linear least squares method (Seber and Wild, 1989) and fit the experimental partitioning data for divalent cations (Zn2+, Mn2+, Ca2+, Sr2+), smaller trivalent cations (Al3+, Cr3+, and Sc3+), larger trivalent cations (REE3+ and Y3+), and tetravalent cations (Ti4+, Hf4+ and Zr4+), respectively, by minimizing the chi-squares as defined below ( ) N χ = ∑ ln Di − ln Dim 2 2 (3) i=1 m where Di is defined by Eq. (2); Di is the measured opx-melt partition coefficient for element i; N is the number of measured partitioning data used in the fit to the lattice strain model for a given group of elements. Logarithmic partition coefficient is used in our chi-square calculation because the absolute values of D are different from one element to another over orders of magnitude and systematic variations in trace element abundances and partition coefficients are usually examined 75 in semi-log spider diagrams. Six-fold coordinated ionic radii (from Shannon, 1976) are used for cations in the M1 and M2 site. Table 5 lists the lattice strain parameters obtained in this study. Figures 5a-5f, often referred to as Onuma diagrams, display the best fits to the measured partition coefficients as a function of ionic radii for each experiments. Figure 5 shows that smaller trivalent cations (Al3+, Cr3+, Sc3+) have higher partition coefficients (D0 = 3.65-5.19) than those of larger cations (REE3+ and Y3+; D0 = 0.171-0.297) and form distinct parabolas with smaller r0 (r0 = 0.654-0.674 Å for Al3+, Cr3+, and Sc3+; r0 = 0.675- 0.760 Å for REE3+ and Y3+) and tighter shape (E = 1060 to 1390 GPa for Al3+, Cr3+, and Sc3+; E = 193-295 GPa for REE3+ and Y3+). This suggests that smaller trivalent cations (Al3+, Cr3+, Sc3+) prefer the M1 site, larger trivalent cations (REE3+ and Y3+) favor the M2 site, and the M1 site is more rigid than the M2 site, which are consistent with previous studies (e.g., Frei et al., 2009; van Kan Parker et al., 2010). With the exception of Cu2+, the divalent cations (Zn2+, Mn2+, Ca2+ and Sr2+) form parabolas with larger r0 (0.786-0.836 Å), smaller D0 (0.683-0.914) and wider shape (E = 100-188 GPa). The larger values of r0 suggest that these divalent cations prefer the M2 site of opx. The tetravalent cations (Ti4+, Zr4+, Hf4+) define parabolas with D0 of 0.081-0.156, r0 of 0.635-0.648 Å, and E of 2059-2818 GPa, and thus prefer the M1 site. In general, D0 and r0 decreases, and E increases as ionic charge increases from 3+ to 4+ for cations in M1 site or from 2+ to 3+ for cations in M2 site of opx (Table 5). Systematic variations of the lattice strain parameters (D0, r0, and E) for trace and minor element partitioning between opx and melt as a function of ionic charge similar to the ones noted above and reported previously (Frei et al., 2009; van Kan Parker et al., 2010, 2011) have also been observed in other mineral-melt systems such as plagioclase, cpx, and garnet (e.g., Blundy and Wood, 1994, 2003; van Westrenen et al., 2000a, 2000b; Wood and Blundy, 2001, 2003). These systematic variations are generally attributed to compressibility or bulk modulus of the crystal and electrostatic forces of the cations and anions. For additional discussion, interested readers are referred to a recent review by Wood and Blundy (2003). 76 The lattice strain parameters obtained from individual experiments may incorporate significant uncertainties for the following reasons: (1) E and r0 have a strong trade-off due to the nonlinear nature of the lattice strain model (Sun and Liang, 2012); (2) parabolas constrained by partition coefficients of three elements (e.g., Ti, Hf and Zr) lack degrees of freedom; and (3) low concentrations of light REE in low-Ca pyroxene may induce larger analytical uncertainties and hence larger uncertainties in the inverted apparent lattice strain parameters. As we demonstrated recently, a simultaneous fit of selected high quality experimental partitioning data to the lattice strain model can significantly increase the degree of freedom, and enables us to explore the P-T-X effects on trace element partitioning in low-Ca pyroxene (Sun and Liang, 2012; Yao et al., 2012). We will return to this point in Section 3.3 below. Our new partitioning data show insignificant Eu anomalies in Onuma diagrams (Fig. 5). Europium can exist in minerals and melts as both Eu2+ and Eu3+, the proportion of which depends on fO2. Our starting materials were conditioned close to the IW buffer and run in graphite-lined molybdenum capsules, so the reducing condition should be imposed and constrained during the runs. Accordingly, a Eu anomaly would be expected in the Onuma diagram for REE. As shown in Fig. 5, the parabola defined by REE3+ is subparallel to the parabola defined by the large 2+ cations. Under this special condition, the partition coefficients of Eu3+ and Eu2+ are comparable to each other. Hence the lack of Eu anomalies is likely a coincidence, specific to the P-T-X conditions examined in this study. A negative Eu anomaly is observed in the opx-basaltic andesite partitioning experiments of Yao et al. (2012) that use a nearly identical capsule and furnace assembly. 3.2. REE partitioning between low-Ca pyroxene and lunar basaltic melts In a recent study Yao et al. (2012) examined published experimental data for REE and Y partitioning between low-Ca pyroxene and basaltic melts and parameterized REE and Y partition coefficients as functions of temperature and pyroxene composition using the lattice strain model. 77 The database used to calibrate their model consists of 344 high quality data compiled from 38 partitioning experiments reported in the literature, including those from the present study; their sources and run conditions are listed in Table 3 in Yao et al. (2012). Figure 6 compares our measured D values of REE and Y from individual experiments with those predicted by the model of Yao et al. (2012). The predicted DREE (blue lines) are generally consistent with our measured values, except for two experiments with high TiO2 melts (runs A15Red217 and A15Red-1) for which predictions exceed measured values by a factor of two. To quantify the melt Ti effect on REE partitioning in low-Ca pyroxene, we apply the simultaneous inversion method described in Sun and Liang (2012) to the 344 partitioning data compiled by Yao et al. (2012). Since D0 determines the height of the parabola defined by the lattice strain model (Eq. 2), one simple way to improve the empirical model of Yao et al. (2012) is to add a melt TiO2 term to the expression for D0 (see Eq. 4 below). The revised model for REE and Y partitioning between low-Ca pyroxene and basaltic melts is ( 3.87 ±0.74 × 104 ) ( ln D0 = −5.37 ±0.49 + ) RT ( ) + 3.54 ±0.61 AlT ( ) ( +3.56 ±1.02 Ca M2 − 0.84 ±0.22 X Timelt ) (4) ( ) ( ) r0 = 0.693 ±0.055 + 0.432 ±0.147 Ca M2 + 0.228 ±0.056 Mg M2 ( ) (5) ( ) ( ) ( E = ⎡⎣1.85 ±0.52 × r0 − 1.37 ±0.47 − 0.53 ±0.11 Ca M2 ⎤⎦ × 103 ) (6) where r0 is the optimum ionic radius in Å; E is the effective Young’s modulus in GPa; numbers in parentheses denote the 2σ errors calculated directly from the inversion; CaM2 is the Ca content in the M2 site of low-Ca pyroxene; AlT is the Al content in the tetrahedral site of low-Ca pyroxene; X Timelt is the molar fraction of Ti in the melt per six-oxygen, calculated following the method of Wood and Blundy (2002). For reasons detailed in Yao et al. (2012) we used eight-fold coordinated ionic radii of REE and Y in the M2 site of low-Ca pyroxene to calibrate Eqs. (4-6). 78 Note the only difference between Eqs. (4-6) and the model of Yao et al. (2012) is the extra melt TiO2 term in Eq. (4). Coefficients for all other terms are the same between the two models. Addition of a melt TiO2 term to the model of Yao et al. (2012) significantly improved the accuracy of REE partitioning between low-Ca pyroxene and high-Ti melts (red lines in Fig. 6) without affecting the accuracy of DREE for low-Ti melts. To compare the goodness of the fit between the two models, we calculate the Pearson’s chi-square ( χ p ) defined below 2 (D − D ) 2 N m χ 2p = ∑ i i (7) i=1 Di A smaller χ 2p value suggests a better predictive model. The Pearson’s chi-square is 1.23 for the present model and is smaller than that ( χ p =1.30) for the model of Yao et al. (2012). The effect 2 of melt TiO2 is statistically significant. The negative coefficient of X Timelt indicates that REE tend to enter melt with high TiO2 abundance and become highly incompatible for very high-Ti melts; however, the absolute value of this coefficient is small, suggesting insignificant Ti effect for low- Ti melts. Similar negative correlations between melt TiO2 abundance and partition coefficients of major and trace elements in olivine and oxide minerals have also been found (e.g., Longhi et al., 1978; Jones, 1988; Dygert et al., 2013), suggesting that melt TiO2 has significant control on major and trace element partitioning. Addition of Ti depolymerizes the melt, and decreases the activity of trace elements in the melt (e.g., Longhi et al., 1978; Jones, 1988; Dygert et al., 2013). Thus, trace elements become less compatible in the minerals coexisting with high-Ti melt. melt melt The molar fraction of Ti in the melt per six-oxygen ( X Ti ) and TiO2 contents ( CTiO ) of 2 the melt in weight fraction from the compiled experiments show a nearly perfect linear correlation (Supplementary Fig. S1) and can be described by the expression: X Timelt = 0.0304 × CTiO melt (8). 2 79 melt melt Equation (8) can also precisely describe the correlation between X Ti and CTiO for lunar 2 picritic glasses, mare basalts and KREEP basalts (Supplementary Fig. S2). However, this expression is not preferred because it will introduce extra fitting errors; nonetheless, it becomes very useful when abundances of other major oxide components in the melt are not available. 3.3. A parameterized model for Ti, Hf, and Zr partitioning in low-Ca pyroxene The abundances of TiO2 in mare basalts and picritic glasses are likely related to the presence of ilmenite and armalcolite in the lunar cumulate mantle (e.g., Delano, 1986; Wagner and Grove, 1997; Beard et al., 1998; Liang and Hess, 2008; Thacker et al., 2009; Liu et al., 2010). Neither ilmenite nor armalcolite has been observed at multiple saturation points of pristine lunar glasses. Since low-Ca pyroxene is a dominant phase in lunar cumulate mantle, variations of its chemical composition may have significant influence on Ti and other high-field strength element fractionation during the LMO crystallization and initial stages of melting of the overturned cumulate mantle. Thus, a composition-, temperature-, and pressure-dependent model quantifying Ti, Hf, and Zr partitioning in low-Ca pyroxene will be especially useful in geochemical modeling of lunar magma petrogenesis. Bédard (2007) analyzed opx-melt partition coefficients from published partitioning experiments and natural samples (phenocrysts/matrix) through linear regression analyses, and suggested that ln(D) for a given trace element could be estimated by a linear combination of mineral and melt composition. He argued that melt composition dominates Ti, Hf, and Zr partitioning in opx, and provided several partitioning models for each of the elements. Comparing these models we found that the linear functions based on Al2O3 content, ln(MgO) and Mg# of the melt appear to give better predictions for DZr and DHf, whereas the linear function based on Al2O3 content, ln(MgO) and ln(FeO) of the melt appear to provide better predictions for DTi (for details, see Eqs. 16, 35, and 36 in Bédard, 2007). There are a total of 12 coefficients in the Ti, Hf and Zr 80 partitioning models of Bédard (2007). Figure 7a compares the predicted D values for Ti, Hf, and Zr by Bédard’s models with the experimentally measured ones from our compiled dataset (a total of 96 data, see section 3.3.1 below). The scatter indicates that Bédard’s models do not constrain Ti, Hf and Zr partitioning in opx very well. In the following sections, we outline a new model for Ti, Hf and Zr partitioning between low-Ca pyroxene and basaltic melt on the basis of a compiled high quality dataset and the lattice strain model (Eq. 2). 3.3.1. Data compilation Following the strategy outlined in Sun and Liang (2012) and Yao et al. (2012), we compiled 33 experiments with long run durations and minimal kinetic effect for Ti, Hf and Zr partitioning in low-Ca pyroxene from the literature (Salters and Longhi, 1999; van Westrenen et al., 2000b; Salters et al., 2002; McDade et al., 2003a, 2003b; Adam and Green, 2006; Tuff and Gibson, 2007; Frei et al., 2009; van Kan Parker et al., 2010; Yao et al., 2012) and this study. Of the 33 experiments, 24 contain opx and 9 contain subcalcic augite. Two of the 23 experiments are conducted under hydrous conditions (McDade et al., 2003a; Adam and Green, 2006). The abundances of Zr and Hf from these studies were collected by LA-ICP-MS or secondary ion mass spectrometry (SIMS). LA-ICP-MS or SIMS data were not reported for Ti from Salters and Longhi (1999) and Salters et al. (2002), but because of the limited high quality partitioning data for Ti, Hf and Zr in low-Ca pyroxene, we used their reported EMP data to calculate DTi. A total of 96 high quality partitioning data were obtained and used to calibrate the HFSE partitioning model for low-Ca pyroxene. The compiled 33 partitioning experiments were conducted over a wide range of pressures (1 atm-3.4 GPa) and temperatures (1160-1660 ºC), and produced low-Ca pyroxene and melt with large variations in composition (e.g., Mg# = 48-100 and TiO2 = 0-16.6% in melt; Mg# = 73-100 and CaO = 1.35-10.81 wt% in low-Ca pyroxene). Partition coefficients from these experiments vary by one order of magnitude (DTi = 0.044-0.240, DHf = 0.011-0.097, 81 and DZr = 0.006-0.048), which can be attributed to the variations in P, T, and mineral and melt compositions. 3.3.2. Parameterization method To obtain a parameterized model for Ti, Hf and Zr partitioning in low-Ca pyroxene, we followed the procedure described in Sun and Liang (2012) and Yao et al. (2012) that consists of two steps: (1) linear least squares analysis to identify key variables that determine the lattice strain parameters from individual experiments, and (2) simultaneous inversion of all filtered experimental data to constrain coefficients of the primary variables identified in step (1). We assume that D0 has the form of Eq. (2) in Sun and Liang (2012) and r0 is a function of pyroxene composition. Sun and Liang (2012) performed Monte Carlo simulations for the lattice strain model (Eq. 2), and found a positive correlation between E and r0 for REE partitioning in the M2 site of clinopyroxene. Yao et al. (2012) then compared E and r0 of clinopyroxene, opx and subcalcic augite from individual experiments, and showed that pyroxene composition also has a significant influence on E for REE partitioning in M2 site. Thus, we assume E is a function of r0 and pyroxene composition. Through an extensive search of various permutations of the composition variables, we find that AlT, CaM2, MgM2, and Fe in the M1 site (FeM1) in low-Ca pyroxene and T are the primary variables determining D0 for the 4+ elements, Ti, Zr and Hf; CaM2 and MgM1 are the major factors affecting r0; and E can be treated as a constant. Fig. S3 shows the relationship between Ti, Zr and Hf partition coefficients for low-Ca pyroxene and AlT, CaM2 × MgM2, and FeM1 in low-Ca pyroxenes. We then use the coefficients from the multiple linear regressions as initial guesses and carry out the global or simultaneous inversion for the 9 coefficients in the parameterized lattice strain model by minimizing the chi-square as defined in Eq. (3). Note that N in Eq. (3) becomes the total number of measured partitioning data from the compiled dataset (N = 96). 82 3.3.3. Model result The global fit of the 96 partitioning data from 33 experiments leads to the following lattice strain parameters for Ti, Hf, and Zr partitioning in low-Ca pyroxene: ( 3.178 ±1.348 × 104) ( ln D0 = −4.825 ±0.999 + ) RT ( + 4.172 ±1.152 AlT ) ( ) +8.551 ±1.630 Ca M2 × Mg M2 − 2.616 ±0.856 Fe M1 ( ) (9) ( ) ( ) r0 = 0.618 ±0.018 + 0.032 ±0.017 Ca M2 + 0.030 ±0.017 Mg M1 ( ) (10) ( E = 2203 ±665 ) (11) where numbers in parentheses are 2σ errors calculated directly from the simultaneous inversion; the units for r0 and E are the same as those in Eqs. (5) and (6). The large 2σ errors (compare to our REE model) is due to a combination of analytical uncertainties, the limited number of trace elements (three) from each experiment used in the model calibration, and trade-offs among lattice strain parameters. Equations (2, 9-11) provide a simple model for Ti, Hf and Zr partitioning between low-Ca pyroxene and basaltic melt. Figure 7b shows that the predicted D values by Eqs. (2, 9-11) and the experimentally measured values follow the 1:1 correlation line and fall between the 1:2 and 2:1 correlation lines. The χ 2p value provided by our model ( χ p 2 = 0.39 ) is much smaller than that calculated using the model of Bédard (2007; χ 2p = 1.23 ), indicating the significant improvement of our new model. Because the major compositions of low-Ca pyroxene vary systematically with pressure and melt composition, DTi, DHf and DZr can indirectly depend on P and melt composition. The effect of water, however, cannot be constrained due to the limited hydrous data for Ti, Hf and Zr partitioning in low-Ca pyroxene in our filtered dataset (only two experiments; McDade et al., 2003a, and Adam and Green, 2006). 83 In summary, our partitioning models suggest that T and pyroxene composition determine the partitioning of REE and HFSE in low-Ca pyroxene. REE and HFSE D0 are negatively correlated with T, and positively correlated with AlT and CaM2 contents in low-Ca pyroxene. REE D0 decreases with addition of TiO2 in the melt, whereas HFSE D0 decreases with the increase of FeM1 in low-Ca pyroxene. Addition of melt TiO2 to the HFSE model does not significantly improve the model prediction. For both REE and HFSE, r0 increases with addition of CaM2 contents in low-Ca pyroxene. REE r0 also shows an inverse correlation with MgM2 in low-Ca pyroxene, but HFSE r0 is negatively correlated with MgM1 in low-Ca pyroxene. For REE, E is negatively correlated with CaM2 in low-Ca pyroxene, and positively correlated with r0 due to the nonlinear nature of the lattice strain model; however, a constant E for HFSE can reproduce all the compiled data very well. Due to their different compositional dependences, REE and HFSE may be fractionated from each other by low-Ca pyroxene during magmatic processes. 4. Lunar Applications The parameterized models allow us to calculate partition coefficients for REE and HFSE in low-Ca pyroxene given major element compositions of the pyroxene and melt and temperature. In this section, we consider two lunar applications. 4.1. REE and HFSE partitioning in low-Ca pyroxene at multiple-saturation points The multiple-saturation point (MSP) of a primary magma can be determined experimentally to investigate the minimum depth of origin, temperature, and mineralogy of the mantle source region (e.g., Green et al., 1975; Delano, 1980; Wagner and Grove, 1997; Elkins et al., 2000; Elkins-Tanton et al., 2003; Asimow and Longhi, 2004; Draper et al., 2006). Multiple- saturation experiments indicate that low-Ti picritic melts are saturated with olivine + low-Ca pyroxene at 1.3-2.4 GPa and 1520-1560 °C (Elkins et al., 2000; Elkins-Tanton et al., 2003), 84 whereas high-Ti picritic melts are saturated with olivine + low-Ca pyroxene at 1.5-2.4 GPa and 1435-1480 °C (Green et al., 1975; Delano, 1980; Wagner and Grove, 1997). The MSP of high-Ti basalts may be difficult to interpret due to the possibility of ilmenite and/or armalcolite assimilation (e.g., Anderson, 1971; Hubbard and Minear, 1975; Wagner and Grover, 1997; Jones and Delano, 1991; Liang et al., 2007; Liang and Hess, 2008; Singletary and Grove, 2008; Grove and Krawczynski, 2009). Nonetheless, multiple-saturation experiments can be used to estimate mineral and melt compositions relevant to lunar magma genesis. Given the large compositional variations of low-Ca pyroxene from multiple-saturation experiments (Fig. 2), we might expect significant variations in trace element partition coefficients for low-Ca pyroxene during melting of the lunar cumulate mantle. Figure 8a shows predicted DREE and DHFSE between low-Ca pyroxene and lunar picritic melts from multiple-saturation experiments. For all multiple-saturation experiments, the predicted DREE are within the range of experimentally determined partition coefficients, and DREE and DHFSE in opx are lower than those in subcalcic augite (circles joined by solid lines). Due to the large variation of Ca abundance the predicted DREE and DHFSE in low-Ca pyroxene vary over one order of magnitude (e.g. DLa = 6×10-4-2×10-2). Predicted partition coefficients for subcalcic augite show large variations for LREE and MREE, but relatively small variations for HREE. Hence subcalcic augite can significantly fractionate LREE from HREE during melting of the cumulate lunar mantle. Low-Ca pyroxene at or close to the MSP may most closely represent compositions of pyroxene in the mantle source of mare basaltic melts. Figure 8b displays the calculated D in low- Ca pyroxene at or close to the MSP of picritic glasses. Those pyroxenes are enstatite, and show smaller variations in DREE than those from the multiple-saturation experiments in Fig. 8a. Red and green glasses show higher D values than black glasses, whereas green glasses show two distinct D values. The lower D values of green glasses are from multiple saturation experiments for Apollo 15C green glass, which also has a distinct MSP with higher P than other green glasses 85 (Elkins-Tanton et al., 2003). For each lunar picritic melt, D values of REE and HFSE in opx show a very small variation and hence may be treated as constant when modeling individual primitive lunar melts. Table 6 lists our recommended partition coefficients of REE and HFSE for different lunar picritic glasses at around the MSP. We note that the predicted D is very sensitive to pyroxene composition from multiple-saturation experiments that often have very short run durations. Significant uncertainties may be involved in the estimation if minerals and melts do not approach chemical equilibrium. Krawczynski and Grove (2012) conducted phase equilibria studies for lunar high-Ti glasses using both graphite and Fe metal capsules. Their experiments suggest that the MSP can shift to higher P under more reducing conditions because the presence of Ti3+ at low fO2 may change Ti-Fe coordination in high-Ti melts and major element partitioning (e.g., Fe-Mg partitioning in olivine). Therefore, variations of fO2 may also give rise to distinct partitioning behaviors of trace elements between low-Ca pyroxenes and lunar picritic melts. Based on the Ti abundances in opx and melts from the experiments of Krawczynski and Grove (2012), we calculate DTi close to the MSP for different fO2. At higher fO2 the measured DTi are 0.064-0.072 for the orange glass and 0.081-0.095 for the red glass, while at lower fO2, the measured values are 0.077-0.086 for the orange glass and 0.109-0.114 for the red glass. The partition coefficient of Ti appears to increase with the increase of fO2. Because Ti3+ has ionic radius between Cr3+ and Sc3+, it probably prefers the M1 site in low-Ca pyroxene and follows the parabola defined by Al3+, Cr3+ and Sc3+. Hence, DTi should increase over one order of magnitude if significant amounts of Ti3+ are present in the melt and opx (cf. parabola defined by Al, Cr, and Sc vs. those defined by HFSE in Fig. 5). The amount of Ti3+ is probably very small in opx at lower fO2. Given the analytical uncertainties and limited number of experiments close to the MSP (two for the orange glass, and three for the red glass), we suggest that the change of fO2 has little effect on DTi under the conditions explored by Krawczynski and Grove (2012). 86 To compare D values of REE and HFSE at the two fO2, we also apply our partitioning models to mineral and melt compositions close to the MSP in Krawczynski and Grove (2012). Fig. S4 shows the calculated D values of low-Ca pyroxenes close to the MSP at fO2 constrained by the graphite (dashed lines) or Fe (solid lines) capsule. Low-Ca pyroxenes for the red glass show slightly higher DTi and DHREE than those for the orange glass; however, the variations of DREE, DHf and DZr due to fO2 are within a factor of two for each melt composition. Although different fO2 can influence the MSP depth and T, the net effect of T and composition may cancel out, resulting in nearly consistent DREE and DHFSE for individual lunar picritic melts at different fO2. 4.2. Trace element partitioning in low-Ca pyroxene during crystallization of the lunar magma ocean Numerous attempts have been made to model the chemical evolution of the LMO (e.g., Taylor and Jakeš, 1974; Longhi, 1980, 2003; Snyder et al., 1992; Elardo et al., 2011; Elkins- Tanton et al., 2011). Here we calculate DREE and DHFSE for low-Ca pyroxenes derived from the LMO crystallization using the parameterized models obtained in this study. The MAGFOX program (Longhi, 1992; Longhi, 2006) is utilized to simulate the fractional crystallization of the LMO. We use the lunar upper mantle composition (LPUM) of Longhi (2006) as the starting composition, and 4 GPa as the initial depth of the LMO. For purpose of demonstration, we choose calculated compositions of three low-Ca pyroxenes that crystallize at 39%, 78% and 89% solidification. The corresponding crystallization temperatures are 1619 ºC, 1250 ºC, and 1144 ºC at pressures of 1.83, 0.46 and 0.2 GPa, respectively. As crystallization proceeds, these pyroxenes become more Fe-rich, but in general have high Mg# (94, 83, and 71) within the range defined by our filtered dataset. The predicted D values are within the literature range, but DREE vary by a factor of six (blue curves in Fig. 9; Table 6). Trace elements generally become more compatible 87 at late crystallization stage due to lower crystallization T and higher Ca contents in the minerals. Phase equilibria experiments have been conducted to investigate equilibrium crystallization of several LMO compositions at 1-4 GPa and 1250-1825 ºC (Elardo et al., 2011). For comparison, we estimate trace element D in low-Ca pyroxenes based on their experiments for LPUM. The predicted DREE and DHFSE (red curves in Fig. 9) are generally consistent with those based on MAGFOX (blue lines in Fig. 9). The partition coefficients of HFSE in low-Ca pyroxene in both cases show smaller variations than REE due to the competing effects of T and pyroxene composition (Fe and Ca). This may explain the variation of Lu/Hf or εHf in low-Ti sources (Beard et al., 1998). This example illustrates that T-X dependent REE and HFSE partitioning in low-Ca pyroxene has to be taken into consideration when modeling the LMO evolution, a subject that will be explored in the future. 5. Summary and Conclusions Trace element partition coefficients between low-Ca pyroxene and lunar picritic melts were determined experimentally at 2 GPa and 1340-1450°C for a large range of melt TiO2 abundances. We demonstrate that the lattice strain model can quantify systematic variations of partition coefficients as a function of ionic radii for divalent cations (Zn2+, Mn2+, Ca2+ and Sr2+), large trivalent cations (REE3+ and Y3+), small trivalent cations (Al3+, Cr3+, and Sc3+), and tetravalent cations (Ti4+, Hf4+, Zr4+) in low-Ca pyroxene, respectively. The very low Cu partition coefficients observed in the present study may be attributed to the presence of significant fraction of Cu+ in our experimental charges that resulted from the reducing condition imposed by graphite-lined molybdenum capsules. The apparent lack of Eu anomalies in our partitioning experiments may be explained by the nearly identical Eu3+ and Eu2+ partition coefficients under the conditions investigated. 88 Based on partitioning data obtained in this study and those reported in the literature, we developed parameterized lattice strain models for REE and Ti, Zr, and Hf partitioning between low-Ca pyroxene and basaltic melt. REE partition coefficients are positively correlated with Ca and Al contents in low-Ca pyroxene, but negatively correlated with T and melt TiO2 abundance. Hence REE become more incompatible in low-Ca pyroxene with the increase of TiO2 content in the melt. HFSE partition coefficients are positively correlated with Al and Ca contents in low-Ca pyroxene, and inversely correlated with T and Fe content in the pyroxene. REE and HFSE could be fractionated by low-Ca pyroxene due to these different compositional effects. Applications of our REE and HFSE partitioning models to low-Ca pyroxenes at the MSP of lunar picritic glasses revealed that REE and HFSE partition coefficients could be treated as constants to model petrogenesis of individual lunar picritic melts. The net effect of T and composition diminishes the indirect influence of fO2 on REE and HFSE partitioning in low-Ca pyroxenes. However, temperature and composition dependent REE and HFSE partitioning in low-Ca pyroxenes are important when modeling the LMO crystallization. REE and HFSE can be significantly fractionated by low-Ca pyroxene during the LMO crystallization. Acknowledgements We thank Katie Kelley and Marion Lytle for their help and advice in LA-ICP-MS analysis, and Nilanjan Chaterjee for his assistance in microprobe analysis. Nicholas Dygert analyzed A15GG210 using LA-ICP-MS for us and is greatly appreciated. We also thank John Longhi for providing the MAGFOX program. 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National Aeronautics and Space Administration Lyndon B. Johnson Space Center, TM-101934. Salpas P. A., Taylor L. A. and Lindstrom M. M. (1987) Apollo 17 KREEPy basalts: Evidence for nonuniformity of KREEP. J. Geophys. Res. 92, E340-E348. Salters V. J. M. and Longhi J. (1999) Trace element partitioning during the initial stages of melting beneath mid-ocean ridges. Earth Planet. Sci. Lett. 166, 15-30. Salters V. J. M., Longhi J. E. and Bizimis M. (2002) Near mantle solidus trace element partitioning at pressures up to 3.4 GPa. Geochem. Geophys. Geosyst. 3, 1038. Seber G. and Wild C. (1989) Nonlinear Regression. Wiley, New York. Shannon R. (1976) Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides. Acta Cryst A 32, 751-767. Shearer C. and Papike J. (1993) Basaltic magmatism on the Moon: A perspective from volcanic picritic glass beads. Geochim. Cosmochim. Acta 57, 4785-4812. Shearer C. K., Hess P. C., Wieczorek M. A., Pritchard M. E., Parmentier E. M., Borg L. E., 95 Longhi J., Elkins-Tanton L. T., Neal C. R. and Antonenko I. (2006) Thermal and magmatic evolution of the Moon. Rev. Mineral. Geochem. 60, 365-518. Shearer C., Papike J., Galbreath K. and Shimizu N. (1991) Exploring the lunar mantle with secondary ion mass spectrometry: A comparison of lunar picritic glass beads from the Apollo 14 and Apollo 17 sites. Earth Planet. Sci. Lett. 102, 134-147. Shearer C., Papike J., Simon S., Shimizu N., Yurimoto H. and Sueno S. (1990) Ion microprobe studies of trace elements in Apollo 14 volcanic glass beads: Comparisons to Apollo 14 mare basalts and petrogenesis of picritic magmas. Geochim. Cosmochim. Acta 54, 851-867. Singletary S. and Grove T. (2008) Origin of lunar high-titanium ultramafic glasses: A hybridized source? Earth Planet. Sci. Lett. 268, 182-189. Snyder G. A., Taylor L. A. and Neal C. R. (1992) A chemical model for generating the sources of mare basalts: Combined equilibrium and fractional crystallization of the lunar magmasphere. Geochim. Cosmochim. Acta 56, 3809-3823. Stevenson D. (1987) Origin of the moon-The collision hypothesis. Annu. Rev. Earth Planet. Sci. 15, 271-315. Sun C. and Liang Y. (2012) Distribution of REE between clinopyroxene and basaltic melt along a mantle adiabat: effects of major element composition, water, and temperature. Contrib. Mineral. Petrol. 163, 807-823. Taylor S. and Jakeš P. (1974) The geochemical evolution of the Moon. Lunar Planet. Sci. Conf. Proc. 5, 1287-1305. Thacker C., Liang Y., Peng Q. and Hess P. (2009) The stability and major element partitioning of ilmenite and armalcolite during lunar cumulate mantle overturn. Geochim. Cosmochim. Acta 73, 820-836. Tuff J. and Gibson S. (2007) Trace-element partitioning between garnet, clinopyroxene and Fe- rich picritic melts at 3 to 7 GPa. Contrib. Mineral. Petrol. 153, 369-387. van Kan Parker M., Liebscher A., Frei D., van Sijl J., van Westrenen W., Blundy J. and Franz G. 96 (2010) Experimental and computational study of trace element distribution between orthopyroxene and anhydrous silicate melt: substitution mechanisms and the effect of iron. Contrib. Mineral. Petrol. 159, 459-473. van Kan Parker M., Mason P. and van Westrenen W. (2011) Experimental study of trace element partitioning between lunar orthopyroxene and anhydrous silicate melt: Effects of lithium and iron. Chem. Geol. 285, 1-14. van Westrenen W., Allan N. L., Blundy J. D., Purton J. A. and Wood, B. J. (2000a) Atomistic simulation of trace element incorporation into garnets—comparison with experimental garnet-melt partitioning data. Geochim. Cosmochim. Acta 64, 1629-1639. van Westrenen W., Blundy J. D. and Wood B. J. (2000b) Effect of Fe2+ on garnet-melt trace element partitioning: experiments in FCMAS and quantification of crystal-chemical controls in natural systems. Lithos 53, 189-201. Wagner T. and Grove T. (1997) Experimental constraints on the origin of lunar high-Ti ultramafic glasses. Geochim. Cosmochim. Acta 61, 1315-1327. Weill D.F. and McKay G.A. (1975) The partitioning of Mg, Fe, Sr, Ce, Sm, Eu, and Yb in lunar igneous systems and a possible origin of KREEP by equilibrium partial melting. Lunar Sci. Conf. Proc. 6, 1143-1158. Wieczorek M. A., Jolliff B. L., Khan A., Pritchard M. E., Weiss B. P., Williams J. G., Hood L. L., Righter K., Neal C. R. and Shearer C. K. (2006) The constitution and structure of the lunar interior. Rev. Mineral. Geochem. 60, 221-364. Wood B. J. and Blundy J. D. (2001) The effect of cation charge on crystal–melt partitioning of trace elements. Earth Planet. Sci. Lett. 188, 59-71. Wood B. J. and Blundy J. D. (2002) The effect of H2O on crystal-melt partitioning of trace elements. Geochim. Cosmochim. Acta 66, 3647-3656. Wood B. J. and Blundy J. D. (2003) Trace element partitioning under crustal and uppermost mantle conditions: the influences of ionic radius, cation charge, pressure, and temperature. 97 Treatise on Geochemistry 2, 395-424. Yao L., Sun C. and Liang Y. (2012) A parameterized model for REE distribution between low-Ca pyroxene and basaltic melts with applications to REE partitioning in low-Ca pyroxene along a mantle adiabat and during pyroxenite-derived melt and peridotite interaction. Contrib. Mineral. Petrol. 164, 261-280. Figure Captions Figure 2-1. Melt compositions from low-Ca pyroxene partitioning experiments. Gray dots are compositions of lunar picritic glass samples collected during the Apollo missions (Delano and Livi, 1981; Delano and Lindsley, 1983; Hughes et al., 1988; Shearer et al., 1990, 1991; Sheaerer and Papike, 1993); star and diamond symbols represent the starting and final melt compositions from this study. Dashed line links the starting and final melts for a given experiment. Figure 2-2. Low-Ca pyroxene compositions from partitioning experiments and multiple saturation experiments. Gray dots represent low-Ca pyroxene from multiple saturation experiments for lunar picritic glasses (Grove and Vaniman, 1978; Delano, 1980; Wagner and Grove, 1997; Elkins et al., 2000; Elkins-Tanton et al., 2003; Draper et al., 2006; Krawczynski and Grove, 2012); blue circles marked as MOCH are low-Ca pyroxene from multiple saturation experiments of Singletary and Grove (2008); plus symbols represent low-Ca pyroxene from laboratory lunar magma ocean crystallization study of Elardo et al. (2011); stars and diamonds represent the starting and final pyroxenes from the present study. The part of the pyroxene quadrilateral in (d) shows that low-Ca pyroxenes from our experiments are all orthopyroxene within the range of low-Ca pyroxenes from multiple saturation experiments. Figure 2-3. Back-scattered electron images of representative experimental products of runs A15GG210 (a) and A15Red219 (b). Opx stands for orthopyroxene, and sp is spinel. Round black 98 holes in melt and opx in (a) are laser ablation spots. Orthopyroxene in (b) appears dark because the electron beam intensity was reduced for the high-Ti melt. Figure 2-4. Spider diagram showing the trace element partition coefficients between low-Ca pyroxene and melt measured in this study and those from literature. Small filled circles denote data from van Kan Parker et al. (2011). The gray field displays the range of filtered literature data from Salters and Longhi (1999), Green et al. (2000), van Westrenen et al. (2000), Salters et al. (2002), McDade et al. (2003a, b), Adam and Green (2006), Tuff and Gibson (2007), Frei et al. (2009), van Kan Parker et al. (2010, 2011), and Yao et al. (2012). Error bars represent one standard deviation of measured partitioning data. Figure 2-5. Onuma diagrams showing the measured partition coefficients between low-Ca pyroxene and lunar picritic melts as a function of ionic radii for the six experiments reported in this study. Squares are tetravalent cations, circles are trivalent cations, and triangles are divalent cations. Solid curves are the best fits to the measured partition coefficients using the lattice strain model (Eq. 2). Error bars represent one standard deviations of measured partitioning data. Six- fold coordinated ionic radii from Shannon (1976) are used in the lattice strain model (Eq. 2). The lattice strain parameters are listed in Table 5. The partition coefficients of Al are for Al in the M1 site of low-Ca pyroxene. Europium partition coefficients are not included in the lattice strain fits. Note that DEu can fit into either the parabola defined by REE3+ or that defined by the divalent cations (Zn2+, Mn2+, Ca2+, Sr2+). This may explain the apparent lack of Eu anomalies in the REE partition coefficients (see text for discussion). Copper partition coefficients are significantly lower than the parabola defined by divalent cations in (e) and (f), suggesting that most copper may be present as Cu+ in our experimental charges. Error bars represent one standard deviation of measured partitioning data. 99 Figure 2-6. Onuma diagrams comparing measured REE and Y partition coefficients of low-Ca pyroxene with model predictions. Eight-fold coordinated ionic radii from Shannon (1976) are used in the model of Yao et al. (2012) and the revised model (Eqs. 2, 4-6) developed in this study. See text for discussion. Figure 2-7. Comparison between predicted Ti, Hf and Zr partition coefficients in low-Ca pyroxene and experimentally measured values. The predicted values by the models of Bédard (2007) are shown in (a), and those by Eqs. (2, 9-11) are shown in (b). The measured partition coefficients are from the literature data listed in the caption of Fig. 4. The solid line represents the 1:1 ratio, and dashed lines represent the 2:1 and 1:2 ratios, respectively. Yellow circles and blue squares are subcalcic augite and orthopyroxene, respectively. Error bars represent one standard deviation for measured partitioning data and 95% confidence interval for the predicted values by Eqs. (2, 9-11). χ p is the Pearson’s chi-square defined by Eq. (7). 2 Figure 2-8. Calculated partition coefficients of low-Ca pyroxene from multiple saturation experiments (a) and those close to multiple-saturation points (b). Black, red, and green curves represent different starting compositions (black glass, red glass, and green glass, respectively). Curves with circle symbols represent subcalcic augite; and those without symbols are opx. Dashed curves in (b) show partition coefficients of opx close to multiple saturation points of Apollo 15C green glass (Elkins-Tanton et al., 2003). Gray areas represent the ranges of low-Ca pyroxene partition coefficients from the literature. Equations (2, 9-11) are utilized to calculate low-Ca pyroxene partition coefficients with temperatures and major element compositions of low-Ca pyroxene from multiple saturation experiments (Green et al., 1975; Delano, 1980; Wagner and Grove, 1997; Elkins et al., 2000; Elkins-Tanton et al., 2003; Draper et al., 2006). 100 Figure 2-9. Variations of REE and HFSE partition coefficients in low-Ca pyroxene during crystallization of the lunar magma ocean (LMO). Three low-Ca pyroxene compositions that form at 39%, 78% and 89% crystallization in MAGFOX are used to calculate their partition coefficients. Low-Ca pyroxene partition coefficients for experimental simulation of the LMO crystallization are calculated on the basis of experiments of Elardo et al. (2011) for equilibrium crystallization of LPUM. Gray area represents the ranges of low-Ca pyroxene partition coefficients defined by the compiled data. See text for discussion. melt Figure 2-S1. Variations of melt Ti in molar fraction per six-oxygen ( X Ti ) as a function of melt melt melt TiO2 contents in weight fraction ( CTiO ) from the compiled experiments. X Ti is calculated 2 using the method of Wood and Blundy (2002). The blue solid line is the regression curve to obtain Eq. (8). Data sources are the same as those in Fig. 4. melt Figure 2-S2. Correlation between Ti molar fraction in the melt per six-oxygen ( X Ti ) and melt melt TiO2 contents in weight fraction ( CTiO ) from the lunar basaltic melts. The blue solid line is 2 defined by Eq. (8). Data sources of picritic glasses are the same as those in Fig. 1; KREEP basalts are from McKay and Weill (1976), Ryder and Bower (1976), McKay et al. (1978, 1979), Salpas et al. (1987) and Ryder and Sherman (1989). Data sources of mare basalts can be found in Neal and Taylor (1992). Figure 2-S3. Variations of Ti, Hf and Zr partition coefficients in low-Ca pyroxene as a function of Al content in the tetrahedral site (AlT), Fe content in the M1 site (FeM1), and the product of Ca and Mg abundances in the M2 site of pyroxene (CaM2 × MgM2). Data sources and symbols are the same as those in Fig. 7. 101 Figure 2-S4. Calculated REE and HFSE partition coefficients in low-Ca pyroxene close to multiple-saturation points for the orange (blue curves) and red glasses (red curves) in experiments conducted by Krawczynski and Grove (2012) using graphite (dashed curves) and Fe-metal (solid curves) capsules. Black and green squares show the ranges of DTi calculated from their reported TiO2 concentrations in opx and melts for graphite and Fe-metal capsules, respectively. Gray area represents the ranges of low-Ca pyroxene partition coefficients defined by the compiled data. 102 Figures Figure 2-1 VKP(2011) 50 10 2 4 5 45 1 2 O (wt%) 8 SiO2 (wt%) 1 3 40 5 4 6 2 3 6 35 6 3 30 4 (a) (c) 25 2 10 4 2 3 20 1 MgO (wt%) CaO (wt%) 5 6 8 1 15 6 5 4 6 3 (b) 2 10 4 0 10 20 30 0 10 20 30 TiO2 (wt%) TiO2 (wt%) 103 Figure 2-2 60 12 (c) 58 10 56 8 O (wt%) SiO2 (wt%) 5 54 1 4 6 2 3 2 3 52 6 3 4 42 6 5 50 1 2 (a) 48 0 80 3 Mg# MOCH 2.5 EDS(2011) VKP(2011) 0.25 2 TiO2 (wt%) 1.5 1 3 2,3,6 6 0.5 4 2 5 4 1 5 (b) 1 En 0.35 0 80 Mg# 104 Figure 2-3 (a) melt opx 500 µm A15GG210 (b) sp opx melt 200 µm A15Red219 105 Figure 2-4 1 10 0 10 10 10 10 10 Nb W Nd S H Eu Gd Ho Yb P V N T L P Mo Z Sm T D Y Lu S M o 106 Figure 2-5 1 10 Cr Cr Cr Mn Zn Mn Zn Mn 0 Sc 10 Partition Coefficient Zn Ca Ca Sc Ca Al Al Lu Lu 10 Al Ti Lu Ti Yb Yb Yb Ti Ho,Y Ho,Y Dy Ho,Y Dy Dy Gd Hf Gd Eu Hf Gd Eu Eu Hf Eu Zr Eu Sm Eu 10 Zr Sm Nd Sm Zr Nd Pr Nd Pr Ce Pr Ce La Ce 10 La La 1 10 Cr Cr Cr 0 Sc Mn Zn Mn Sc Mn 10 Partition Coefficient Zn Ca Sc Zn Ca Ca Al Lu Al Cu Al Cu 10 Lu Lu Ti Yb Ti Yb Yb Ho,Y Ho,Y Ti Ho,Y Dy Gd Cu Dy Cu Dy Hf Eu Gd Eu Hf Hf Gd Sr 10 Eu Sm Eu Eu Eu Zr Zr Sm Zr Sm Nd Nd Sr Pr Nd Pr Pr Ce Ce Ce 10 La La La 0.6 0.8 1 0.6 0.8 1 0.6 0.8 1 Ionic Radius (Å) Ionic Radius (Å) Ionic Radius (Å) 107 Figure 2-6 Lu Lu Partition Coefficient 10 Yb Lu Y Yb Y Yb Y Ho Dy Ho Ho Dy Gd Dy Gd Gd Eu Sm 10 Eu Sm Eu Sm Nd Nd Pr Nd Pr Ce Pr Ce Ce 10 La Revised model La La Lu Partition Coefficient 10 Lu Yb Lu Yb Yb Ho,Y Dy Ho,Y Ho,Y Dy Dy Gd Gd Gd 10 Eu Eu Eu Sm Sm Sm Nd Nd Nd Pr Pr Pr Ce Ce Ce 10 La La La 0.8 1 1.1 0.8 1 1.1 0.8 1 1.1 Ionic Radius (Å) Ionic Radius (Å) Ionic Radius (Å) 108 Figure 2-7 0 10 (a) Bédard’s models Predicted D of Ti, Hf, Zr 10 10 p 10 0 10 (b) This study Predicted D of Ti, Hf, Zr 10 10 p Opx 10 0 10 10 10 10 Observed D of Ti, Hf, Zr 109 Figure 2-8 0 10 10 D 10 10 10 0 10 10 D 10 10 10 L P Sm Gd D Ho Tm Lu Hf Nd Eu Tb Y E Yb Ti 110 Figure 2-9 0 10 10 D 10 10 10 MAGFOX L P Sm Gd D Ho Tm Lu Hf Nd Eu Tb Y E Yb Ti 111 Figure 2-S1 0.6 0.5 0.4 0.3 Xmelt Ti 0.2 2 0.1 R = 1.00 X Timelt 0.0304 melt CTiO 0 2 0 5 10 15 20 Melt TiO (wt%) 2 112 Figure 2-S2 0.7 Mare basalt Picritic glass 0.6 KREEP basalt 0.5 0.4 Xmelt Ti 0.3 0.2 0.1 X Timelt 0.0304 melt CTiO 2 0 0 5 10 15 20 TiO2 (wt%) 113 Figure 2-S3 0 10 Ti 10 D 10 10 DHf 10 10 DZr 10 Opx 10 0 0.1 0 0.1 0 0.1 T Al FeM1 Ca ×Mg 114 Figure 2-S4 0 0 10 10 10 D 10 10 10 10 L P Sm Gd D Ho Tm Lu Hf Nd Eu Tb Y E Yb Ti 115 Tables Table 2-1 Nominal major element compositions of starting materials Starting material A15GG A15YG YG-1d A15Red Opxa SiO2 (wt%) 43.24 41.93 41.76 34.86 54.25 TiO2 1.47 4.28 4.42 13.51 0.11 Al2O3 7.22 8.41 8.36 7.04 5.43 Cr2O3 0.49 0.53 0.58 0.77 0.56 FeO 20.18 21.08 21.10 21.45 5.57 MnO 0.29 0.47 0.47 0.24 0.13 MgO 16.88 12.71 12.77 11.84 32.87 CaO 8.04 8.27 8.24 7.73 1.58 Na2O 0.24 0.37 0.36 0.47 0.16 K 2O - - - 0.12 - NiO - - - - 0.09 Total 98.05 98.05 98.05 98.03 100.75 Traceb 1.95 1.95 1.95 1.97 c Mg# 60.09 52.04 52.14 49.84 91.40 a Orthopyroxene composition from Lo Cascio (2008) b total trace element oxides in the starting material. c Mg# = 100×Mg/(Mg+Fe); Mg and Fe are in molar fraction. 116 Table 2-2 Compositions of experimental run products Run # A15GG210 A15YG217 A15Red219 YG-1d-1 YG-1d-4 A15Red-1 A15YG + opx A15Red + opx YG-1d + YG-1d + Starting material A15GG A15Red (top)a (bottom) opx (bottom) opx (top) P (GPa) 2 2.1 2 2.1 2.05 2.1 Tinitial (°C) 1500 1500 1400 - 1500 - Cooling rate 0.5 1 1 - 1 - (°C/min) Tfinal (°C) 1450 1425 1340 1400 1425 1340 tinitial (h) 2 2 0.1 - 2 - tfinal (h) 49 50 48 48 50 48 opx + melt + opx + melt Run products opx + melt opx + melt opx + melt opx + melt spb +sp a the position of the opx layer in the capsule; opx denotes orthopyroxene b sp represents spinel 117 Table 2-3 Experimental conditions and run products Run # A15GG210 A15YG217 A15Red219 Phase opx melt opx melt opx melt a EMP n =7 n=5 n = 12 n=9 n = 16 n = 15 b SiO2 (wt%) 53.67(44) 45.3(10) 52.7(6) 42.36(26) 51.29(57) 32.57(43) TiO2 0.12(2) 1.58(15) 0.37(4) 4.57(21) 1.05(6) 16.58(32) Al2O3 2.62(48) 7.79(17) 4.21(62) 9.46(9) 5.36(40) 7.55(14) Cr2O3 0.82(11) 0.51(6) 0.97(8) 0.39(3) 1.33(26) 0.38(2) FeO 13.26(12) 20.35(89) 13.17(72) 20.01(42) 12.86(31) 20.67(37) MnO 0.26(2) 0.35(1) 0.37(3) 0.48(2) 0.30(2) 0.37(1) MgO 27.45(33) 14.60(91) 26.7(9) 11.29(42) 26.03(38) 10.75(37) CaO 2.05(8) 8.90(13) 1.84(20) 8.94(15) 2.00(16) 9.08(15) Na2O 0.03(1) 0.19(4) 0.04(1) 0.40(4) 0.07(1) 0.43(5) K2O - 0.01(1) - 0.01(1) - 0.06(4) P2O5 - 0.006(4) - 0.028(13) - 0.046(16) Total 100.29(36) 99.62(1.15) 100.36(47) 97.94(48) 100.30(34) 98.49(58) c Mg# 78.67 56.10 78.31 50.14 78.29 48.10 - - - - - - LA-ICP- MS n=6 n=5 n=6 n=6 n=8 n=7 Na2O (wt.%) 0.036(2) 0.355(47) 0.057(4) 0.402(20) 0.090(4) 0.646(67) P (ppm) 27(1) 77(7) 44(2) 91(6) 47(6) 264(24) Sc 1.99(0.00) - 4.96(50) 6.98(27) 4.40(84) 8.46(24) Ti 741(117) 11116(608) 2245(181) 25849(1217) 6359(296) 107135(2374) V 3.3(5) 5.0(4) 24.8(18) 22.2(9) 12.1(52) 25.2(6) Cr 5698(711) 3352(266) 6419(413) 2393(86) 8539(1321) 2412(42) Mn 2570(18) 3543(254) 3487(104) 3824(188) 2958(113) 3471(82) Co 5.48(18) 5.78(55) 17.40(64) 12.01(47) 16.53(363) 19.92(85) Ni 53(2) 31(3) 188(20) 52(2) 258(62) 157(9) Cu - 11(1) - 7.9(10) - 18(4) Zn 8.3(10) 14(1) 18.9(7) 27(1) 21(2) 36(2) Sr - - - - - - Y 60(12) 1575(102) 56(5) 1072(58) 65(5) 1499(60) Zr 9(2) 1577(107) 12(2) 1083(59) 13(1) 1472(62) Nb 0.67(10) 1202(115) 0.91(27) 819(45) 0.57(12) 1292(57) Mo 5(1) 575(56) 13(3) 593(31) 2(1) 737(45) La 1.01(21) 1565(143) 1.14(22) 1008(58) 0.83(15) 1535(134) Ce 2.33(45) 1498(136) 2.82(83) 1105(58) 1.97(21) 1445(94) Pr 3.53(74) 1388(112) 3.69(51) 1034(52) 3.26(35) 1399(78) Nd 5(1) 1334(107) 5.65(73) 970(53) 5.29(67) 1378(76) Sm 14(3) 1444(106) 13(1) 1041(56) 14(1) 1499(70) 118 Eu 16(3) 1653(123) 15(2) 1164(58) 17(2) 1610(82) Gd 30(7) 1656(116) 30(3) 1194(59) 32(3) 1662(73) Dy 48(10) 1619(113) 48(4) 1191(59) 53(4) 1659(67) Ho 64(14) 1803(126) 61(6) 1262(63) 68(5) 1715(69) Yb 109(21) 1779(111) 114(10) 1347(68) 117(8) 1652(64) Lu 153(30) 2089(135) 146(13) 1489(72) 138(9) 1655(65) Hf 20(6) 1793(114) 27(4) 1301(71) 31(3) 1646(55) Ta 0.81(15) 1815(136) 1.13(34) 1204(57) 0.83(13) 1638(55) W 0.41(15) 1413(194) 1.18(76) 929(66) 0.24(22) 1351(143) (Continued) Run # YG-1d-1 YG-1d-4 A15Red-1 Phase opx melt opx melt opx melt EMP n=9 n = 11 n=8 n =7 n=7 n=8 SiO2 (wt%) 53.15(68) 41.49(97) 54.36(41) 41.31(101) 51.98(52) 34.05(43) TiO2 0.42(2) 4.81(61) 0.34(5) 4.83(83) 0.78(10) 14.81(40) Al2O3 3.93(21) 9.02(36) 3.22(60) 8.93(52) 3.53(48) 7.11(9) Cr2O3 1.12(8) 0.42(7) 0.97(9) 0.39(9) 1.06(13) 0.62(6) FeO 13.72(34) 19.69(93) 11.96(59) 20.33(120) 13.14(23) 21.03(46) MnO 0.40(4) 0.52(4) 0.34(3) 0.51(4) 0.28(4) 0.42(3) MgO 25.31(44) 11.59(71) 27.99(72) 12.30(93) 26.44(42) 11.01(77) CaO 2.03(3) 9.43(26) 1.53(16) 8.43(49) 1.79(3) 8.26(32) Na2O 0.04(1) 0.18(5) 0.04(2) 0.26(1) 0.04(2) 0.41(7) K2O - 0.01(1) - 0.01(1) - 0.06(5) P2O5 - 0.03(2) - 0.03(2) - 0.06(3) Total 100.12(88) 97.21(68) 100.76(58) 97.33(1.03) 99.04(61) 97.83(132) c Mg# 76.67 51.19 80.66 51.89 78.18 48.26 - - - - - - LA- ICP- MS n=4 n=5 n=8 n=6 n=9 n=6 Na2O (wt.%) - 0.254(11) 0.028(3) 0.259(31) 0.072(3) 0.433(43) P (ppm) - 79(5) 29(4) 86(11) 42(7) 178(11) Sc 5.40(74) 6.76(36) 6.12(24) 8.27(68) 5.05(30) 4.11(20) Ti 1981(170) 33708(1874) 1814(277) 30384(3137) 4460(639) 101241(5850) V 5.4(17) 12.5(8) 14.3(22) 20.2(14) 2.1(3) 3.7(3) Cr 6163(212) 2495(175) 5764(588) 2555(141) 6511(782) 3445(258) Mn 3724(63) 4897(254) 3489(119) 4672(411) 2607(57) 3542(274) Co 10.39(68) 11.91(57) 15.76(52) 14.76(128) 6.95(30) 6.87(40) Ni 144(2) 81(5) 221(14) 93(6) 75(3) 39(2) Cu - 9.26(68) 0.63(3) 10(1) 0.45(5) 8(2) 119 Zn 18(2) 26(1) 19.1(9) 32(3) 15.8(7) 25(3) Sr - 12.53(56) 0.07(1) 12(2) 0.09 11(1) Y 49(3) 1251(74) 38(7) 1100(112) 40(5) 1245(72) Zr 10(1) 1185(67) 7(2) 1066(115) 7(1) 1188(66) Nb 0.54(11) 1025(60) 0.51(9) 957(112) 0.55(41) 1044(88) Mo 9.26(55) 1278(88) 11(2) 1512(179) 2.45(63) 1287(141) La 0.83(9) 1127(57) 0.56(10) 1044(128) 0.64(28) 1072(93) Ce 1.57(16) 1069(51) 1.31(21) 1031(119) 1.31(42) 1042(112) Pr 2.55(32) 1061(49) 2.12(34) 1015(117) 2.07(41) 1037(86) Nd 4.45(42) 1108(55) 3.48(62) 1029(119) 3.25(61) 1067(88) Sm 11(1) 1193(63) 9(2) 1103(125) 8(1) 1185(85) Eu 13(1) 1200(55) 10(2) 1118(131) 10(1) 1159(80) Gd 24(2) 1349(72) 19(4) 1225(135) 19(3) 1332(88) Dy 41(4) 1372(77) 32(6) 1238(136) 32(5) 1362(90) Ho 50(3) 1267(68) 39(7) 1143(125) 41(6) 1295(70) Yb 87(3) 1355(75) 70(13) 1241(134) 72(10) 1377(93) Lu 103(7) 1253(75) 82(15) 1142(125) 85(12) 1276(68) Hf 21(2) 1334(76) 16(4) 1242(143) 15(4) 1358(72) Ta 0.79(23) 1240(61) 0.59(13) 1169(144) 0.75(59) 1250(61) W 0.32(12) 987(66) 0.26(15) 1016(131) 0.46(49) 986(129) a numbers of spot analyses b numbers in parentheses are one standard deviation (1σ) of replicate analyses in terms of last significant numbers; 53.67(44) should be read as 53.67 ± 0.44 c Mg# = 100×Mg/(Mg+Fe); Mg and Fe are in molar fraction 120 Table 2-4 Orthopyroxene-melt partition coefficients Run # A15GG210 A15YG217 A15Red219 YG-1d-1 YG-1d-4 A15Red-1 a d Ca 0.230(9) 0.206(23) 0.220(18) 0.215(7) 0.181(22) 0.216(9) AlM1,a,b 0.098(18) 0.159(23) 0.209(16) 0.200(13) 0.149(29) 0.128(17) AlT,a,c 0.239(44) 0.286(42) 0.501(39) 0.235(16) 0.212(42) 0.369(50) Na 0.102(15) 0.142(12) 0.139(16) - 0.109(16) 0.166(18) P 0.349(31) 0.485(36) 0.178(29) - 0.341(64) 0.235(40) Sc - 0.71(8) 0.52(10) 0.80(12) 0.74(7) 1.23(9) Ti 0.067(11) 0.087(8) 0.059(3) 0.059(6) 0.060(11) 0.044(7) V 0.67(11) 1.12(9) 0.48(21) 0.43(14) 0.71(12) 0.56(8) Cr 1.70(25) 2.68(20) 3.54(55) 2.47(19) 2.26(26) 1.89(27) Mn 0.725(52) 0.912(52) 0.852(38) 0.760(41) 0.747(70) 0.736(59) Co 0.95(9) 1.45(8) 0.83(19) 0.87(7) 1.07(10) 1.01(7) Ni 1.72(19) 3.65(41) 1.64(40) 1.77(12) 2.38(21) 1.92(13) Cu - - - - 0.063(8) 0.059(15) Zn 0.597(90) 0.708(41) 0.587(68) 0.674(66) 0.604(70) 0.625(68) Sr - - - - 0.0059(10) 0.0084(11) Y 0.0381(81) 0.0523(58) 0.0435(36) 0.0390(34) 0.0348(72) 0.0325(48) Zr 0.0059(15) 0.0108(15) 0.0089(8) 0.0083(8) 0.0066(16) 0.0056(12) Nb 0.00056(10) 0.00111(34) 0.00044(10) 0.00053(11) 0.00053(11) 0.00052(39) Mo 0.0078(19) 0.0223(48) 0.0032(17) 0.0073(7) 0.0073(17) 0.0019(5) La 0.00065(15) 0.00113(23) 0.00054(11) 0.00073(9) 0.00054(12) 0.00059(27) Ce 0.00155(33) 0.00256(76) 0.00137(17) 0.00147(16) 0.00127(25) 0.00125(42) Pr 0.00254(57) 0.00356(52) 0.00233(28) 0.00241(32) 0.00209(41) 0.00199(43) Nd 0.00401(94) 0.00583(81) 0.00384(53) 0.00402(43) 0.00338(72) 0.00304(62) Sm 0.0094(23) 0.0129(15) 0.0093(9) 0.0090(10) 0.0078(17) 0.0070(12) Eu 0.0097(21) 0.0125(15) 0.0106(11) 0.0107(12) 0.0087(19) 0.0088(13) Gd 0.0183(44) 0.0249(29) 0.0190(18) 0.0176(19) 0.0157(35) 0.0139(21) Dy 0.0294(67) 0.0406(43) 0.0320(28) 0.0300(33) 0.0262(57) 0.0238(37) Ho 0.0356(80) 0.0484(51) 0.0395(34) 0.0394(34) 0.0344(74) 0.0313(47) Yb 0.061(12) 0.084(8) 0.071(5) 0.065(4) 0.056(12) 0.052(8) Lu 0.073(15) 0.098(10) 0.084(6) 0.082(7) 0.072(15) 0.067(10) Hf 0.0111(32) 0.0210(32) 0.0189(16) 0.0156(20) 0.0125(33) 0.0110(28) Ta 0.00045(9) 0.00094(29) 0.00051(8) 0.00064(19) 0.00051(12) 0.00060(47) W 0.00029(11) 0.00127(82) 0.00018(16) 0.00032(12) 0.00025(15) 0.00047(50) a Partition coefficients are calculated using EMP data b Al content in the M1 site of pyroxene c Al content in the tetrahedral site of pyroxene, calculated according to the following scheme. If Altotal > 2 - Si, AlT = 2 - Si; if Altotal < 2 - Si, AlT = Altotal. AlM1 = Altotal - AlT. Here Altotal and Si denote the molar proportions of Al and Si per six-oxygen in opx, respectively. The partition coefficients of AlM1 and AlT are calculated using weight fractionations of the two. d numbers in parentheses are one standard error (1σ) propagated from uncertainties in Table 3; 0.230(9) should be read as 0.230 ± 0.009. 121 Table 2-5 List of lattice strain parameters for individual experiments Run # A15GG210 A15YG217 A15Red219 YG-1d-1 YG-1d-4 A15Red-1 2+ M2 D0 0.727 0.914 0.853 0.771 0.683(149) 0.697(92) r0 (Å) 0.822 0.822 0.836 0.809 0.786(58) 0.794(36) E (GPa) 146 186 188 137 109(31) 100(18) 3+ M2 D0 0.139(51)a 0.275(180) 0.171(66) 0.283(211) 0.172(84) 0.297(244) r0 (Å) 0.760(33) 0.718(62) 0.759(32) 0.700(67) 0.737(43) 0.675(75) E (GPa) 295(52) 227(61) 294(50) 220(60) 268(54) 193(53) 3+ M1 D0 - 4.36 5.19 3.84 3.72 3.65 r0 (Å) - 0.661 0.654 0.662 0.663 0.674 E (GPa) - 1345 1390 1168 1261 1060 4+ M1 D0 0.090 0.156 0.150 0.104 0.095 0.081 r0 (Å) 0.635 0.643 0.648 0.644 0.640 0.644 E (GPa) 2059 2427 2818 2298 2259 2341 a numbers in parentheses are one standard errors (1σ); 0.139(51) should be read as 0.139 ± 0.051. The standard error cannot be obtained when there are only three partition coefficients available. 122 Table 2-6 Recommended REE and HFSE partition coefficients between orthopyroxene and lunar melts Lunar Lunar picritic melt Lunar magma ocean melt Green A15C Red Black type F = 39%e F = 78% F = 89% glassa Greenb glassc glassd La 0.0012 0.0005 0.0010 0.0005 0.0005 0.0006 0.0013 Ce 0.0023 0.0011 0.0019 0.0009 0.0010 0.0013 0.0025 Pr 0.0040 0.0020 0.0035 0.0016 0.0018 0.0025 0.0047 Nd 0.0068 0.0036 0.0059 0.0029 0.0032 0.0047 0.0083 Sm 0.0152 0.0086 0.0135 0.0070 0.0077 0.0124 0.0201 Eu 0.0207 0.0121 0.0185 0.0098 0.0107 0.0179 0.0281 Gd 0.0273 0.0164 0.0247 0.0133 0.0144 0.0250 0.0383 Tb 0.0351 0.0216 0.0322 0.0176 0.0189 0.0339 0.0507 Dy 0.0441 0.0278 0.0408 0.0228 0.0240 0.0445 0.0653 Y 0.0501 0.0320 0.0467 0.0263 0.0274 0.0519 0.0754 Ho 0.0533 0.0342 0.0497 0.0282 0.0292 0.0558 0.0807 Er 0.0622 0.0405 0.0586 0.0337 0.0342 0.0672 0.0962 Tm 0.0706 0.0465 0.0670 0.0390 0.0388 0.0782 0.1110 Yb 0.0781 0.0520 0.0748 0.0440 0.0430 0.0883 0.1247 Lu 0.0848 0.0569 0.0817 0.0484 0.0465 0.0974 0.1370 Ti 0.0677 0.0458 0.0912 0.0577 0.0388 0.0695 0.0715 Hf 0.0193 0.0143 0.0224 0.0151 0.0153 0.0178 0.0148 Zr 0.0108 0.0081 0.0120 0.0082 0.0091 0.0091 0.0071 a The average partition coefficients of opx close to the MSP of lunar picritic green glasses except for Apollo 15C green glass (Elkins et al., 2000; Elkins-Tanton et al., 2003) b Apollo 15C green glass has distinct MSP pressure and temperature (Elkins-Tanton et al., 2003), and therefore shows different opx partition coefficients from those of other green glasses c The average partition coefficients of opx close to the MSP of lunar picritic red glasses (Delano, 1980) d The average partition coefficients of opx close to the MSP of lunar picritic black glasses (Wagner and Grove, 1997) e The partition coefficients of opx as F = 39%; F denotes the degree of crystallization in the lunar magma ocean. See the caption to Fig. 9 and text for details. 123 CHAPTER 3 3 The Importance of Crystal Chemistry on REE Partitioning between Mantle Minerals (Garnet, Clinopyroxene, Orthopyroxene, and Olivine) and Basaltic Melts Chenguang Sun and Yan Liang Department of Geological Sciences, Brown University Providence, RI 02912, USA Published in Chemical Geology, 358, 23-36, 2013 124 Abstract Partitioning of rare earth elements (REEs) between mantle minerals and basaltic melts is fundamental to understanding of crystal-melt fractionation processes and can be quantitatively described by the lattice strain model. We analyzed published REE and Y partitioning data between garnet and basaltic melt and REE, Y, and Sc partitioning data between olivine and basaltic melt using the nonlinear regression method, and parameterized key partitioning parameters in the lattice strain model (D0, r0 and E) as functions of temperature, pressure, and mineral and melt compositions. We show that REE and Y partition coefficients between garnet and basaltic melt are inversely correlated with temperature and pressure, and that the correlation between REE partition coefficients and Ca content in garnet (XCa) is convoluted by the inverse relationship between D0 and XCa and the positive correlation between r0 and XCa. REE, Y, and Sc partition coefficients between olivine and basaltic melt are positively correlated with Al content in olivine and inversely correlated with forsterite content in olivine and pressure. To test the validity of the assumptions and simplifications used in the model development, we combined the garnet and olivine models with a recent model for REE partitioning between clinopyroxene and basaltic melt to obtain two mineral-mineral partitioning models. We found that the model-derived garnet-clinopyroxene and olivine-clinopyroxene REE partition coefficients are consistent with the measured data from well-equilibrated eclogite and peridotite xenoliths at subsolidus conditions. This demonstrates the internal consistency of our parameterized lattice strain models for REE partitioning in garnet, olivine, clinopyroxene and orthopyroxene. Taken collectively, the partitioning models for garnet, olivine, clinopyroxene and orthopyroxene all suggest the importance of crystal chemistry, temperature and pressure in determining REE partitioning between mantle minerals and basaltic melts, and that melt composition has only a secondary or indirect effect. 125 1. Introduction Nominally anhydrous major-rock forming minerals in the Earth’s upper mantle include olivine, clinopyroxene (cpx), orthopyroxene (opx), garnet, spinel, and plagioclase. The distribution of rare earth elements (REEs) between these major rock-forming minerals and basaltic melts is important to the interpretation of origin and evolution of mafic and ultramafic igneous rocks. In general, REE partition coefficients between a mineral and melt depend on pressure (P), temperature (T), oxygen fugacity (fO2), and mineral and melt compositions (X). Both P and T can affect the partition coefficients of trace elements to varying extents due to the enthalpy change and volume change, respectively, in the chemical exchange between minerals and melt (e.g., Blundy and Wood, 2003; Wood and Blundy, 2003). Because they are convoluted with the effects of P and T, compositional effects are difficult to identify and quantify. The effect of melt composition on trace element partitioning has been investigated experimentally since the pioneering studies of Watson (1976) and Ryerson and Hess (1978). They conducted partitioning experiments for two immiscible melts and found that a depolymerized melt can accommodate more trace elements. Ryerson and Hess (1978) further suggested that mineral-melt trace element partition coefficients would increase with melt polymerization. This has been examined experimentally for trace element partitioning between olivine and basaltic melt and between cpx and melt in several recent studies (Mysen, 2004; Gaetani, 2004; Huang et al., 2006; Evans et al., 2008; Tuff and O’Neill, 2010). These partitioning studies suggest a principal control of melt polymerization on trace element partitioning especially for more depolymerized melts. A number of partitioning studies, however, have also shown significant influence of crystal chemistry on trace element partitioning between minerals and melt (e.g., Blundy and Wood, 2003; Wood and Blundy, 2003; and references therein). For instance, it has been demonstrated that the partitioning of REE and high-field strength element in pyroxene is strongly correlated with the tetrahedrally 126 coordinated Al in pyroxene (AlT) [e.g., Gaetani and Grove, 1995; Lundstrom et al., 1998; Hill et al., 2000; see also Fig. 9 in Lo Cascio et al. (2008) for a recent compilation]. Rare earth elements and Y partition into major-rock forming minerals as trivalent cations that have ionic radii (0.977 – 1.16 Å at VIII-fold coordination; Shannon, 1976) similar to those of Ca2+, Mg2+ and Fe2+ (ionic radii at VIII-fold coordination 1.12 Å, 0.89 Å, and 0.92 Å, respectively). Thus, they replace the divalent cations in minerals charge-balanced by coupled substitutions. For instance, REEs partition into the M2 site of cpx charge-balanced by Al3+ replacing Si4+ on the tetrahedral site. In Onuma diagrams (partition coefficients vs. ionic radii; Onuma et al., 1968), REE and Y partition coefficients from a given mineral-melt pair vary systematically as a function of their ionic radii (Fig. 1), which can be quantitatively described by the lattice strain model (Brice, 1975; Blundy and Wood, 1994): ⎡ −4π EN A ⎛ r0 3⎞ ⎤ ( ) 1 ( ) 2 D min-melt = D0 exp ⎢ ⎜ r0 − rj − r0 − rj ⎟ ⎥ , (1) ⎣ RT ⎝ 2 ⎠⎦ j 3 where D min-melt j is the mineral-melt partition coefficient of element j; D0 is the partition coefficient for strain-free substitution; r0 is the ionic radius of the “ideal” cation for the strain-free lattice site; rj is the ionic radius of element j; E is the apparent Young’s modulus for the lattice site; NA is Avogadro’s number; R is the gas constant; and T is temperature. In general, the lattice strain parameters (D0, r0, and E) are functions of P-T-X and may be quantified using (empirical) parameterized models. It is possible to distinguish and quantify the primary compositional effects on REE partitioning between mineral and melt using such parameterized models. We will use this approach in the present study. Much effort has been devoted to pyroxene-melt partitioning studies because pyroxene has high affinity for incompatible trace elements relative to other mantle minerals. Several models have been proposed to quantitatively describe REE partitioning between pyroxene and melt based on the lattice strain model and pyroxene-melt partitioning experiments (Wood and Blundy, 1997, 127 2002; Sun and Liang, 2012, 2013a; Yao et al., 2012). Wood and Blundy (1997) parameterized the lattice strain parameters as functions of P, T and X, and constructed the first predictive model for REE partitioning between cpx and melt. Their model suggests that cpx-melt REE partitioning is mainly controlled by P, T, melt Mg# [100×Mg/(Mg+Fe), in molar], and Mg in the M1 (MgM1) site in cpx, and that Ca in the M2 site (CaM2) and Al in the M1 site (AlM1) in cpx can also affect REE partitioning through their influence on r0. Addition of water to melt can decrease the degree of melt polymerization, which decreases mineral-melt REE partition coefficients (e.g., Gaetani, 2004). Wood and Blundy (2002) further improved their original model by taking account of the H2O effect in hydrous systems. Based in part on their cpx model, Wood and Blundy (2003) also proposed a preliminary model for REE partitioning between opx and basaltic melt. Similar to their cpx model, the opx model suggests that opx-melt REE partitioning is mainly controlled by P, T, melt Mg#, and MgM1 site in opx, but that CaM2 and total Al in opx can affect REE partitioning through their positive correlations with r0. Through linear regression analysis of a compilation of published opx-melt partitioning experiments and natural samples, Bédard (2007) parameterized several models for the partitioning of each trace element in opx as a linear function of opx or melt compositions. By evaluating all the models in Bédard (2007), Yao et al. (2012) found that the model based on MgO content in melt most closely reproduces the experimentally determined opx-melt partition coefficients. In general, all the aforementioned models for cpx and opx quantified the effects of P, T and X on pyroxene-melt REE partitioning; however, they did not account for the first order effect of AlT or possible effect of melt polymerization on pyroxene- melt REE partitioning (e.g., Lundstrom et al., 1998; Hill et al., 2000; Gaetani, 2004). More importantly, these models cannot accurately reproduce experimentally determined pyroxene-melt REE partition coefficients [cf. Fig. 2 in Sun and Liang (2012) and Fig. 1 in Yao et al. (2012)]. In three recent studies, we examined experimentally determined REE and Y partition coefficients between cpx and basaltic melt and between low-Ca pyroxene and basaltic melt compiled from the literature and measured in our laboratory (Sun and Liang, 2012, 2013a; Yao et 128 al., 2012). In order to reduce the uncertainties of input data used in the parameterization, we selected a subset of high quality data from partitioning experiments that have no obvious signs of chemical disequilibrium and that were analyzed either by ion probe or laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS). Utilizing the selected subset of partitioning data (344 data from 43 experiments for cpx, and 344 data from 38 experiments for low-Ca pyroxene), we systematically examined the effects of P, T, and X and identified key parameters in determining REE partitioning in the pyroxenes. We found that temperature and pyroxene composition are the principal controls on pyroxene-melt REE partitioning and that melt composition has only a secondary effect. Specifically, cpx-melt REE partitioning is mainly controlled by T, AlT in cpx, Mg in the M2 (MgM2) site in cpx, whereas low-Ca pyroxene-melt REE partitioning is mainly determined by T, AlT in low-Ca pyroxene, and CaM2 in low-Ca pyroxene. AlM1 and MgM2 in cpx can affect cpx-melt REE partition coefficients by decreasing r0, whilst MgM2 and CaM2 in low-Ca pyroxene have influence on low-Ca pyroxene-melt REE partitioning by increasing r0. Melt H2O content can decrease cpx-melt REE partition coefficients, and melt TiO2 content can decrease low-Ca pyroxene-melt REE partition coefficients. These melt composition effects are significant only when the water and/or TiO2 abundances in melt are very high. Through a simultaneous inversion of all the compiled high quality data, we further developed models to quantify those principal effects on REE and Y partition coefficients for cpx and low-Ca pyroxene. These new models reproduced all the high quality partitioning data to within a factor of two, and accounted for the significant effect of AlT in pyroxene. Combination of these two models leads to a predictive model for REE and Y partitioning between cpx and opx (Yao et al., 2012; Liang et al., 2013). For well-equilibrated spinel peridotite xenoliths reported in the literature, the model predicted opx-cpx REE partition coefficients were in excellent agreement with the measured values, demonstrating the internal consistency of the two REE partitioning models for high- and low-Ca pyroxenes. The excellent reproducibility and internal consistency of these models raise three important questions. (1) Can the same method be used to obtain REE 129 partitioning models for other mantle minerals such as garnet and olivine? (2) Is mineral composition also the principal compositional factor determining REE partitioning between garnet and basaltic melt and between olivine and basaltic melt? (3) What are the major factors controlling REE partitioning in major-rock forming minerals in the mantle, in general? In this study, we present new parameterized lattice strain models for REE and Y partitioning in garnet and olivine, respectively. Taken collectively, our new partitioning models for garnet, cpx, opx, and olivine suggest that crystal chemistry is the principal compositional factor determining REE and Y partitioning between mantle minerals and basaltic melts, and that melt composition only has a secondary or indirect effect. 2. Review of Previous Partitioning Models 2.1. Garnet models Garnet is a ubiquitous aluminous phase in the Earth’s upper mantle and transition zone. The presence of garnet during mantle melting or magma differentiation can significantly fractionate REE, giving rise to a heavy REE (HREE) depleted melt due to the preferential incorporation of HREE in garnet. On the basis of the lattice strain model and published garnet- melt partitioning experiments, van Westrenen et al. (2001) developed the first predictive model for REE, Y, and Sc partitioning between garnet and anhydrous silicate melt (referred to as WvW01 hereafter). They parameterized r0 as a linear combination of P and garnet composition, constrained E through a power law relationship with r0, and used a thermodynamic model for a hypothetic REE-garnet (REEMg2Al3Si2O12) to estimate D0. Their model suggested that T, P, and Ca abundance in garnet, and garnet-melt Mg partition coefficient primarily control garnet-melt REE partition coefficients. To quantify the hydrous partitioning data, Wood and Blundy (2002) revised the WvW01 model by including a H2O term and a P2 term in the D0 model. As realized by Draper and van Westrenen (2007) and van Westrenen and Draper (2007), the original WvW01 130 model, however, fails to reproduce REE partition coefficients for majoritic garnet due to limited experimental data available when the WvW01 model was constructed. van Westrenen and Draper (2007) presented a new model for REE, Y and Sc partitioning between garnet and anhydrous silicate melt based on a more comprehensive garnet-melt partitioning dataset that included more recent majoritic garnet-melt partitioning experiments. To further improve the WvW01 model, they added a temperature term in the r0 equation and replaced the hypothetic garnet component of REEMg2Al3Si2O12 by REEFe2Al3Si2O12. The change of hypothetic REE-garnet in their model means that garnet-melt Fe partition coefficient primarily determines garnet-melt REE partition coefficients, rather than garnet-melt Mg partition coefficient in the WvW01 model. Corgne et al. (2012) noticed that the model of van Westrenen and Draper (2007) underestimated their new partitioning experiments at pressures of 10 - 17 GPa by a factor of about 2. With three new experiments, Corgne et al. (2012) revised the expression of D0 in van Westrenen and Draper (2007) by adding a second order pressure term. Taken collectively, the four partitioning models show that garnet-melt REE partition coefficients are mainly determined by P, T, Ca, Mg and/or Fe contents in garnet, Mg and/or Fe and perhaps water contents in melt. Utilizing the equations of r0 and E in van Westrenen and Draper (2007), Draper and van Westrenen (2007) proposed a statistical model for both hydrous and anhydrous systems by parameterizing D0 as a linear combination of garnet-melt Mg partition coefficient and Fe-Mg exchange coefficient. Accordingly, Draper and van Westrenen’s model suggests that Mg and Fe contents in garnet and in melt primarily determine garnet-melt REE partitioning and that the effects of P and T are incorporated through garnet-melt Mg and Fe partitioning. Recently, Girnis et al. (2013) developed a model for REE partitioning between garnet and silico-carbonate melt using most of their new experiments and those published in the literature. They found that REE partition coefficients between garnet and silico-carbonate melts only depend on Ca content in garnet and the ionic radii of REEs, and thus suggested that the crystal chemistry control on REE partitioning in garnet is dominant over that of T, P, and the activities of CO2 and H2O in melt. 131 The aforementioned models have considerably improved our understanding of REE and Y partitioning between garnet and melts. Nonetheless, significant uncertainties remain. Figure 2 compares the predicted REE and Y partition coefficients by the models of van Westrenen and Draper (2007) and Draper and van Westrenen (2007) with the experimentally determined values from anhydrous partitioning experiments in Table 1 and hydrous partitioning experiments in Green et al. (2000), Barth et al. (2002), Gaetani et al. (2003), and Adam and Green (2006). Comparisons with other models are present in Fig. S1. The models of van Westrenen et al. (2001) and van Westrenen and Draper (2007) systematically overestimate hydrous partitioning data by up to three to four orders of magnitude because they were calibrated only for anhydrous systems (Fig. S1a and Fig. 2a). The original WvW01 model reproduces many of anhydrous partitioning data, but cannot reproduce anhydrous partitioning data for majoritic garnet at high pressure as noted earlier (Fig. S1a). Because Wood and Blundy’s model accounted for the water effect and pressure effect, it shows significant improvement over the WvW01 model for hydrous partitioning data; however, it fails to reproduce a considerable amount of anhydrous partitioning data, which were determined for majoritic garnet at high pressure (Fig. S1b). The model of van Westrenen and Draper (2007) also shows significant improvement over the original WvW01 model. Yet it still has large uncertainties; most of the predicted partitioning data for light and middle REEs are lower than the experimentally measured values by factors of two to about one hundred (Fig. 2a). The model of Corgne et al. (2012), though revised from the model of van Westrenen and Draper (2007), shows limited improvement (Fig. S1c). Because the most recent model from Girnis et al. (2013) was only calibrated for silico-carbonate systems, it shows significant uncertainties for both anhydrous and hydrous silicate systems (Fig. S1d). Among the six models, the model of Draper and van Westrenen (2007) best reproduces the partitioning data for both hydrous and anhydrous systems; however, many of the predicted partition coefficients are out of the range defined by the 1:2 and 2:1 lines (Fig. 2b). It is also evident that the model of Draper and van Westrenen (2007) systematically underestimates hydrous partitioning data by up 132 to three orders of magnitude. Note that all previous models based on the lattice strain model systematically overestimate light and middle REE partition coefficients from the compiled experiments (Fig. 2 and Fig. S1a-c). Although van Westrenen et al. (2001) have demonstrated that melt contamination in crystal analyses can significantly increase the measured light REE partition coefficients in garnet, it is unlikely that light and middle REE partition coefficients from different experimental studies were nearly all contaminated by significant amounts of melt during crystal analyses. The large discrepancies between the model predicted and the measured partition coefficients indicate a need for reexamination of the garnet-melt REE partitioning model. 2.2. Olivine models Although it has low affinity for REE, olivine may play an important role in HREE fractionation because of its high modal abundance in the Earth’s upper mantle. According to the model of Workman and Hart (2005), the depleted mid-ocean ridge basalt mantle (DMM) has 57% olivine, 13% cpx, and 28% opx. Given an olivine-melt Lu partition coefficient of 0.03 (the averaged values in Evans et al., 2008), a cpx-melt Lu partition coefficient of 0.54 (Sun and Liang, 2012) and an opx-melt Lu partition coefficient of 0.14 (Yao et al., 2012), the contribution of olivine to the bulk partition coefficient of Lu is 14%, which is about one fourth of that of cpx and two fifth of that of opx. Thus, a parameterized model to quantify REE partitioning between olivine and basaltic melt is also useful for understanding the chemical evolution of the Earth’s mantle. Although attempts have been made to develop models for REE partitioning between olivine and basaltic melt, a generalized lattice strain model has not been available. Through linear regression analysis of a compilation of published olivine-melt partitioning experiments and natural samples, Bédard (2005) suggested that olivine-melt REE partition coefficients strongly depend on MgO in melt. Bédard (2005) further parameterized models to quantify each REE partition coefficient as a linear function of ln(MgO) of melt. Evans et al. (2008) conducted 133 olivine-melt partitioning experiments in the simple system CaO-MgO-Al2O3-SiO2 (CMAS), and found a strong inverse correlation between olivine-melt REE partition coefficients and SiO2 content in melt. Based on their experimental data, Evans et al. (2008) developed models for individual REEs to quantify the effect of melt SiO2 on olivine-melt REE partitioning. The above two types of models suggest that either MgO or SiO2 in melt determines olivine-melt REE partitioning, and that the effects of P, T and olivine composition may be secondary or implicitly incorporated in melt MgO or SiO2. Figure 3 shows a comparison of the model predicted olivine-melt partition coefficients of REE, Y and Sc (Bédard, 2005; Evans et al., 2008) and the experimentally determined values from the compiled partitioning experiments in Table 1. The partition coefficients of light REEs significantly deviate from the 1:1 line for Bédard’s model (Fig. 3a). Many of the partitioning data used in Bédard’s model were derived from natural samples, which may introduce significant uncertainties to the model. Figure 3b shows that the model of Evans et al. (2008) reproduces the experimentally determined partition coefficients much better than Bédard’s model. The model of Evans et al. (2008) was solely calibrated using their 1 atm partitioning experiments in the CMAS system, such that the effects of P and olivine composition were excluded. For partitioning experiments at higher P and/or in more complicated systems, the model of Evans et al. (2008) overestimates the partition coefficients by up to a factor of four (Fig. 3b). Neither of the two models, however, can reproduce many of partitioning data from published partitioning experiments over a large range of P, T and olivine composition (Fig. 3), indicating that these models need to be improved to accurately describe olivine-melt REE partitioning. In summary, considerable uncertainties remain in quantifying REE partitioning between garnet and basaltic melt and between olivine and basaltic melt, though significant progress has been made. Further work is required to establish more accurate models and to distinguish the principal factors controlling REE partitioning in garnet and olivine. 134 3. Methods We use high quality garnet-melt and olivine-melt partitioning data reported in the literature and develop new parameterized lattice strain models for REE and Y partitioning between garnet and basaltic melt and between olivine and basaltic melt. 3.1. Data compilation Numerous experimental studies have been carried out to determine REE and other trace element partition coefficients between garnet and basaltic melt and between olivine and basaltic melt. To ensure high quality partitioning data in our model calibration, we followed the procedures established in our pyroxene-melt REE partitioning studies by excluding experiments that show obvious signs of disequilibrium [e.g., zoning or inclusions in runs reported in Hauri et al. (1994)] and those with partitioning data measured by electron microprobe (EMP). Three partitioning experiments for grossular-rich garnets from van Westrenen et al. (1999) were excluded in the model parameterization. Partitioning experiments for olivine under sodium-fluxed conditions from Mallmann and O'Neill (2013) were also excluded. Because the Al content in olivine is one of the key compositional factors controlling REE partitioning between olivine and melt (see section 3.2 below), we excluded partitioning studies in which the Al content in olivine was not reported. Application of the filtering procedures outlined above, we obtained 77 partitioning experiments for garnet in hydrous and anhydrous systems and 177 partitioning experiments for olivine in anhydrous systems. Among the 77 partitioning experiments for garnet, 64 experiments were conducted under anhydrous conditions, and 14 experiments from four studies (Green et al., 2000; Barth et al., 2002; Gaetani et al., 2003; Adam and Green, 2006) were performed under hydrous conditions with 2.25 – 24.86 wt% water in melt. Water abundances in the melts from 13 out of 14 hydrous experiments, however, were calculated according to mass balance, which may introduce large uncertainties. To exclude potential uncertainties involved in 135 melt water contents in hydrous systems, we first developed a model for REEs and Y partitioning in garnet on the basis of the 64 anhydrous partitioning experiments, and then explored the effect of water. Because Eu partition coefficients may be sensitive to fO2 in individual experiments, we excluded Eu partition coefficients in garnet and olivine for all the compiled experiments to decrease potential uncertainties in the model calibration. As demonstrated by van Westrenen et al. (2001), melt contamination in crystal analyses can significantly increase light REE partition coefficients. So we also excluded La and Ce partition coefficients when they significantly deviate from the parabola defined by other REEs in Onuma diagrams. After carefully filtering the compiled partitioning data, we obtained 538 partitioning data from 64 experiments for garnet and 684 partitioning data from 177 experiments for olivine, respectively. Table 1 summaries the 64 anhydrous partitioning experiments for garnet and 177 anhydrous partitioning experiments for olivine that are used to calibrate the partitioning models for garnet and olivine as described below. The selected 64 partitioning experiments for garnet are from 16 studies and were conducted at 1325 – 2300 ºC and 2.4 – 25 GPa. Garnets produced in these experiments are pyrope-rich or majoritic (Fig. 4) and show a large variation in composition (e.g., CaO = 1.14 – 10.58 wt%, Mg# = 54 – 100). Melts from the 64 experiments also show a large variation in composition (e.g., SiO2 = 24.18 – 57.62 wt%; Mg# = 38 – 100). The selected 177 experiments for olivine were from 6 studies that cover a wide range of temperature, pressure, and composition space (1190 – 2150 ºC, 1 bar – 10 GPa, olivine Fo = 60 – 100, melt Mg# = 32 – 100, and melt SiO2 = 40.08 – 58.55 wt%; Table 1). 3.2. Parameterization strategies and methods Previous lattice strain models for REE and Y partitioning in garnet all treated Sc and REE + Y as a group, placing them in the X site (van Westrenen et al., 2001; Wood and Blundy, 2002; van Westrenen and Draper, 2007; Draper and van Westrenen, 2007; Corgne et al., 2012). The 136 distribution of Sc among the structural sites in garnet remains controversial especially in natural low-Sc systems. The substitution of Sc into the Y site has been observed in natural garnets (Geller, 1967); however, van Westrenen et al. (1999) suggested that Sc may also enter the X site due to its relatively large ionic radius. Using synthetic garnets heavily doped with Sc, Oberti et al. (2006) observed that Sc mainly enters the X site in synthetic pyrope, whereas Quartieri et al. (2006) and Kim et al. (2007) found that Sc exclusively enters the Y site in synthetic andradite and grossular garnet. Interestingly, one synthetic garnet (40% grossular + 60% pyrope) doped with the smallest amount of Sc (Sc2O3 = 2.83 wt%) in Oberti et al. (2006) also shows that about 90% of Sc substitute into the Y site while no detectable Sc presents in the X site (See their Table 1). The substitution of Sc into all the structural sites would lead to a bulk partition coefficient for Sc larger than that in the parabola defined by REE + Y for the X site, whereas the exclusive substitution of Sc into the Y site may give rise to a partition coefficient for Sc smaller than that in the REE + Y parabola. In Fig. 1a, we compared the two parabolas defined by REE + Y + Sc and REE + Y partition coefficients for garnet (56% pyrope + 13% grossular + 31% almandine) from run 18 in van Westrenen et al. (2000) as an example. It is evidence that the Sc partition coefficient is smaller than the corresponding value in the parabola defined by REE + Y. This suggests that Sc may preferentially enter the Y site rather than the X site in this garnet. To avoid potential errors introduced by the uncertainty of site selection of Sc partitioning in garnet, our strategy in this study is to focus on the trivalent REE + Y in the parameterization of the garnet model. On the contrary, the partition coefficients of REE, Y and Sc may be treated as a group in the lattice strain fit for olivine (Fig. 1b). This has been supported by recent partitioning experiments (Evans et al., 2008; Spandler and O’Neill, 2010; Imai et al., 2012; Mallmann and O’Neill, 2013), and thus enables us to take advantage of more experimental partitioning data. Therefore, we treat REEs, Y and Sc as a group in the parameterization of olivine model. 137 In order to develop parameterized models for REE and Y partitioning between garnet and basaltic melt and between olivine and basaltic melt, we performed multi-variable nonlinear regression analysis of the compiled experimental partitioning data from studies listed in Table 1. Following the procedure of Sun and Liang (2012), we conduct least squares analysis of REE, Y and/or Sc partitioning in garnet and olivine in two steps: (1) identification of key parameters that affect D0, r0, and E in the lattice strain model through least squares analysis of individual experiments, and (2) simultaneous inversion of all the filtered experimental data using the primary parameters identified in step (1). We first fit the partition coefficients of REEs, Y and/or Sc from individual experiment to Eq. (1) to obtain D0, r0, and E by minimizing the Chi-squares as defined below using nonlinear least squares method (e.g., Seber and Wild, 1989). ( ) N 2 χ 2 = ∑ ln D j − ln D mj , (2) j=1 where D j is defined by Eq. (1); D jm is the measured mineral-melt partition coefficient for element j; N is the total number of measured partitioning data used in the fit to the lattice strain model. Logarithmic partition coefficient is used in our Chi-square calculation because the absolute values of D are different from one element to another over orders of magnitude and systematic variations in trace element abundances and partition coefficients are usually examined in semi-log spider diagrams. Since REE + Y exclusively enter the dodecahedral X site in garnet and REE + Y + Sc may preferentially enter the octahedral M2 site in olivine, we use VIII-fold coordinated ionic radii for garnet and VI-fold coordinated ionic radii for olivine, respectively. Ionic radii are from Shannon (1976). Similar to the observations for pyroxenes in Sun and Liang (2012) and Yao et al. (2012), we also found a strong positive correlation between E and r0 for REE and Y partitioning in garnet. Thus, we assumed that E is a linear function of r0 for garnet and that r0 is a linear combination of garnet composition. The assumption for r0 is consistent with 138 previous experimental observations by van Westrenen et al. (1999, 2000). However, because E and r0 show very small variations and no obvious correlation for REE, Y and Sc partitioning in olivine, we assumed constant E and r0 for olivine. We assumed that D0 for both garnet and olivine have the same form as Eq. (2) in Sun and Liang (2012) and are functions of mineral and melt composition. To identify the primary variables for D0 and r0 in garnet and for D0 in olivine, we carried out multiple linear regressions by extensively exploring various permutations of T, P and mineral and melt compositions. To compare different combinations of T, P and compositions, we calculated the coefficients of determination for D0 and r0. We only accept the intensive parameters to obtain the best fit with possibly the highest degree of freedom. For REE and Y partitioning in garnet, we found that T, P and Ca content in garnet (XCa) primarily determines D0, and that XCa dominates the variation of r0. Hence, the lattice strain parameters D0, r0 and E can be described by the following linear expressions: a1 + a2 P + a3 P 2 ln D0gt = a0 + + a4 X Ca , (3) RT r0gt = a5 + a6 X Ca , (4) E gt = a7 + a8r0gt . (5) For REE, Y and Sc partitioning in olivine, we found that P, forsterite in olivine, and Al content in olivine or in melt are the primary variables in determining D0. The effects of melt composition on REE partitioning in olivine, specifically Al and Si content in melt, will be discussed in detail in section 5. Here we first examine the effect of olivine composition on REE partitioning between olivine and basaltic melt. The expressions of D0, r0 and E for REE, Y and Sc partitioning in olivine take the following forms: ln D0ol = b0 + b1 P + b2 Alol + b3 Fo , (6) r0ol = b4 , (7) 139 E ol = b5 . (8) The coefficients a0, a1, …, a8 and b0, b1, …, b5 in Eqs. (3-8) are constants determined by stepwise multiple linear regression analyses of the lattice strain parameters (D0, r0, and E); superscripts gt and ol represent garnet and olivine, respectively; XCa is the cation number of Ca (per 12-oxygen) in garnet; Alol is the cation number of Al (per 4-oxygen) in olivine; Fo is the forsterite content in olivine defined as 100×Mg/(Mg+Fe) (in molar). The P2 term in Eq. (3), which is also present in the models of Wood and Blundy (2002) and Corgne et al. (2012), suggests that the P dependence of the volume change for REE partitioning between garnet and melt is significant. To better assess the uncertainties for the fitting coefficients and to include more partitioning experiments with less than 3 elements [e.g., olivine-melt partitioning data reported in Tuff and O’Neill (2010) and Mallmann and O’Neill (2009); Fig. S3], we performed global nonlinear least squares analyses for garnet and olivine by substituting Eqs. (3-5) and Eqs. (6-8) into Eq. (1), respectively. For the garnet model (Eqs. 1, 3-5), we inverted the 9 coefficients (a0, a1,…, a8) simultaneously through a global inversion of a total of 538 filtered data; for the olivine model (Eqs. 1, 6-8), we solved the 6 coefficients (b0, b1, …, b5) by a simultaneous inversion of a total of 684 filtered data. To carry out the global inversions, we used the coefficients from the stepwise multiple linear regressions as initial values in the nonlinear least squares analysis and minimize the Chi-square as defined in Eq. (2). Although convenient in nonlinear regression analysis, the absolute values of the Chi-square defined by Eq. (2) depend on the number of data used in the inversion. To better assess the goodness of fit and to compare with previous models, we calculated the Pearson’s Chi-square ( χ p ) after the inversion using the expression 2 (D − D ) 2 N m χ 2p = ∑ j j . (9) j=1 Dj 140 A better predictive model should provide partition coefficients closer to measured values and hence has a smaller χ 2p . The results are shown in Fig. 5 and discussed below. 4. Results The global fit to the 538 partitioning data from 64 anhydrous experiments for garnet produces the following expressions for the lattice strain parameters for REE and Y partitioning in garnet: 9.03( ±0.98) × 104 − 93.02 ( ±17.06 ) P ( 37.78 − P ) ln D = −2.01( ±0.70 ) + gt 0 RT , (10) − 1.04 ( ±0.44 ) X Ca r0gt = 0.785( ±0.031) + 0.153( ±0.029 ) X Ca , (11) E gt = ⎡⎣ −1.67 ( ±0.45) + 2.35( ±0.51) r0gt ⎤⎦ × 103 , (12) where R (= 8.3145 J mol-1 K-1) is the gas constant, r0 is optimum ionic radius in Å, E is the effective Young’s modulus in GPa, T is temperature in K, and numbers in parentheses are 2σ uncertainties estimated directly from the simultaneous inversion. Equations (1) and (10-12) provide a simple model for REE and Y partitioning between garnet and anhydrous basaltic melt. This simple model suggests that to the first order REE partition coefficients in garnet decrease with the increase of T, P and XCa in garnet, as D0 defines the peak value of parabola in the lattice strain model (Eq. 1). The global fit to the 684 partitioning data from 177 experiments for olivine produces the following expressions for the lattice strain parameters for REE, Y and Sc partitioning in olivine: ln D0ol = −0.67 ( ±0.27 ) − 0.17 ( ±0.01) P + 117.30 ( ±12.79 ) Alol −1.47 ( ±0.27 ) × 10−2 Fo , (13) 141 r0ol = 0.725( ±0.004 ) , (14) E ol = 442 ( ±13) . (15) Equations (1) and (13-15) provide a simple model for REE, Y and Sc partitioning between olivine and basaltic melt. According to this simple model, REE partition coefficients in olivine increase with the increase of the Al content in olivine and decreases with the increase of P and forsterite content in olivine. 5. Discussion 5.1. Garnet model Our new garnet model reproduces the 538 partitioning data from the compiled 64 anhydrous partitioning experiments (fits to individual experiments are shown in Fig. S2). Figure 5a shows that the partition coefficients predicted by Eqs. (1) and (10-12) and the experimentally measured values follow the 1:1 correlation line and generally fall between the 1:2 and 2:1 correlation lines. The χ p value derived from our model ( χ p = 64 ) is much smaller than that ( 2 2 χ 2p = 342 ) calculated using the model of Draper and van Westrenen (2007), indicating the better reproducibility of our new model. In addition, the new model only has 3 primary variables (T, P, XCa) and 9 coefficients, which is significantly less than those (10 variables with 18 coefficients) in the model of Draper and van Westrenen (2007). The new garnet model can also reproduce the hydrous partitioning data from the 14 hydrous partitioning experiments very well, despite the fact that these hydrous partitioning data are not included in the model calibration (Fig. 5a and Fig. S2). Figure 5a shows that the predicted and measured hydrous partitioning data also follow the 1:1 correlation line except for some HREEs (see individual experiments in Fig. S2). Even though Draper and van Westrenen’s model was calibrated based on both anhydrous and hydrous partitioning data, it cannot reproduce most of the hydrous partitioning data (Fig. 2b). The better 142 reproducibility for anhydrous partitioning data, fewer variables and coefficients, and the excellent extrapolation to hydrous partitioning data indicate the significant improvement of the new garnet model. Figures 6a-c show garnet-melt Lu partition coefficient as a function of T, P, and XCa in garnet from the compiled partitioning experiments in Table 1. It is evident that, to the first order, garnet-melt REE partition coefficients inversely correlate with T and P, which is consistent with Eq. (10). However, the inverse correlation between XCa and garnet-melt REE partition coefficients is not evident in Fig. 6c. The effects of T and P may overwhelm the influence of XCa on garnet-melt REE partition coefficients. The increase of XCa can also increase partition coefficients by increasing r0, which may lead to the apparent relationship between XCa and garnet- melt REE partition coefficient. In order to demonstrate the primary effect of XCa, we normalize gt-melt garnet-melt Lu partition coefficients ( DLu ) by taking out the effects of T, P, and the lattice strain energy through the following expression ⎡ 4π EN A ⎛ r0 3⎞ ( ) 1 ( ) 2 gt-melt DLu = DLu gt-melt exp ⎢ ⎜ r0 − rj − r0 − rj ⎟ ⎣ RT ⎝ 2 3 ⎠ , (16) 9.17 × 10 4 − 91.35P ( 38 − P ) ⎤ − ⎥ RT ⎦ where DLu gt-melt is the normalized garnet-melt Lu partition coefficient; r0 and E can be calculated using Eqs. (11-12). Figure 6d shows a robust inverse relationship between the normalized garnet- melt Lu partition coefficients and XCa, which is consistent with Eq. (10). Girnis et al. (2013) also identified the effect of XCa on garnet-melt REE partitioning for silico-carbonate systems, though their model suggests a positive correlation between garnet-melt REE partition coefficients and XCa, and fails to reproduce a significant amount of partitioning experiments in both anhydrous and hydrous silicate systems compiled in the present study (Fig. S1d). 143 5.2. Olivine model Our new olivine model successfully reproduces the 684 partitioning data from the compiled 177 partitioning experiments (fits to individual experiments are shown in Fig. S3). Figure 5b shows that the partition coefficients predicted by the new olivine model (Eqs. 1, 13-15) and the experimentally measured values follow the 1:1 correlation line and fall between the 1:2 and 2:1 correlation lines. The χ p value provided by the new model ( χ p = 2.3 ) is considerably 2 2 smaller than that ( χ p = 4.0 ) calculated using the model of Evans et al. (2008). Note that Evans 2 et al. (2008) did not provide models for Tb, Dy and Er partition coefficients between olivine and melt due to limited data in their experiments. This reduces the number of data in χ p calculation 2 from 684 to 541 in Evans et al.’s models. The number of coefficients in the new olivine model (6 coefficients) is significantly less than that (26 coefficients) in Evans et al. (2008), though the number of variables in the new olivine model (4 variables: P, T, Alol, Fo) is greater than that (1 variable: melt SiO2) in Evans et al. (2008). Given the smaller χ p value and fewer coefficients, 2 our simple model for REE + Y + Sc partitioning in olivine shows significant improvement over the models of Evans et al. (2008). According to Eqs. (13-15), olivine-melt REE + Y + Sc partition coefficients show negative correlations with P and Fo but a positive correlation with the Al content in olivine. Interestingly, there is no significant T effect on olivine-melt REE partition coefficients, and r0 and E can be treated as constants. In Figs. 7a-d, we take Sc partition coefficient as a proxy for REE + Y + Sc partition coefficients and plot olivine-melt Sc partition coefficient as functions of T, P, Fo, and Al2O3 in olivine. Figures 7a-c show that olivine-melt Sc partition coefficient is insensitive to T and slightly decreases with the increases of P and Fo. However, olivine-melt Sc partition coefficient shows a strong positive correlation with Al2O3 in olivine, indicating the significant effect of Al in olivine on REE + Y + Sc partitioning (Fig. 7d). It is also interesting to note that for 144 many of the partitioning experiments the partition coefficients of Al fall on the parabola determined by Eqs. (1) and (13-15) though Al partition coefficients are not included in the model parameterization (Fig. S3). In section 3.2, we noted that Al content in melt is also strongly correlated with REE + Y + Sc partition coefficients in olivine. To further explore the effect of melt Al2O3, we replaced Alol in melt Eq. (6) by the cation fraction of Al3+ in melt ( X Al ) and refit the compiled experimental partitioning data for olivine through the procedure described in section 3.2. We obtained the following expressions for the lattice strain parameters of REE + Y + Sc partitioning in olivine: ln D0ol = −0.45( ±0.26 ) − 0.11( ±0.01) P + 1.54 ( ±0.15) X Al melt −1.94 ( ±0.26 ) × 10−2 Fo , (17) r0ol = 0.720 ( ±0.004 ) , (18) E ol = 426 ( ±12 ) . (19) Equations (1) and (17-19) can also reproduce the 684 experimental partitioning data for olivine (Fig. S4a), and provide a slightly smaller χ p value (= 1.9) than that ( χ p = 2.3 ) by Eqs. (1) and 2 2 (13-15). It is interesting to note that r0 and E for the Al-in-melt model (Eqs. 18 and 19) are almost the same as those for the Al-in-olivine model (Eqs. 14 and 15). The Al abundance in olivine can be related to the Al content in melt through a partition coefficient or solubility model. This can be demonstrated by combining Eqs. (13) and (17), viz., Alol = 1 117.30 ( 0.22 + 0.06P − 0.47 × 10−2 Fo + 1.54 X Almelt ) . (20) Hence to the first approximation, the Al-in-melt model (Eqs. 1 and 17-19) is equivalent to the Al- in-olivine model (Eqs. 1 and 13-15). The former can be used to calculate REE + Y + Sc partition coefficients in olivine when the Al content in olivine is not available. As suggested by Beattie (1994) and further demonstrated by our parameterized models, trivalent cation (REE3+, Y3+ and 145 Sc3+) partitioning in olivine may be strongly coupled with Al, because Al in natural olivine is sufficient to charge balance other trivalent cations. Evans et al. (2008) identified SiO2 content of melt as the key factor determining REE + Y + Sc partitioning in olivine. Here we further examine the melt SiO2 effect using the larger database compiled in this study. We replace the Al term in Eq. (13) or (17) by melt Si content, and refit the compiled experimental partitioning data for olivine through the procedure described in section 3.2. The expressions for the three lattice strain parameters are shown as inset to Fig. S4b. The new model can generally reproduce the 684 experimental partitioning data for olivine (Fig. S4b), but has a larger χ p value ( χ p = 2.9 ) than those calculated using Eqs. (1, 13-15; 2 2 χ 2p = 2.3 ) and Eqs. (1, 17-19; χ 2p = 1.9 ), suggesting that the effect of Al in olivine or Al in melt is more significant than that of Si in melt. 5.3. Sources of uncertainties and model limitations Small discrepancies are evident between predicted and measured partitioning data for both garnet and olivine in Fig. 5. The discrepancies can be attributed to several sources, such as inter- laboratory biases in the partitioning experiments, analytical uncertainties, kinetic effects in the experiments, and model deficiencies. Because light REEs are highly incompatible in garnet and olivine, their abundances are often very low, which can introduce large analytical uncertainties in compiled partitioning data. One of the key compositional variables in the olivine model is Al content in olivine (Eq. 13). The abundance of Al in olivine is usually low (< 1 wt%) and generally measured by electron microprobe with large uncertainties. These analytical uncertainties may make a great contribution to the discrepancies shown in Fig. 5. Among the compiled garnet partitioning experiments, many of the high-pressure experiments were run for short durations that may not be adequate for attainment of chemical equilibrium. Our models may not fully incorporate all the secondary compositional effects on REE partitioning in garnet and 146 olivine, which may result in some discrepancies. However, addition of more variables only marginally improves the models. Several limitations exist in our simple models for REE, Y and/or Sc partitioning in garnet and olivine. Due to the limited published partitioning experiments for garnet, the calibration of REE + Y partitioning model focuses on pyrope-rich and majoritic garnet, as such our garnet model cannot reproduce the partitioning data for grossular-rich garnet (Fig. S5a). Similarly, application of the olivine model to fayalite-rich olivine may not provide accurate predictions either. Although melt composition is not the primary variable affecting REE partitioning in garnet and olivine, extrapolation of the model to extreme melt composition may also lead to considerable discrepancies between predicted and measured partition coefficients. For instance, the olivine model underestimates REE + Y + Sc partition coefficients by factors of 2 to 5 for sodium-fluxed experiments from Mallmann and O'Neill (2013) (Fig. S5b). Whether these models can be extrapolated to a broader range of mineral and/or melt composition requires more experimental tests. Below we present two independent tests using mineral-mineral REE partition coefficients measured directly from natural mafic samples. 5.4. Model validation using field data Because the new parameterized models indicate that REE partitioning between mantle minerals and basaltic melts strongly depends on mineral composition, T and/or P, we can combine our garnet-melt REE partitioning model (Eqs. 1, 10-12) with cpx-melt REE partitioning model of Sun and Liang (2012) to obtain a predictive model for garnet-cpx REE partitioning, viz., D gt-melt D gt-cpx j = j cpx-melt , (21) Dj 147 gt-cpx where D j denotes the garnet-cpx partition coefficients for element j. Similarly, we can combine the Al-in-olivine version of our olivine model (Eqs. 1, 13-15) with the cpx model of Sun and Liang (2012) to obtain a predictive model for olivine-cpx REE partitioning, viz., D olj -melt D ol -cpx j = cpx-melt , (22) Dj ol -cpx where D j is olivine-cpx partition coefficients for element j. Comparison of the garnet-cpx and olivine-cpx models to data from well-equilibrated mantle xenoliths enables us to independently test the internal consistency of the garnet, olivine, and cpx models. Gréau et al. (2011) and Huang et al. (2012) systematically studied the petrological and geochemical characteristics of two main types (Type I and Type II) of eclogite xenoliths from Roberts Victor kimberlite in South Africa. These two types of eclogites were originally classified according to their microstructures: Type I with unequilibrated microstructure and Type II with more equilibrated microstructure. Based on systematic variations in major element, trace element, and isotopes, Huang et al. (2012) suggested that Type II eclogites represent protoliths without significant alteration or metasomatism. Using the measured major element and REE + Y abundances in garnet and cpx from Type II eclogites reported in Huang et al. (2012), we calculated garnet-cpx REE + Y partition coefficients using Eq. (21). The equilibrium temperatures (810 - 1176 ºC) were calculated using the garnet-cpx thermometer of Krogh (1988). Because there is no good barometer available for bi-mineralic eclogites, we assumed a pressure of 3 GPa to calculate the equilibrium temperatures and partition coefficients. However, the garnet- cpx thermometer may have large uncertainties in temperature estimation because of its strong pressure dependence (e.g., ±100ºC for ±1 GPa). The large uncertainties in temperature estimation and the crude assumption for pressure can potentially result in significant errors in model predicted garnet-cpx REE + Y partition coefficients. Nonetheless, Fig. 8a shows that the predicted garnet-cpx partition coefficients are in very good agreement with those reported in 148 Huang et al. (2012). The deviation of some light REEs from the general trend can be attributed to their enrichment in garnet that may be affected by metasomatism. Because of analytical errors, one HREE has predicted value greater than the measured one by a factor of four (Fig. 8a). Witt-Eickschen and O’Neill (2005) and Witt-Eickschen et al. (2009) measured the abundance of REEs and other trace elements in olivine and cpx from two suites of well- equilibrated spinel-lherzolite xenoliths using LA-ICP-MS. Light- and middle-REEs in olivine were usually below detection limits and not reported. We calculated olivine-cpx partition coefficients for REE using Eq. (22) and their reported major element compositions. Equilibrium temperatures (903 - 1245 ºC) were calculated using the cpx-opx thermometer of Brey and Köhler (1990) by assuming a pressure of 1.5 GPa. This pressure was also used to calculate olivine-cpx partition coefficients. Figure 8b shows that the predicted and measured olivine-cpx REE partition coefficients are in excellent agreement despite the large uncertainties in analysis of REEs and Al in olivine. Although our partitioning models for garnet, olivine and cpx were calibrated independently at magmatic conditions, they can reproduce garnet-cpx and olivine-cpx REE + Y partition coefficients for mantle eclogites and peridotites at subsolidus conditions. The excellent results of this extrapolation indicate the internal consistency of our partitioning models for garnet, olivine, and cpx (and opx, Yao et al., 2012), further justifying the assumptions and simplifications made in our parameterization and the lattice strain model. With these internally consistent REE partitioning models for mantle minerals, it is possible to develop thermometers and perhaps barometers based on REE partitioning between mantle minerals (Sun et al., 2012; Liang et al., 2013; Sun and Liang, 2013b). 6. Crystal Chemistry Controls on REE Partitioning Our internally consistent models for garnet, olivine, cpx, and opx indicate that crystal chemistry is one of the dominant factors controlling REE partitioning between mantle minerals 149 and basaltic melts, and that the effect of melt composition is secondary or indirect. This conclusion is further supported by REE partitioning in plagioclase, which indicates that T and Ca (or anorthite) content in plagioclase controls REE partitioning between plagioclase and basaltic melt (e.g., Bindeman et al., 1998; Bindeman and Davis, 2000; Sun and Liang, 2013b). To further understand the mechanism of crystal chemistry control on REE partitioning in mantle minerals, we consider an exchange reaction of REE between a mantle mineral and basaltic melt: ( REE ) melt ⇔ ( REE )min . (23) The equilibrium constant (K) can be expressed as ⎛ aREE min ⎞ ⎛ X REEγ REE ⎞ min min ΔG f + ΔGstrain min ln K = ln ⎜ melt ⎟ = ln ⎜ melt melt ⎟ = − , (24) ⎝ aREE ⎠ ⎝ X REEγ REE ⎠ RT where aREE , X REE , and γ REE are activity, concentration, and activity coefficient of REE, respectively; superscripts min and melt represent the mineral and melt; ΔG f is the change in Gibbs free energy for REE exchange between the strain-free mineral and melt; ΔGstrain min is the change in strain energy for REE substituting in the mineral as defined by Brice (1975), viz., ⎡r ( ) − 13 ( r − r ) ⎤⎥⎦ . 2 3 ΔGstrain min = 4π EN A ⎢ 0 r0 − rj 0 j (25) ⎣2 Mineral-melt REE partition coefficients can be obtained from Eq. (24) and expressed as ΔG f ΔGstrain min min-melt ln DREE =− RT − RT ( + ln γ REE melt − ln γ REE min ). (26) We can deduce the lattice strain model of Blundy and Wood (1994; Eq. 1) by defining ⎛ ΔG f ⎞ − ⎜ RT + ln γ melt REE − ln γ min REE ⎟ in Eq. (26) as lnD0 and substituting Eq. (25) into Eq. (26). The ⎝ ⎠ change of Gibbs free energy, ΔG f , equals ΔH f − T ΔS f + PΔV f , where ΔH f , ΔS f , ΔV f are 150 the changes of enthalpy, entropy and volume, respectively, for the exchange reaction under strain- free condition (Eq. 23). The enthalpy change mainly determines the effect of temperature, and the volume change determines the effect of pressure on mineral-melt REE partitioning. The change of strain energy is controlled by mineral composition owing to the mineral-composition dependent r0 and E, as suggested by our parameterized partitioning models for cpx, opx and garnet. Rare-earth elements obey Henry’s law in mantle minerals and basaltic melts due to their low abundances. Many partitioning studies, however, have shown that REE substitution into minerals is strongly coupled with major elements (e.g, AlT for cpx; Gaetani and Grove, 1995; Lundstrom et al., 1998; Hill et al., 2000). Changes in major elements in the mineral may lead to a significant variation in the local environment of REEs in the mineral as well as their activity coefficients. The coupling between REEs and major element cations is perhaps insignificant in basaltic melt because REEs and most major element cations are network modifiers in melt structure. Thus, REE activity coefficients in the basaltic melt are less sensitive to the variations in melt composition. Because of ubiquitous solid solutions in mantle minerals, mineral composition may also change correspondingly with melt composition, which in turn indirectly incorporates the effect of melt composition on REE partitioning (Blundy and Wood, 2003). When melt structure becomes extremely polymerized or depolymerized, the activities or activity coefficients of REE in melt can decrease or increase accordingly (e.g., Watson, 1976; Ryerson and Hess, 1978), so that melt compositional effect may become significant. However, mineral composition generally determines the strain energy change and shows strong coupling with REE substitution into the mineral, consequently controlling REE partitioning between minerals and basaltic melts. Melt composition, including water content, only shows a secondary or indirect effect. 151 7. Summary and Conclusions Based on published high quality partitioning experiments we have developed parameterized lattice strain models for REE and Y partitioning between garnet and basaltic melt and between olivine and basaltic melt. We have demonstrated that REE and Y partition coefficients between garnet and basaltic melt are inversely correlated with T, P and XCa in garnet, and that REE, Y, and Sc partition coefficients between olivine and basaltic melt are positively correlated with Al content in olivine (or melt) and inversely correlated with P and forsterite content in olivine. The partitioning models for garnet, olivine, cpx, and opx were independently calibrated and verified by well-equilibrated mantle eclogites and peridotites at subsolidus conditions. Extrapolation of our models to subsolidus conditions demonstrates their internal consistency, giving added assurance to their applicability to natural geochemical systems. Taken collectively, the partitioning models for cpx, opx, garnet, and olivine point to the importance of crystal chemistry, T and/or P in determining REE partitioning between mantle minerals and basaltic melts, and that melt compositional effect is secondary or indirect. 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Quantifying garnet-melt trace element partitioning using lattice-strain theory: new crystal-chemical and thermodynamic constraints. Contributions to Mineralogy and Petrology 154, 717-730. van Westrenen, W., Blundy, J., Wood, B., 1999. Crystal-chemical controls on trace element partitioning between garnet and anhydrous silicate melt. American Mineralogist 84, 838-847. van Westrenen, W., Wood, B. J., Blundy, J. D., 2001. A predictive thermodynamic model of garnet–melt trace element partitioning. Contributions to Mineralogy and Petrology 142, 219- 234. van Westrenen, W., Blundy, J. D., Wood, B. J., 2000. Effect of Fe2+ on garnet–melt trace element partitioning: experiments in FCMAS and quantification of crystal-chemical controls in natural systems. Lithos 53, 189-201. Walter, M. J., Nakamura, E., Trønnes, R. G., Frost, D. J., 2004. Experimental constraints on crystallization differentiation in a deep magma ocean. Geochimica et Cosmochimica Acta 68, 4267-4284. Watson, E. B., 1976. Two-liquid partition coefficients: experimental data and geochemical implications. Contributions to Mineralogy and Petrology 56, 119-134. Witt-Eickschen, G., O’Neill, H. S. C., 2005. The effect of temperature on the equilibrium distribution of trace elements between clinopyroxene, orthopyroxene, olivine and spinel in upper mantle peridotite. Chemical Geology 221, 65-101. Witt-Eickschen, G., Palme, H., O’Neill, H. S. C., Allen, C. M., 2009. The geochemistry of the volatile trace elements As, Cd, Ga, In and Sn in the Earth’s mantle: New evidence from in situ analyses of mantle xenoliths. Geochimica et Cosmochimica Acta 73, 1755-1778. Wood, B. J., Blundy, J. D., 1997. A predictive model for rare earth element partitioning between clinopyroxene and anhydrous silicate melt. Contributions to Mineralogy and Petrology 129, 166-181. Wood B. J., Blundy J. D., 2003. Trace element partitioning under crustal and uppermost mantle 159 conditions: the influences of ionic radius, cation charge, pressure and temperature. In: Carlson RW (ed) The Mantle and Core. Treatise on geochemistry, vol 2. Elsevier, Amsterdam, pp 395-424. Wood, B. J., Blundy, J. D., 2002. The effect of H2O on crystal-melt partitioning of trace elements. Geochimica et Cosmochimica Acta 66, 3647-3656. Workman, R. K., Hart, S. R., 2005. Major and trace element composition of the depleted MORB mantle (DMM). Earth and Planetary Science Letters 231, 53-72. Yao, L., Sun, C., Liang, Y., 2012. A parameterized model for REE distribution between low-Ca pyroxene and basaltic melts with applications to REE partitioning in low-Ca pyroxene along a mantle adiabat and during pyroxenite-derived melt and peridotite interaction. Contributions to Mineralogy and Petrology 164, 261-280. Yurimoto, H., Ohtani, E., 1992. Element partitioning between majorite and liquid: a secondary ion mass spectrometric study. Geophysical Research letters 19, 17-20. Figure Captions Figure 3-1 Onuma diagrams showing experimentally determined REE, Y and Sc partition coefficients in garnet (a) and olivine (b) as a function of their ionic radii. The garnet-melt partition coefficients are from run 18 in van Westrenen et al. (2000), and the olivine-melt partition coefficients are from run C1 in Beattie (1994). Ionic radii are from Shannon (1976; VIII- fold coordination for garnet, and VI-fold coordination for olivine). Solid lines are the regression to Eq. (1) excluding elements with light blue markers. The dashed line in (a) is the regression to Eq. (1) including Sc. Error bars are 1σ errors of measured partitioning data from the experiments. Figure 3-2 Comparisons between experimentally determined garnet-melt REE+Y partition coefficients (D) and those predicted by the models of van Westrenen and Draper (2007; a) and 160 Draper and van Westrenen (2007; b). Anhydrous partitioning data are from experiments listed in Table 1. Hydrous partitioning data are from Green et al. (2000), Barth et al. (2002), Gaetani et al. (2003), and Adam and Green (2006). Solid blue lines are 1:1 lines, and dashed lines are 1:2 and 2:1 lines. Error bars are 1σ errors of measured partitioning data from the experiments. χ p is the 2 Pearson’s Chi-square for compiled garnet-melt partitioning data in anhydrous systems (Table 1), as defined by Eq. (9) to aid model evaluation. Figure 3-3 Comparisons between experimentally determined olivine-melt REE + Y + Sc partition coefficients and those predicted by the models of Bédard (2005; a) and Evans et al. (2008; b). Sources for experimental partitioning data are listed in Table 1. See the caption to Figure 2 for legends for solid and dashed lines, error bars, and definition of χ p . 2 Figure 3-4 Ternary diagram showing the composition of garnet from compiled anhydrous and hydrous partitioning experiments. Py, Alm, and Spess represent garnet end-members, pyrope, almandine, and spessartine, respectively. Sources for anhydrous and hydrous partitioning experiments are the same as those used in Figure 2. Figure 3-5 Comparisons between model-predicted partition coefficients and experimentally determined values for garnet-melt (a) and olivine-melt (b). The predicted garnet-melt partition coefficients are calculated for REE + Y using Eqs. (1, 10-12). The predicted olivine-melt partition coefficients are calculated for REE + Y + Sc using Eqs. (1, 13-15). See the caption to Figure 2 for legends for solid and dashed lines, and definition of χ p . Error bars for predicted partition 2 coefficients are 2σ errors estimated directly by the two models, and are smaller than the symbols for most of the data. Data sources are the same as those used in Figures 2 and 3. 161 Figure 3-6 Plots of garnet-melt Lu partition coefficients as functions of T (a), P (b), and XCa (mole per 12-oxygen) in garnet (c-d). The partition coefficients of Lu in (d) are normalized using Eq. (16). The partitioning data are from the compiled experiments listed in Table 1. Figure 3-7 Plots of olivine-melt Sc partition coefficients as functions of T (a), P (b), forsterite content (Fo) in olivine (c), and Al2O3 content in olivine (d). See Table 1 for data sources. Figure 3-8 Comparisons of model predicted and LA-ICP-MS measured REE+Y partition coefficients for garnet-cpx from eclogites (a) and for olivine-cpx from peridotites (b). The eclogite samples are Type II eclogites collected from the kimberlite pipe in South Africa (Huang et al., 2012). The peridotite samples are well-equilibrated spinel-peridotite xenoliths from cratonic lithospheric mantle (Witt-Eickschen and O’Neill, 2005; Witt-Eickschen et al., 2009). See text for additional information. Figure 3-S1 Comparisons of experimentally determined garnet-melt REE+Y partition coefficients and those predicted by the models of van Westrenen et al. (2001; a), Wood and Blundy (2002; b), Corgne et al. (2012; c), and Girnis et al. (2013; d). See the caption to Figure 2 for data sources, legends for solid and dashed lines, error bars, and definition of χ p . 2 Figure 3-S2 Comparisons of measured garnet-melt partitioning data (circles) and those predicted by different models for individual experiments. Thick red lines denote predicted partition coefficients by Eqs. (1, 10-12). vW&D07 is the model of van Westrenen and Draper (2007); D&vW07 is the model of Draper and van Westrenen (2007); CvD12 represents the model of Corgne et al. (2012); WvW01 is the model of van Westrenen et al. (2001); W&B02 is the model 162 of Wood and Blundy (2002); Girnis13 is the model of Girnis et al. (2013). Markers with light blue color represent partitioning data excluded in the model calibration. H2O is the water content in melt. Note that all hydrous partitioning experiments are not included in the model parameterization. Figure 3-S3 Comparisons of measured olivine-melt partitioning data and those predicted by this study for individual experiments. Thick red lines denote predicted partition coefficients by Eqs. (1, 13-15). Markers with light blue color represent partitioning data excluded in the model calibration. Although Al partition coefficients are not included in the regression analysis, our model reproduces Al partition coefficients for many of the compiled partitioning experiments. Figure 3-S4 Comparisons of experimental olivine-melt partitioning data and those predicted by parameterized lattice strain models based on Al in melt (a) and Si in melt (b). The insets are expressions for the lattice strain parameters. Error bars for predicted partition coefficients are 2σ errors estimated directly by our models. See the caption to Figure 3 for data sources, legends for solid and dashed lines, and definition of χ p . 2 Figure 3-S5 Plots of experimental REE, Y and Sc partition coefficients for garnet (a) and olivine (b) as a function of their ionic radii. The partitioning data for garnet are from run 13 in van Westrenen et al. (1999), and those for olivine are from run C15/03/11-4 in Mallmann and O’Neill (2013). Red solid lines show predicted partition coefficients by our models (Eqs. 1, 10-12 for garnet, and Eqs. 1, 13-15 for olivine). The blue solid line in (a) represents predicted partition coefficients by the model of van Westrenen et al. (2001; WvW01). See text for discussion. 163 Figures Figure 3-1 1 Sc 10 (a) (b) 10 Garnet-melt partition coefficient Olivine-melt partition coefficient Yb Sc Lu Er Y 0 Tb Yb 10 10 Y Ho Sm Tb 10 10 Pr Sm 10 10 Py56Gr Alm Fo Pr Ce Run# 18 from La Run# C1 from La van Westrenen et al. (2000) 10 0.8 0.9 1 1.1 1.2 0.6 0.7 0.8 0.9 1 1.1 Ionic Radius (Å) Ionic Radius (Å) 164 Figure 3-2 10 (a) van Westrenen 10 (b) Draper & van Westrenen 10 10 Predicted garnet-melt D Predicted garnet-melt D 1 10 1 10 Anhydrous Hydrous 0 0 10 10 10 10 10 10 10 10 10 10 2 2 10 p 10 p 0 1 0 1 10 10 10 10 10 10 10 10 10 10 10 10 10 10 Observed garnet-melt D Observed garnet-melt D 165 Figure 3-3 0 0 10 10 10 10 10 10 10 10 10 10 2 2 p p 0 0 10 10 10 10 10 10 10 10 10 10 166 Figure 3-4 50 Anhydrous 50 Hydrous 30 30 10 10 Py 50 Alm+Spess 167 Figure 3-5 0 10 10 (a) Anhydrous (b) Hydrous 1 10 10 0 10 10 10 10 10 10 10 2 2 10 p = 64 p 0 1 0 10 10 10 10 10 10 10 10 10 10 10 10 168 Figure 3-6 (a) (b) 1 1 10 10 DLu DLu 0 0 10 10 3.5 4 4.5 5 5.5 6 6.5 7 0 5 10 15 20 25 4 P (GPa) 10 /T (K ) (c) (d) 1 10 Normalized DLu 10 DLu 0 10 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 XCa XCa 169 Figure 3-7 0 0 10 10 (a) (b) DSc 10 10 4 4.5 5 5.5 6 6.5 7 0 2 4 6 8 10 4 P (GPa) 10 /T (K ) 0 0 10 10 (c) (d) DSc 10 10 60 70 80 90 100 0 0.1 0.2 0.3 0.4 Fo O 2 3 170 Figure 3-8 10 1 10 0 10 10 10 0 1 10 10 10 10 10 10 10 10 10 10 10 10 10 171 Figure 3-S1 van Westrenen 2 p 0 0 2 p 0 0 2 2 p p 0 0 0 0 172 Figure 3-S2 1 10 Lu Tm Y 0 10 Lu Y Y Dy Sm Eu Sm 10 Sm Nd Nd Pr Ce Nd 10 Ce Run# La Run#A67 La C C C 10 H O = 0 wt% H O = 0 wt% H O = 0 wt% 10 1 10 0 10 Y Y Dy Y Dy Sm Sm Dy Nd Nd Sm Nd 10 10 T = 1600 C T = 1600 C C 10 H O = 0 wt% H O = 0 wt% H O = 0 wt% 10 1 10 0 Y 10 Y Dy Y Sm Dy Dy Sm Nd 10 Nd Sm Nd 10 C C T = 1700 C 10 H O = 0 wt% H O = 0 wt% H O = 0 wt% 10 1 1 1 173 1 10 Lu Y Dy 0 10 Y Dy Y Dy Sm Sm Sm 10 Nd Nd Nd 10 Run#A161 P = 5.50 GPa P = 7.00 GPa Ce T = 1670 C T = 1650 C C La 10 H O = 0 wt% H O = 0 wt% H O = 0 wt% 10 1 10 Lu Y Lu Y Lu Y 0 10 Dy Gd Eu Gd Sm Gd Sm Eu Sm 10 Nd Nd Pr Pr 10 Pr Ce Ce La Ce La C C C 10 H O = 0 wt% La H O = 0 wt% H O = 0 wt% 10 1 10 Lu Lu Y Y 0 10 Lu Sm Eu Gd Sm 10 Nd Pr Nd Pr Ce Pr 10 Ce La La La P = 5.00 GPa P = 7.00 GPa T = 1500 C T = 1750 C T = 1560 C 10 H O = 0 wt% H O = 0 wt% H O = 0 wt% 10 1 1.1 1 1.1 1 1.1 174 1 10 Lu Lu Yb Lu Yb Y Y 0 Er 10 Tb Tb Tb Sm Sm Sm 10 Pr Pr Pr La 10 Run#11 Run#16 Run#18 La La T = 1565 C C C 10 H O = 0 wt% H O = 0 wt% H O = 0 wt% 10 1 Lu 10 Er Yb Y 0 Lu Lu Dy 10 Yb Yb Y Er Eu Eu 10 Dy Sm Sm Sm Nd Eu Nd Nd Pr Ce 10 Pr La Ce La La Ce C C C 10 H O = 0 wt% H O = 0 wt% H O = 0 wt% 10 1 Lu Lu 10 Yb Lu Er Yb Y Yb Y Er 0 Dy Dy Dy 10 Sm Eu Eu Eu Sm 10 Nd Nd Nd 10 Ce Ce Ce La La C C C 10 H O = 0 wt% La H O = 0 wt% H O = 0 wt% 10 1 1 1 175 Lu Lu Lu 1 Yb Yb Yb 10 Er Y Y Er Y Dy Dy 0 10 Eu Sm Eu Sm Eu Sm 10 Ce Ce 10 Ce La La C C C 10 H O = 0 wt% La H O = 0 wt% H O = 0 wt% 10 Lu 1 Yb 10 Er Lu Er Y Lu Y Yb Yb Dy Dy Y 0 Er 10 Eu Sm Eu Sm Sm 10 Ce Ce Ce 10 La La C C C 10 H O = 0 wt% H O = 0 wt% H O = 0 wt% 10 1 Lu Lu 10 Lu Yb Yb Yb Y Y Y 0 10 Sm Sm Sm 10 Ce Ce Ce 10 C C C 10 H O = 0 wt% H O = 0 wt% H O = 0 wt% 10 1 1 1 176 1 Lu Lu 10 Yb Lu Yb Y Y Y 0 10 Sm Sm Sm Nd Nd 10 Nd Ce Ce 10 Ce C T = 1500 C T = 1510 C 10 H O = 0 wt% H O = 0 wt% H O = 0 wt% 10 1 Lu Lu Lu 10 Yb Yb Yb Y Er Y Y 0 10 Sm Sm Sm 10 Nd Nd Nd Ce Ce Ce 10 T = 1515 C C T = 1580 C 10 H O = 0 wt% H O = 0 wt% H O = 0 wt% 10 1 10 Lu Lu Lu Yb Yb Yb Y Y Y 0 10 Er Er Er Sm Sm Sm 10 Nd Nd Nd Ce Ce 10 Ce C C C 10 H O = 0 wt% H O = 0 wt% H O = 0 wt% 10 1 1 1 177 1 10 Lu Yb Y 0 10 Y Yb Sm Y Sm La 10 Nd Ce 10 Run#59 T = 1675 C T = 1900 C T = 1900 C 10 H O = 0 wt% H O = 0 wt% H O = 0 wt% 10 1 10 0 10 Lu Lu Y Y Y 10 Sm Sm Nd Nd 10 C C C 10 H O = 0 wt% H O = 0 wt% H O = 0 wt% 10 1 10 Lu Lu 0 Lu Dy 10 Y Eu Eu Sm Sm 10 Sm Nd Nd Pr Pr Ce 10 Run#M955 Nd Ce La T = 1975 C T = 1550 C La C 10 H O = 0 wt% H O = 0 wt% H O = 0 wt% 10 1 1 1 178 1 10 Lu Tm Lu Lu Tm 0 Tb Dy 10 Tb Eu Tb Sm Eu Eu Sm Sm 10 Nd Pr Nd Nd Ce Pr Pr 10 Ce Ce P = 5.00 GPa La P = 5.00 GPa P = 5.00 GPa T = 1580 C T = 1580 C T = 1580 C La 10 H O = 0 wt% H O = 0 wt% La H O = 0 wt% 10 1 10 Lu Lu Lu 0 10 Tm Tm Y Eu Tb Tb Sm Eu Eu 10 Sm Sm Nd Pr Nd Nd 10 Pr Ce Pr P = 8.00 GPa P = 10.00 GPa Ce Ce C La T = 1850 C C La 10 H O = 0 wt% H O = 0 wt% La H O = 0 wt% 10 1 10 Lu Lu 0 Lu 10 Tm Dy Dy Gd Gd Dy Gd 10 Eu Sm Eu Eu Sm Sm Nd Nd Nd Pr Pr 10 Pr P = 15.00 GPa Ce P = 18.00 GPa Ce Ce La La La C C C 10 H O = 0 wt% H O = 0 wt% H O = 0 wt% 10 0.8 1 1.1 0.8 1 1.1 0.8 1 1.1 179 Lu Er 1 Lu Y 10 Lu Yb Tm Dy Y Y 0 Tb 10 Tb Sm Eu Sm Nd 10 Sm Nd Nd 10 Run#1955 La Ce Ce T = 1190 C T = 1180 C T = 1000 C 10 H H La H La 10 Lu Lu 1 10 Y Y Lu Yb Dy Dy Dy 0 10 Sm Sm Sm Eu Nd 10 Nd Eu Nd Eu Ce Ce 10 La T = 1000 C C C 10 H H H 10 1 10 Lu Lu Yb Er Y Dy Dy Tb 0 Tb Eu 10 Eu Sm Sm Eu Sm Nd 10 Nd Pr Nd Ce 10 Ce Run#1787 Pr Ce La C C La C 10 H H H 10 1 1 1 180 Lu Lu Lu Yb 1 10 Yb Yb Dy Dy Dy Tb 0 Tb Tb 10 Eu Gd Eu Eu Sm Sm Sm 10 Nd Nd Nd Pr Pr 10 Run#MA10 Run#1798 Run#1807 Pr Ce P = 6.00 GPa Ce C Ce T = 1100 C T = 1160 C 10 H H La H La La 10 0.8 0.9 1 1.1 Lu 1 Lu Yb 10 Yb Er Er Dy 0 Dy Tb 10 Tb Gd Eu vW&D07 Gd Sm D&vW07 10 Eu Sm Nd Nd Pr WvW01 10 Run#MA8 Pr Run#MA9 Ce P = 6.00 GPa Ce C La T = 1180 C La 10 H H 10 0.8 0.9 1 1.1 0.8 0.9 1 1.1 181 Figure 3-S3 0 10 10 Yb Yb Yb 10 Al Y Al Al Y Y Tb Tb Tb 10 Sm Sm Sm 10 Run#B7 Run#C1 Run#C10 Pr Pr Pr Ce P = 0.0001 GPa Ce P = 0.0001 GPa Ce P = 0.0001 GPa La C La C La C 10 10 0 10 10 Yb Yb Al Yb 10 Al Al Y Y Y Tb Tb Tb 10 Sm Sm Sm 10 Run#C11 Ce Pr Pr P = 0.0001 GPa P = 0.0001 GPa Ce P = 0.0001 GPa Pr 10 C C T = 1190 C Ce La La 10 0 10 10 Lu Lu Lu Tm Yb Tm 10 Yb Tm Yb Y Y Al Y Al Al 10 Gd Gd Gd Eu Eu Eu Sm Sm Sm 10 Nd Nd Nd P = 0.0001 GPa Pr P = 0.0001 GPa Pr P = 0.0001 GPa Pr C Ce C Ce C Ce 10 La La La 10 0.7 0.8 0.9 1 1.1 0.7 0.8 0.9 1 1.1 0.7 0.8 0.9 1 1.1 182 0 10 10 Lu Lu Lu Tm 10 Tm Y Tm Y Al Y Al Al Gd 10 Gd Eu Gd Sm Eu Eu Sm Sm Nd 10 Pr Nd Nd P = 0.0001 GPa P = 0.0001 GPa P = 0.0001 GPa Pr Pr Ce Ce C Ce C La C 10 La La 10 0 10 10 Lu Lu Lu Tm Tm Tm Y Y 10 Y Al Al Al Gd Gd Eu Gd Eu 10 Eu Sm Sm Sm Nd Nd 10 Nd Pr Pr Pr P = 0.0001 GPa P = 0.0001 GPa Ce P = 0.0001 GPa Ce Ce La 10 C La C La C 10 0 10 10 10 Y Al Y Y Al Al 10 10 P = 0.0001 GPa P = 0.0001 GPa P = 0.0001 GPa 10 C C C 10 0.7 0.9 1 1.1 0.7 0.9 1 1.1 0.7 0.9 1 1.1 183 0 10 10 10 Al Y Al Y Y Al 10 10 Run#N100B1 P = 0.0001 GPa P = 0.0001 GPa P = 0.0001 GPa 10 C C C 10 0 10 10 10 Y Al Al Y Y Al 10 10 P = 0.0001 GPa P = 0.0001 GPa P = 0.0001 GPa 10 C C C 10 0 10 10 10 Al Y Al Y Al Y 10 10 Run#N89B1 P = 0.0001 GPa P = 0.0001 GPa P = 0.0001 GPa 10 C C C 10 0.7 0.8 0.9 1 1.1 0.7 0.8 0.9 1 1.1 0.7 0.8 0.9 1 1.1 184 0 10 10 10 Y Al Y Al Y Al 10 10 P = 0.0001 GPa P = 0.0001 GPa P = 0.0001 GPa 10 C C C 10 0 10 10 10 Y Y Al Y 10 10 Run#N81B1 P = 0.0001 GPa P = 0.0001 GPa P = 0.0001 GPa 10 C C C 10 0 10 10 10 Y Al Al Al Y Y 10 10 P = 0.0001 GPa P = 0.0001 GPa P = 0.0001 GPa 10 C C C 10 0.7 0.8 0.9 1 1.1 0.7 0.8 0.9 1 1.1 0.7 0.8 0.9 1 1.1 185 0 10 10 10 Al Al Y Y Y Al 10 10 P = 0.0001 GPa P = 0.0001 GPa P = 0.0001 GPa 10 C C C 10 0 10 10 10 Al Y Y Al Al Y 10 10 P = 0.0001 GPa P = 0.0001 GPa P = 0.0001 GPa 10 C C C 10 0 10 10 10 Al Y Al Y Y Al 10 10 P = 0.0001 GPa P = 0.0001 GPa P = 0.0001 GPa 10 C C C 10 0.7 0.8 0.9 1 1.1 0.7 0.8 0.9 1 1.1 0.7 0.8 0.9 1 1.1 186 0 10 10 10 Y Al Al Y Y Al 10 10 P = 0.0001 GPa P = 0.0001 GPa P = 0.0001 GPa 10 C C C 10 0 10 10 Y Y 10 Al Al Y Al 10 10 P = 0.0001 GPa P = 0.0001 GPa P = 0.0001 GPa 10 C C C 10 0 10 10 10 Y Al Al Y Y Al 10 10 P = 0.0001 GPa P = 0.0001 GPa P = 0.0001 GPa 10 C C C 10 0.8 0.9 1 1.1 0.8 0.9 1 1.1 0.8 0.9 1 1.1 187 0 10 10 Al Y Al Y 10 Al Y 10 10 P = 0.0001 GPa P = 0.0001 GPa P = 0.0001 GPa 10 C C C 10 0 10 10 10 Al Y Al Y Y Al 10 10 P = 0.0001 GPa P = 0.0001 GPa P = 0.0001 GPa 10 C C C 10 0 10 10 10 Al Y Al Y Y Al 10 10 P = 0.0001 GPa P = 0.0001 GPa P = 0.0001 GPa 10 C C C 10 0.8 0.9 1 1.1 0.8 0.9 1 1.1 0.8 0.9 1 1.1 188 0 10 10 Y Al Y 10 Al Al Y 10 10 P = 0.0001 GPa P = 0.0001 GPa P = 0.0001 GPa 10 C C C 10 0 10 10 Y Y 10 Al Y Al Al 10 10 P = 0.0001 GPa P = 0.0001 GPa P = 0.0001 GPa 10 C C C 10 0 10 10 Y 10 Al Y Al Al Y 10 10 P = 0.0001 GPa P = 0.0001 GPa P = 1 GPa 10 C C C 10 0.9 1 1.1 0.9 1 1.1 0.9 1 1.1 189 0 10 10 10 Al Al Y Y Al Y 10 10 P = 0.0001 GPa P = 0.0001 GPa P = 0.0001 GPa 10 C C C 10 0 10 10 10 Al Al Y Al Y Y 10 10 P = 0.0001 GPa P = 0.0001 GPa P = 0.0001 GPa 10 C C C 10 0 10 10 10 Al Y Al Y Y Al 10 10 P = 0.0001 GPa P = 0.0001 GPa P = 0.0001 GPa 10 C C C 10 0.8 1 1.1 0.8 1 1.1 0.8 1 1.1 190 0 10 10 10 Al Y Al Y Al Y 10 10 P = 0.0001 GPa P = 0.0001 GPa P = 0.0001 GPa 10 C C C 10 0 10 10 10 Y Y Al Al Al Y 10 10 P = 0.0001 GPa P = 0.0001 GPa P = 0.0001 GPa 10 C C C 10 0 10 10 10 Al Al Al Y Y Y 10 10 P = 0.0001 GPa P = 1 GPa P = 0.0001 GPa 10 C C C 10 0.8 1 1.1 0.8 1 1.1 0.8 1 1.1 191 0 10 10 10 Al Y Al Y Y 10 10 P = 0.0001 GPa P = 0.0001 GPa P = 0.0001 GPa 10 C C C 10 0 10 10 10 Al Y Y Y Al Al 10 10 P = 0.0001 GPa P = 0.0001 GPa P = 1 GPa 10 C C C 10 0 10 10 10 Y Y Y Al Al Al 10 10 P = 0.0001 GPa P = 0.0001 GPa P = 0.0001 GPa 10 C C C 10 0.8 1 1.1 0.8 1 1.1 0.8 1 1.1 192 0 10 10 10 Y Y Y Al Al Al 10 10 P = 0.0001 GPa P = 0.0001 GPa P = 0.0001 GPa 10 C C C 10 0 10 10 10 Y Y Y Al Al 10 10 P = 0.0001 GPa P = 0.0001 GPa P = 0.0001 GPa 10 C C C 10 0 10 10 Al Y 10 Al Y Al Y 10 10 P = 0.0001 GPa P = 0.0001 GPa P = 0.0001 GPa 10 C C C 10 1 1.1 1 1.1 1 1.1 193 0 10 10 10 Al Y Y Al Y Al 10 10 P = 0.0001 GPa P = 0.0001 GPa P = 0.0001 GPa 10 C C C 10 0 10 10 Lu Yb Tm 10 Y Al Y Al Er Al Dy Tb 10 10 P = 0.0001 GPa P = 0.0001 GPa P = 0.0001 GPa 10 C C C 10 0 10 10 Lu Lu Lu Yb Tm Yb Tm Al 10 Al Al Er Yb Er Tm Y Tb Tb Er Gd 10 10 Run#P777 10 C T = 1700 C C 10 0.7 1 1.1 0.7 1 1.1 0.7 1 1.1 194 0 10 10 Al Al Lu Lu Lu Al 10 Yb Tm Y Sm Yb Er Yb Tb 10 10 10 C C C 10 0 10 10 Yb Yb 10 Er Yb Y Er Y Al Al Er Y Tb Tb Al Tb 10 10 10 C C C 10 0 10 10 Yb Yb Yb 10 Er Y Al Er Y Er Y Tb Al Al Tb Tb 10 10 10 C C C 10 0.7 0.8 1 1.1 0.7 0.8 1 1.1 0.7 0.8 1 1.1 195 0 10 10 Yb Yb 10 Yb Er Er Y Y Er Y Al Al Al Tb Tb Tb 10 10 P = 0.0001 GPa P = 0.0001 GPa P = 0.0001 GPa 10 C C C 10 0 10 10 Yb Yb 10 Yb Er Er Y Y Al Er Y Al Al Tb Tb Tb 10 10 P = 0.0001 GPa P = 0.0001 GPa P = 0.0001 GPa 10 C C C 10 0 10 10 Yb Yb Yb 10 Er Y Er Er Y Al Y Al Al Tb Tb Tb 10 10 P = 0.0001 GPa P = 0.0001 GPa P = 0.0001 GPa 10 C C C 10 0.8 0.9 1 1.1 0.8 0.9 1 1.1 0.8 0.9 1 1.1 196 0 10 10 Yb Yb Yb 10 Er Er Y Er Y Y Al Al Al Tb Tb Tb 10 10 P = 0.0001 GPa P = 0.0001 GPa P = 0.0001 GPa 10 C C C 10 0 10 10 Yb Yb Yb 10 Er Y Er Er Y Al Y Al Tb Al Tb Tb 10 10 P = 0.0001 GPa P = 0.0001 GPa P = 0.0001 GPa 10 C C C 10 0 10 10 Yb Yb Yb 10 Er Er Er Y Y Y Al Al Al Tb Tb Tb 10 10 P = 0.0001 GPa P = 0.0001 GPa P = 0.0001 GPa 10 C C C 10 0.7 0.8 0.9 1 1.1 0.7 0.8 0.9 1 1.1 0.7 0.8 0.9 1 1.1 197 0 10 10 Yb Yb Yb 10 Er Er Er Y Y Y Al Al Al Tb Tb Tb 10 10 P = 0.0001 GPa P = 0.0001 GPa P = 0.0001 GPa 10 C C C 10 0 10 10 Yb Yb Yb 10 Er Er Er Y Y Y Al Al Al Tb Tb Tb 10 10 P = 0.0001 GPa P = 0.0001 GPa P = 0.0001 GPa 10 C C C 10 0 10 10 Yb Yb Yb 10 Er Er Er Al Y Y Y Al Al Tb Tb Tb 10 10 P = 0.0001 GPa P = 0.0001 GPa P = 0.0001 GPa 10 C C C 10 0.7 0.8 0.9 1 1.1 0.7 0.8 0.9 1 1.1 0.7 0.8 0.9 1 1.1 198 0 10 10 Yb Yb Yb Er 10 Er Y Er Y Y Al Al Al Tb Tb Tb 10 10 P = 0.0001 GPa P = 0.0001 GPa P = 0.0001 GPa 10 C C C 10 0 10 10 Yb Yb Yb Er Er Y Y 10 Er Y Al Al Tb Tb Al Tb 10 10 P = 0.0001 GPa P = 0.0001 GPa P = 0.0001 GPa 10 C C C 10 0 10 10 Yb Yb Yb Er Er Al Y Al Er 10 Al Y Y Tb Tb Tb 10 10 P = 0.0001 GPa P = 0.0001 GPa P = 0.0001 GPa 10 C C C 10 0.8 0.9 1 1.1 0.8 0.9 1 1.1 0.8 0.9 1 1.1 199 0 10 10 Yb Yb Yb Al Er Er Al Er Y 10 Y Al Y Tb Tb Tb 10 10 P = 0.0001 GPa P = 0.0001 GPa P = 0.0001 GPa 10 C C C 10 0 10 10 Yb Yb Er Yb 10 Al Y Al Er Al Er Y Y Tb Tb Tb 10 10 P = 0.0001 GPa P = 0.0001 GPa P = 0.0001 GPa 10 C C C 10 0 10 10 Yb Yb 10 Al Er Al Er Yb Y Y Al Er Tb Y Tb 10 Tb 10 P = 0.0001 GPa P = 0.0001 GPa 10 C C C 10 1 1.1 1 1.1 1 1.1 200 0 10 10 Yb Yb 10 Al Al Al Er Er Y Y Y Tb 10 Tb 10 10 C C C Mallmann and 10 0 10 10 Yb Yb 10 Er Er Yb Al Y Al Y Al Er Y Tb Tb Tb 10 10 10 C C C Mallmann and 10 0.7 0.9 1 1.1 0.7 0.9 1 1.1 0.7 0.9 1 1.1 201 Figure 3-S4 0 10 ln D0ol 0.45 0.26 0.11 0.01 P 10 1.54 0.15 X Almelt 1.94 0.26 10 2 Fo 10 r0ol 0.720 0.004 E ol 426 12 10 10 10 2 p = 1.9 (a) 0 10 10 10 10 10 10 0 10 ln D0ol 2.98 0.38 0.16 0.01 P 10 2.84 0.27 X Smelt i 1.50 0.25 10 2 Fo 10 r0ol 0.720 0.004 E ol 421 12 10 10 10 2 p (b) 0 10 10 10 10 10 10 202 Figure 3-S5 0 (a) 10 (b) WvW01 Sc 1 10 Olivine-melt partition coefficient Garnet-melt partition coefficient Yb Y Yb Tb 10 Lu Er 0 Er Sm Y 10 Sc Pr Tb 10 Al La 10 This study 10 This study 10 10 XCa = 2.72 in garnet Na 2O = 12.5 wt% in melt 10 10 van Westrenen Run# from et al. (1999) 10 10 0.8 0.9 1 1.1 1.2 0.5 0.6 0.7 0.8 0.9 1 1.1 Ionic Radius (Å) Ionic Radius (Å) 203 Tables Table 3-1 Data sources and experimental run conditions Melt SiO2 Garnet CaO Olivine Al2O3 Reference na P (GPa) T (ºC) Duration (h) (wt%) Melt Mg#b (wt%) (wt%) Mineral Mg# Garnet-melt partitioning experiments Yurimoto and Ohtani (1992) 3 16.0-20.0 1900-2000 0.07-0.08 47.70-49.11 90.9-93.4 1.14-1.86 - 95.4-97.6 Johnson (1998) 1 3.0 1430 48 51.40 47.7 7.05 - 64.6 Salters and Longhi (1999) 10 2.4-2.8 1465-1580 24 44.20-45.80 62.0-80.5 3.65-5.52 - 79.1-89.2 van Westrenen et al. (1999) 2 3.0 1560-1565 21 48.40-48.90 100.0 6.70-7.50 - 100.0 van Westrenen et al. (2000) 2 2.9-3.0 1538-1540 21.5 47.44-47.64 55.4-83.0 5.18-7.71 - 64.0-88.4 Klemme et al. (2002) 1 3.0 1400 70 56.70 100.0 6.7 - 100.0 Salters et al. (2002) 4 3.2-3.4 1615-1675 19-24 45.70-47.50 75.0-81.3 2.90-4.09 - 86.8-90.3 Bennett et al. (2004) 2 3.0 1330-1402 24 52.40 100.0 10.00 - 100.0 Corgne and Wood (2004) 1 25.0 2300 0.5 42.08 70.6 2.57 - 88.8 Pertermann et al. (2004) 9 2.9-3.1 1325-1390 4.0-34 52.37-57.05 37.8-63.0 6.27-9.34 - 53.9-66.5 Walter et al. (2004) 2 23.0-23.5 2300 0.83-1.00 44.75-46.49 86.2-90.8 3.64-4.32 - 94.9-96.5 Draper et al. (2006) 5 3.5-7.0 1600-1775 30-141 44.00-49.40 61.7-70.6 3.76-5.18 - 74.3-78.8 Dwarzski et al. (2006) 4 5.5-7.0 1650-1700 0.03-2.25 24.18-30.81 38.7-44.9 3.10-4.66 - 56.6-66.5 Tuff and Gibson (2007) 4 3.0-7.0 1425-1750 4.0-25 48.43-51.53 61.3-70.8 4.74-5.19 - 70.1-76.7 Corgne et al. (2012) 3 10.0-17.0 1975-2220 0.75-2.50 46.60-48.50 85.1-88.8 1.67-2.12 - 93.7-95.5 Suzuki et al. (2012) 11 3.0-20.0 1550-2200 0.17-2.00 47.75-57.62 54.0-63.9 7.38-10.58 - 65.6-77.0 Total range 64 2.4-25.0 1325-2300 0.03-141 24.18-57.62 37.8-100.0 1.14-10.58 53.9-100.0 Olivine-melt partitioning experiments Beattie (1994) 6 0.0001 1190-1495 24-720 43.81-48.44 47.7-87.0 - 0.059-0.225 74.4-95.9 Evans et al. (2008) 9 0.0001 1400 192 43.83-58.32 100.0 - 0.011-0.159 100.0 Mallmann and O'Neill (2009) 42 0.0001-1.0 1300-1325 47-48 45.43-56.51 94.1-100.0 - 0.003-0.380 98.1-100.0 Tuff and O'Neill (2010) 56 0.0001 1370-1400 20-72 40.08-58.55 62.3-99.7 - 0.010-0.340 85.1-99.9 Imai et al. (2012) 7 0.0001-10.0 1590-2150 1-20 44.94-48.92 82.1-91.1 - 0.060-0.170 93.0-96.1 Mallmann and O'Neill (2013) 57 0.0001-2.0 1200-1530 6-288 43.39-56.00 31.6-100.0 - 0.002-0.115 60.2-100 Total range 177 0.0001-10.0 1190-2150 1-720 40.08-58.55 31.6-100.0 0.002-0.380 60.2-100 a n represents the number of experiments used in model parameterization b Mg# = 100×Mg/(Mg+Fe) in mole 204 CHAPTER 4 4 An Assessment of Subsolidus Re-Equilibration on REE Distribution among Mantle Minerals Olivine, Orthopyroxene, Clinopyroxene, and Garnet in Peridotites Chenguang Sun and Yan Liang Department of Geological Sciences, Brown University Providence, RI 02912, USA Published in Chemical Geology, 372, 80-91, 2014 205 Abstract The distribution of rare earth elements (REEs) in mantle minerals depends on temperature, pressure, and mineral composition. We developed parameterized lattice strain models for REE partitioning among mantle minerals (olivine, orthopyroxene, clinopyroxene, and garnet) using mineral-melt partitioning models that were calibrated against experimentally determined high quality mineral-melt REE partition coefficients. The validity of the mineral-mineral REE partitioning models were independently tested using measured REE abundances in minerals from well-equilibrated mantle peridotites and eclogites reported in the literature. Using the new partitioning models, we critically assessed the extent of subsolidus re-equilibration on REE distribution among major rock-forming minerals in spinel and garnet peridotites. During subsolidus re-equilibration, REE are preferentially partitioned into clinopyroxene in peridotites. The extent of REE redistribution in clinopyroxene depends on the modal abundance of clinopyroxene in the peridotite. Subsolidus exchange with orthopyroxene and olivine can increase heavy REE abundances in clinopyroxene from spinel harzburgite and middle REE abundances in clinopyroxene from garnet harzburgite by a factor of three. The higher than expected heavy REE abundances in clinopyroxene from spinel harzburgite may give rise to a false garnet signature in residual peridotites. The extents of melting for abyssal peridotites based on REE abundances in clinopyroxene can be significantly over-estimated without proper correction for subsolidus re- equilibration. REE abundances in both clinopyroxene and orthopyroxene are needed to assess the melting processes from residual peridotites. 206 1. Introduction Major rock-forming minerals in the Earth’s upper mantle include olivine, orthopyroxene (opx), clinopyroxene (cpx), garnet, spinel and plagioclase. These minerals constitute the dominant lithology, peridotite, in the upper mantle. During partial melting in the upper mantle, cpx in peridotite is preferentially consumed to produce melt (e.g., Walter, 2003). Because cpx has high affinity for incompatible elements, trace element abundances in cpx from peridotite have been extensively used to infer melting processes in the upper mantle (e.g., Johnson et al., 1990). However, trace elements would redistribute among residual minerals during subsequent cooling under subsolidus conditions, which can potentially affect the interpretation of high temperature magmatic processes. The purpose of the present study is to quantify and critically assess the effect of subsolidus re-equilibration on REE distribution among major rock-forming minerals in the upper mantle. The distribution of trace elements between mantle minerals depends on temperature (T), pressure (P), major element compositions (X) of the minerals, and ionic radii of the trace elements, and can be quantified by empirical or semi-empirical models (e.g., Stosch, 1981, 1982; Seitz et al., 1999; Witt-Eickschen and O’Neill, 2005; Lee et al., 2007; Liang et al., 2013). In a recent study, Liang et al. (2013) developed a parameterized model for REE partitioning between coexisting cpx and opx in mafic and ultramafic rocks by combining two independently calibrated lattice strain models for REE partitioning between cpx and basaltic melt (Sun and Liang, 2012) and between low-Ca pyroxene and basaltic melt (Yao et al., 2012). Figure 1 displays calculated opx-cpx REE partition coefficients for a well-equilibrated spinel harzburgite xenolith and a well- equilibrated spinel lherzolite xenolith using the model of Liang et al. (2013). For comparison, we also plot calculated opx-cpx REE partition coefficients for the same samples using the empirical model of Witt-Eickschen and O’Neill (2005) and the semi-empirical model of Lee et al. (2007). All or part of the data used to calibrate the latter two models is from well-equilibrated mantle 207 xenoliths whose equilibrium temperatures are model dependent. Figure 1 shows the significant improvement of the model of Liang et al. (2013) over the model of Witt-Eickschen and O’Neill (2005) and the model of Lee et al. (2007). Liang et al. (2013) also demonstrated that their model predicted opx-cpx REE partition coefficients are in excellent agreement with the measured values from well-equilibrated spinel peridotites reported in the literature (see Section 2.4 for more discussion). The excellent agreement not only justifies the application of their model to subsolidus conditions but also indicates that similar approaches may also be valid for REE partitioning in other mineral-melt and mineral-mineral systems. This leads to the development of parameterized lattice strain models for REE partitioning between olivine and basaltic melt and between garnet and basaltic melt (Sun and Liang, 2013a). In this study, we expand the opx-cpx REE partitioning model of Liang et al. (2013) and integrate our garnet-melt and olivine-melt REE partitioning models to build internally consistent lattice strain models for mineral-mineral REE partitioning. These new models quantify the effects of pressure, temperature and mineral compositions on REE partitioning between two minerals and enable us to critically assess the effect of subsolidus re-equilibration on REE distribution in spinel and garnet peridotites and its implication for the interpretation of melting processes in the upper mantle. 2. Mineral-Mineral REE Partitioning Models 2.1. The lattice strain model The partition of a REE between two phases α and β can be described by the exchange reaction: (REE)α ! (REE)β (1) The equilibrium constant (K) can be expressed as 208 ⎛ aREE β ⎞ ⎛ X REE β β γ REE ln K = ln ⎜ α ⎟ = ln ⎜ α α ⎟ = − ⎞ β ΔG0 + ΔGstrain ( α − ΔGstrain ) , (2) ⎝ aREE ⎠ ⎝ X REEγ REE ⎠ RT where aREE , X REE , and γ REE are activity, concentration, and activity coefficient of a REE, respectively; R is the gas constant; and T is temperature; ΔG0 is the change in Gibbs free energy for strain-free exchange of REE between phases α and β; ΔGstrain is the change in lattice strain energy for REE substituting in the phase. Brice (1975) derived an expression to describe ΔGstrain for the substitution of cation i of ionic radius ri into an “ideal” or strain-free cation site of radius r0 in a crystal, ⎡r 1 3⎤ ΔGstrain = 4π EN A ⎢ 0 ( r0 − ri ) − ( r0 − ri ) ⎥ , 2 (3) ⎣2 3 ⎦ where E is the apparent Young’s modulus for the lattice site; NA is Avogadro’s number. In a mineral-melt system, ΔGstrain for the melt phase can be neglected since the melt structure is much more relaxed than the crystal. The mineral-melt REE partition coefficient ( min-melt DREE ) takes on the simple form ⎛ X REE min ⎞ ΔG0 + ΔGstrain min ln D min-melt REE = ln ⎜ melt ⎟ = − + ln γ REE melt − ln γ REE min . (4) ⎝ REE ⎠ X RT Substituting Eq. (3) into Eq. (4), we obtain the well-known lattice strain model of Blundy and Wood (1994) for mineral-melt REE partitioning ⎧⎪ 4π EN A ⎡ r0 1 3 ⎤⎫ ⎪ ( r0 − rREE ) − ( r0 − rREE ) ⎥ ⎬ , 2 min-melt DREE = D0 exp ⎨− ⎢ (5a) ⎪⎩ RT ⎣ 2 3 ⎦ ⎭⎪ ΔG0 ln D0 = − + ln γ REE melt − ln γ REE min , (5b) RT 209 where D0 is the partition coefficient for strain-free substitution; rREE is the ionic radius of a given REE. In general, the lattice strain parameters (D0, r0 and E) vary as functions of temperature, pressure and compositions of the mineral and melt (e.g., Blundy and Wood, 1994; Wood and Blundy, 2003). In a mineral-mineral system, the free energy change ΔG0 in Eq. (2) can be described by ( ΔG β 0 ) − ΔG0α , where ΔG0β and ΔG0α are the changes in Gibbs free energy for strain-free exchange of REE between mineral β and melt and between mineral α and the same melt, respectively. Similar to Eq. (4), we can obtain an expression for the mineral-mineral REE partitioning, β -α ⎛ X β ⎞ ⎡⎛ ΔG0β + ΔGstrain β β ⎞ ln DREE = ln ⎜ REE α ⎟ = ⎢ ⎜ − + ln γ melt REE − ln γ REE ⎟ ⎝ X REE ⎠ ⎢⎣⎝ RT ⎠ . (6) ⎛ ΔG0α + ΔGstrain α α ⎞⎤ −⎜ − + ln γ REE melt − ln γ REE ⎟⎥ ⎝ RT ⎠ ⎥⎦ Substituting Eq. (3) for minerals α and β into Eq. (6), we obtain a lattice strain model for REE partitioning between minerals β and α, β -melt D0β ⎡ 4π N A E β ⎛ r0β β 3⎞ DREE ( ) ( 1 β ) 2 β -α D = α -melt = α exp ⎢ − r − rREE − r0 − rREE ⎟ REE DREE D0 ⎣⎢ RT ⎜⎝ 2 0 3 ⎠ , (7a) 4π N A E α ⎛ r0α α 3⎞ ⎤ ( ) 1 ( ) 2 + r − rREE − r0α − rREE ⎟ ⎥ RT ⎜⎝ 2 0 3 ⎠ ⎥⎦ ΔG0β ln D0β = − + ln γ REE melt β − ln γ REE , (7b) RT ΔG0α ln D0α = − + ln γ REE melt α − ln γ REE . (7c) RT Equation (7a) is similar to the mineral-mineral partitioning model of Lee et al. (2007), except β −α DREE in the latter study is pinned to Lu partitioning between two minerals for all the REEs. 210 However, given the parameterized lattice strain models for mineral-melt REE partitioning, the latter procedure is unnecessary, as demonstrated in Liang et al. (2013) and further below. 2.2. Mineral-melt REE partitioning models We have recently developed parameterized lattice strain models for REE and Y partitioning between mantle minerals (olivine, clinopyroxene, low-Ca pyroxene, and garnet) and basaltic melts following a new protocol that involves careful selection of high quality data from mineral-melt partitioning experiments and rigorous statistical treatment of partitioning data through parameter swiping and simultaneous or global nonlinear least squares inversion of all the filtered partitioning data for each mineral-melt system (for details see Sun and Liang, 2012, 2013a, 2013b; Yao et al, 2012). Our database includes 43 cpx-melt partitioning experiments (conducted at 1042–1470ºC and 0–4 GPa), 38 low-Ca pyroxene-melt partitioning experiments (1080–1660ºC and 0–3.4 GPa), 64 garnet-melt partitioning experiments (1325–2300ºC and 2.4– 25 GPa), and 177 olivine-melt partitioning experiments (1190–2150ºC and 1 atm–10 GPa). Figure 2 shows the large ranges of cpx, low-Ca pyroxene and garnet compositions from the compiled experiments. The pyroxenes are mostly Mg-rich with Mg# [= 100 × Mg/(Mg + Fe) in mole] of 54–100 for cpx (circles) and Mg# of 70–100 for low-Ca pyroxene (squares, Fig. 2a), while the compiled garnets are rich in pyrope or majorite components (Fig. 2b). The olivine from the compiled experiments also covers a wide range in composition (e.g., Mg# = 60–100, and Al2O3 = 0.002–0.38wt%). The supplementary material lists the parameterized lattice strain models for REE partitioning between mantle minerals (olivine, low-Ca pyroxene, cpx, and garnet) and basaltic melts. For convenience and consistency among the minerals, we chose VIII-fold coordinated ionic radii of REE and Y for the four mineral-melt pairs, which also eliminates an inconsistency between the VI- and VIII-fold coordinated ionic radii of REE listed in Shannon (1976) (Yao et al., 2012; see also supplementary material in the supplementary material for additional 211 discussion). In the cpx model, D0 is correlated positively with Al in the tetrahedral site (AlT) and Mg in the M2 site (MgM2) of pyroxene but negatively with temperature and water content in the melt; r0 shows inverse relationships with MgM2 and AlM1; E and r0 are positive correlated due to the nonlinear nature of Eq. (5a). In the low-Ca pyroxene model, D0 increases with the increases of Ca on the M2 site (CaM2) and AlT in pyroxene but the decrease of temperature and TiO2 content in the melt, r0 correlates positively with CaM2 and MgM2 in pyroxene, and E correlates positively with r0 but negatively with CaM2 in pyroxene. In the garnet model, D0 is negatively correlated with temperature, pressure and Ca in garnet, r0 increases with the increase of Ca in garnet, and E and r0 are positively correlated. Finally, We found that constant E and r0 are adequate to fit the compiled olivine partitioning data and that in the olivine mode, D0 increases with the addition of Al in olivine but decreases with the increases of forsterite content in olivine and pressure. These parameterized lattice strain models reproduce the compiled high quality experimental partitioning data to within a factor of two, indicating significant improvement over previous models. 2.3. Mineral-mineral REE partitioning models According to the parameterized lattice strain models listed in the supplementary material, distributions of REEs between mantle minerals and basaltic melts are mainly controlled by mineral composition, pressure and temperature. The effect of melt composition is either indirect (i.e., acting through mineral composition) or insignificant unless H2O or TiO2 in the melt is very high. Hence for typical mafic and ultramafic systems relevant to the Earth’s upper mantle and lower crust, we can construct mineral-mineral REE partitioning models using Eq. (7a) and the lattice strain parameters listed in the supplementary material. Liang et al. (2013) discussed the calibration and implementation of the opx-cpx REE partitioning model in details. Here we focus on olivine-cpx and garnet-cpx REE partitioning models. From Eq. (7a), we have 212 ol-melt D0ol ⎡ 4π N A E ol ⎛ r0ol ol 3⎞ DREE ( ) ( 1 ol ) 2 D ol-cpx = cpx-melt = cpx exp ⎢ − r − rREE − r0 − rREE ⎟ REE DREE D0 ⎢⎣ RT ⎜⎝ 2 0 3 ⎠ , (8a) 4π N A E cpx ⎛ r0cpx cpx 3⎞ ⎤ ( ) 1 ( ) 2 + ⎜ 2 r0 − rREE − r0cpx − rREE ⎟ ⎥ RT ⎝ 3 ⎠ ⎥⎦ grt-melt D0grt ⎡ 4π N A E grt ⎛ r0grt grt 3⎞ DREE ( ) ( 1 grt ) 2 D grt-cpx REE = cpx-melt = cpx exp ⎢ − ⎜ 2 r0 − rREE − r0 − rREE ⎟ DREE D0 ⎢⎣ RT ⎝ 3 ⎠ . (8b) 4π N A E cpx ⎛ r0cpx cpx 3⎞ ⎤ ( ) 1 ( ) 2 + ⎜ 2 r0 − rREE − r0cpx − rREE ⎟ ⎥ RT ⎝ 3 ⎠ ⎥⎦ 2.4. Model validation The validity of the two models can be independently tested through comparing mineral- mineral REE and Y partition coefficients predicted by Eqs. (8a and 8b) with those directly measured in well-equilibrated mantle xenoliths. For the olivine-cpx partitioning model, we use mineral major and trace element compositions reported by Witt-Eickschen and O’Neill (2005) and Witt-Eickschen et al. (2009) in well-equilibrated spinel peridotites from Germany, Monglia, Mexico, and Southwestern USA. The same samples were also used by Liang et al. (2013) to validate their opx-cpx REE partitioning model. For the garnet-cpx partitioning model, we use mineral compositions reported by Harte and Kirkley (1997) and Huang et al. (2012) in well- equilibrated eclogites (Type II) from the Roberts Victor kimberlite pipe in South Africa. The two- pyroxene thermometer of Brey and Köhler (1990) was used to calculate the equilibrium temperatures of the peridotite samples by assuming a pressure of 1.5 GPa, and the garnet-cpx thermometer of Ravna (2000) was used to calculate the equilibrium temperatures of the eclogite samples by assuming a pressure of 3 GPa. Figure 3 shows that the model-derived opx-cpx, olivine-cpx, and garnet-cpx REE and Y partition coefficients are generally in good agreement with the measured values reported in the literature. The outliers presumably can be attributed to secondary alterations or poor analytical 213 precisions (i.e., some light REEs in Figs. 3a and 3c). The good agreement indicates that the lattice strain parameters that we independently calibrated for olivine, opx, cpx and garnet under magmatic conditions are internally consistent and can be extrapolated to subsolidus conditions. 3. P-T-X Dependent REE Partitioning among Mantle Minerals Equation (7a) with the lattice strain parameters listed in the supplementary material allows us to investigate the effects of temperature, pressure and mineral composition on REE partitioning between minerals under subsolidus conditions. Figures 4 and 5 display mineral- mineral REE partition coefficients as a function of ionic radii for different temperatures, pressures and mineral compositions. The mineral-mineral REE partition coefficients were calculated for three temperatures (700ºC, 1000ºC, and 1300ºC) and three pressures (2 GPa, 8 GPa, and 14 GPa) to cover wide ranges of P-T conditions. To demonstrate the effect of mineral composition, we selected two spinel peridotites (a harzburgite and a lherzolite: solid and dashed curves, respectively) for major element compositions in olivine, cpx and opx in Figs. 4a-b, two eclogites (low-Ca garnet and high-Ca garnet: solid vs. dashed curves) for major element compositions in garnet and cpx in Figs. 4c-d, and two garnet peridotites (a harzburgite and a lherzolite: solid vs. dashed curves) for major element compositions in olivine, opx and garnet in Figs. 5a-d. The spinel peridotite samples are MM766 (harzburgite) and DW196A (lherzolite) from Witt- Eickschen and O’Neill (2005) and Witt-Eickschen et al. (2009), eclogite samples are RV07-12 (low-Ca garnet) and RV07-34 (high-Ca garnet) from Huang et al. (2012), and the garnet peridotite samples are F-5 (harzburgite) and F-16 (lherzolite) from Lazarov et al. (2012). Figure 4 shows that olivine-cpx, opx-cpx and garnet-cpx REE partition coefficients decrease systematically with the increase of ionic radii and the decrease of temperature. As temperature decreases from 1300 ºC to 700 ºC, olivine-cpx REE partition coefficients decrease by two to three orders of magnitude from heavy to light REEs (Fig. 4a); opx-cpx REE partition coefficients decrease by factors of five to twenty from heavy to light REEs (Fig. 4b); garnet-cpx 214 light REE partition coefficients decrease by factors of ten to eighteen, while garnet-cpx heavy REE partition coefficients are relatively insensitive to the temperature variation (Fig. 4c). Finally, garnet-cpx REE partition coefficients all decrease with the increase of pressure, and vary by one order of magnitude in the pressure range of 2-14 GPa (Fig. 4d). With the increase of ionic radii, olivine-garnet REE partition coefficients also decrease while opx-garnet REE partition coefficients increase (Fig. 5). Nonetheless, they both decrease with the decrease of temperature. As temperature decreases from 1300ºC to 700ºC, olivine-garnet REE partition coefficients decrease uniformly by two orders of magnitude (Fig. 5a); however, opx-garnet REE partition coefficients decrease by only factors of one to five from light to heavy REEs (Fig. 5b), indicating that the partitioning of heavy REEs between opx and garnet is more sensitive to the temperature change. As pressure decreases from 14 GPa to 2 GPa, olivine-garnet REE partition coefficients show marginal variations (i.e., within a factor of two), whereas opx- garnet REE partition coefficients decrease by one order of magnitude. The very small variation of olivine-garnet REE partition coefficients indicates that the pressure effects on D0 for olivine and garnet nearly cancell each other in Eq. (7a). If temperature and pressure both decrease during cooling, the combining effects of temperature and pressure may lead to a larger variation in the opx-garnet REE partition coefficients. Mineral compositions are also important in controlling mineral-mineral REE partition coefficients. Figures 4a-b show that olivine-cpx and opx-cpx heavy REE partition coefficients are both about factors of two to three lower in the fertile spinel peridotite (dashed curves), whereas opx-cpx light REE partition coefficients are about factors of two to three higher. Thus, for a more fertile spinel peridotite, olivine-cpx and opx-cpx REE partition coefficients in the Onuma diagram (partition coefficients vs. ionic radii; Onuma et al., 1968) would rotate around middle REEs to a shallower slope at a given temperature. Figures 4c-d shows that garnet-cpx REE partition coefficients for the eclogite with high-Ca garnet (dashed curves) are greater than those for the eclogite with low-Ca garnet (solid curves) by factors of two to ten from heavy to light 215 REEs at a given temperature and pressure. This suggests that garnet-cpx REE partition coefficients also strongly depend on mineral major element compositions. In Fig. 5, we compare the olivine-garnet and opx-garnet REE partition coefficients for a garnet lherzolite (dashed curves) and a garnet harzburgite (solid curves). There are no obvious differences in heavy REE partition coefficients for olivine-garnet and opx-garnet between these two garnet peridotites. Olivine-garnet and opx-garnet partition coefficients for light REEs, however, are about factors of two to three smaller in the garnet lherzolite. Overall, mineral compositions have strong influence on the absolute values of mineral-mineral REE partition coefficients and the curvatures in the Onuma diagram, especially for garnet-cpx REE partition coefficients. 4. Implications for Subsolidus Re-Equilibration The mineral-mineral REE partitioning models developed in this study and that in Liang et al. (2013) allow us to assess the extent of REE redistribution among mantle minerals during subsolidus re-equilibration. In this section, we utilize four types of mantle peridotites (spinel lherzolite, spinel harzburgite, garnet lherzolite, and garnet harzburgite) to demonstrate the influence of subsolidus re-equilibration on REE abundances in different mantle minerals. Because spinel is a minor mineral phase in typical mantle peridotites and has extremely low abundances of REEs, it will not be considered here. Four samples from Witt-Eickschen and O’Neill (2005) and Lazarov et al. (2012) are chosen to represent these four types of mantle peridotites. According to these studies, the four samples are well equilibrated, contain no secondary minerals or interstitial glasses, and display little evidence of mantle metasomatism. The major element and REE abundances in the minerals and bulk rocks as well as the mineral modal abundances are listed in Table S1. Although the major element compositions and modal abundances of minerals in a sample also change with temperature and pressure during subsolidus re-equilibration, an accurate 216 thermodynamic model is still not available to account for these changes. Here for purpose of demonstration, we neglect the variations of major element compositions and modal abundances for a given sample during cooling and use the measured major element compositions in the mantle xenoliths to calculate mineral-mineral REE partition coefficients through Eq. (7a). We assume chemical equilibrium during subsolidus re-equilibration. With reported mineral proportions (p) and REE concentrations in the bulk rocks (Cbulk), we calculate REE concentrations in cpx (Ccpx) at selected temperatures (1300ºC, 1200ºC, 1100ºC, 1000ºC, 900ºC, and 800ºC) using the mass balance equation, Cbulk Ccpx = . (9) pcpx + popx D opx-cpx REE + pgrt DREE grt-cpx + pol DREE ol-cpx The concentrations of REE in other minerals can then be obtained from mineral-cpx REE partition coefficients. Since the equilibrium pressure is insignificant in determining REE partitioning among olivine, cpx and opx at low pressures, we assume a pressure of 1 GPa to calculate REE re-distribution in the spinel peridotites. The effect of pressure, however, is very significant on REE partitioning in garnet. To incorporate both the effects of temperature and pressure, we examine the subsolidus distribution of REEs in garnet peridotites at the selected temperatures along the 42 mW/m2 conductive geotherm of Chapman and Pollack (1977). The calculated REE concentrations in minerals are normalized by their respective values at 1300ºC and are shown in Figs. 6 and 7. Figure 6 displays the variations of REE abundances in cpx, opx and olivine in the spinel lherzolite and spinel harzburgite at selected temperatures. As temperature decreases from 1300ºC to 800ºC, in the spinel lherzolite, REE abundances in cpx increase by within a factor of 1.5, those in opx decrease by factors of 6 to 14, whereas those in olivine decrease by 1.5 to 3 orders of magnitude. Light REEs in olivine and opx show larger variations, while heavy REEs in cpx show larger variations. The decreases of REE abundances in olivine and opx are due to the decreases of olivine-cpx and opx-cpx REE partition coefficients with decreasing temperature, corresponding 217 to the increase of REE abundances in cpx. However, REE concentrations in cpx do not significantly change during subsolidus re-equilibration because of the high initial REE concentrations in cpx and the large proportion of cpx in the spinel lherzolite (14%). One would expect even smaller variations of REE abundances in cpx for a higher cpx modal proportion in the spinel lherzolite (cf. Eq. 9). With the decrease of temperature from 1300ºC to 800ºC, in the spinel harzburgite, REE abundances in olivine decrease by one to three orders of magnitude; light REE abundances in opx decrease by about one order of magnitude, while heavy REE abundances in opx decrease by factors of two to five; light REE abundances in cpx increase by within a factor of 1.2, but heavy REE abundances in cpx increase by up to a factor of 2.8. Due to the small modal proportion of cpx in the spinel harzburgite, the concentrations of REEs, especially those of heavy REEs, in cpx become significantly higher than those at magmatic conditions during subsolidus re-equilibration. We will examine the geochemical implication of this last observation in the next section. Figure 7 shows the variations of REE concentrations in garnet, cpx and opx in the garnet lherzolite and garnet harzburgite at selected temperatures along the 42 mW/m2 conductive geotherm of Chapman and Pollack (1977). As temperature decreases from 1300ºC to 800ºC (with a pressure decrease from 5.8 to 2.9 GPa), heavy REE contents in garnet slightly increase because heavy REEs are highly compatible in garnet. Light REEs are incompatible in garnet such that their abundances in garnet gradually decrease by one order of magnitude. For both the garnet lherzolite and garnet harzburgite, REE contents in opx systematically decrease with the decrease of temperature, by factors of 8 to 13 from heavy to light REEs. Light and middle REEs in cpx increase with the decrease of temperature, with middle REEs more sensitive to temperature changes than light REEs. However, heavy REEs in cpx decrease with the decrease of temperature and pressure. The small variations of light REEs in cpx are due to their higher compatibility in cpx, while the decrease of heavy REEs in cpx results from the strong pressure dependence of REE partitioning in garnet. 218 With temperature decreasing from 1300ºC to 800ºC, middle REE contents in cpx in the garnet lherzolite only increase by up to a factor of 2, whereas those in the garnet harzburgite increase by up to a factor of 3.2. Light REE contents in cpx in the garnet harzburgite also show larger variations than those in the garnet lherzolite. Overall, REE abundances in cpx from garnet peridotites would not be significantly affected by subsolidus re-equilibration along a conductive geotherm as long as cpx modal abundance is high (i.e., greater than 6.5%). This conclusion also applies to mantle eclogites. The preceding examples demonstrate that subsolidus re-equilibration of mantle peridotites can significantly change REE abundances in olivine and opx, and light and middle REE abundances in garnet. For peridotites with high cpx modal abundances, REEs in cpx retain most of their magmatic signatures and thus are robust tracers for melting processes. However, when cpx modal abundances are very low, heavy REE abundances in cpx from spinel peridotites may become considerably higher at lower subsolidus temperatures, and middle REE abundances in cpx from garnet peridotites may increase by up to a factor of 3 at lower subsolidus temperatures. Therefore, REE abundances in cpx from harzburgites that have experienced extensive subsolidus re-equilibration may mislead the interpretation of magmatic processes, such as the extent of mantle melting and presence of garnet in the mantle source. 5. Application to Mantle Melting REEs in cpx from abyssal peridotites have been widely used to decipher mantle-melting processes (e.g., Johnson et al., 1990). Based on the measured REE abundances in cpx from abyssal peridotites collected along the Central Indian Ridge, Hellebrand et al. (2002) argued that high heavy REE concentrations in cpx indicate melting in the garnet stability field. However, through inversion of the measured REE abundances in cpx reported by Hellebrand et al. (2002) using a steady-state melting model, Liang and Peng (2010) found that heavy REE abundances in 7 of the 10 examined samples are about a factor of two higher than those predicted by the best-fit 219 values from the least squares analyses (see their Fig. 8). They further demonstrated that melting of a garnet lherzolite could not significantly improve the fit to the measured heavy REEs in residual cpx. They suggested that the slightly elevated heavy REE patterns in residual cpx may result from the composition-dependent cpx-melt partition coefficients or melting of a garnet pyroxenite-veined lherzolite. However, using a parameterized lattice strain model for cpx-melt REE partitioning, Sun and Liang (2012) demonstrated that the competing effects between temperature and cpx composition give rise to nearly constant cpx-melt REE partition coefficients during adiabatic melting of a spinel lherzolite mantle. According to the REE-in-two-pyroxene thermometer of Liang et al. (2013), abyssal peridotites from the Gakkel Ridge reported in Hellebrand et al. (2005) have closure or apparent temperatures between 1074-1256°C, while abyssal peridotites from the Southwest Indian Ridge (SWIR) reported in Seyler et al. (2011; 52°E – 68°E) and Warren et al. (2009; 9ºE – 16ºE and the Atlantis II Fracture Zone) have closure or apparent temperatures between 1115 – 1281°C. The apparenttemperatures of REEs in most of these abyssal peridotites are below the potential temperatures (1280ºC – 1400ºC; Herzberg et al., 2007) of the Earth’s upper mantle. Thus, it is possible that heavy REE abundances in cpx from abyssal peridotites are reset by subsolidus re- equilibration. To examine the influence of subsolidus re-equilibration on REE abundances in residual cpx cpx from abyssal peridotites, we calculate the REE abundances in residual cpx ( Cs ) from melting of a depleted mantle using the steady-state melting model of Liang and Peng (2010) k p −1 Cscpx = kcpx C ⎡ 0 s ⎢1+ ( ) 1− k p − R ⎤ F⎥ 1−k p −R , (10) k0 ⎢ k0 ⎥⎦ ⎣ where k0 is the bulk solid-melt partition coefficient for a trace element at the onset of melting; kp is the bulk solid-melt partition coefficient from the melting reaction; kcpx is the cpx-melt partition 0 coefficient; Cs is the initial concentration of a trace element in the bulk solid; F is the degree of 220 melting; and R is the ratio of melt suction rate and melting rate; Equation (10) recovers the perfect fractional melting model when R = 1 and the batch melting model when R = 0 . We consider two examples in the following discussion. In the first example, we assume near fractional melting ( R = 0.95 ) of a spinel lherzolite followed by subsolidus re-equilibration. For comparison, we use the same initial mineral proportions, starting mantle composition, and mineral-melt partition coefficients as those used in Liang and Peng (2010) (see caption of Fig. 8 for details). We correct the REE abundances in residual cpx using Eq. (9) at three subsolidus temperatures (1200ºC, 1000ºC and 800ºC) and 1 GPa. The major element compositions of minerals were derived from pMELTS (Ghiorso et al., 2002) by near fractional melting of the same starting mantle composition along the 1350ºC adiabat. The calculation results are compared with global abyssal peridotite data in Fig. 8. Clearly, near fractional melting of a spinel lherzolite (heavy red line) cannot explain the variations of heavy REE abundances in residual cpx from abyssal peridotites for a given extent of melting (grey field in Fig. 8). Interestingly, subsolidus re-equilibration of residual peridotites can recover a significant range of variations of heavy REE abundances in residual cpx without introducing additional assumptions (e.g., melting of a garnet lherzolite or a heterogeneous mantle source). In the second example, we invert for the degree of melting (F) and relative melt suction rate ( R ) using Eq. (10) and REE abundances in cpx reported in Hellebrand et al. (2002) after correction for subsolidus re-equilibration. With measured REE concentrations in cpx, mineral major element compositions and modal proportions reported in Hellebrand et al. (2002), we corrected the effect of subsolidus equilibration on REE concentrations in these cpx using the following steps: first, we used Eq. (7a) to estimate REE concentrations in olivine and opx at an equilibrium temperature; we then calculated the bulk REE concentrations in the peridotite; and finally, we used Eq. (9) to calculate REE concentrations in cpx at a magmatic temperature of 221 1350ºC. Since REE abundances in opx were not reported in Hellebrand et al. (2002), we are unable to make estimates on the subsolidus re-equilibration temperature (or closure temperature) for REE in the two pyroxenes in the Central Indian Ridge samples. For purpose of illustration, we use the average temperature (1183ºC) and the upper (1281ºC) and lower bounds (1074ºC) as equilibrium temperatures for the abyssal peridotites to explore the subsolidus effects for the Central Indian Ridge samples that have high heavy REE abundances in cpx (Hellebrand et al., 2002). The corrected REE concentrations in these cpx are shown with the measured values in Fig. 9 and Supplementary Fig. S1. As expected, the measured heavy REE concentrations in the cpx are higher than the corrected values by about factors of two to three. To obtain the melting parameters for the corrected data, we used the nonlinear regression cpx method as described in Liang and Peng (2010) and fit the REE concentrations in cpx ( Cs ) to the steady-state melting model (Eq. 10). For simplicity, we assume that melting starts in the spinel lherzolite field. The initial mineral proportions, starting mantle composition, and mineral- melt partition coefficients are the same as those used in Fig. 8. The nonlinear least squares fits for the measured and corrected REE concentrations in cpx are shown as dashed and solid curves, respectively, in Fig. 9 and Supplementary Fig. S1, and the inverted melting parameters are listed in Table 1. As shown in Figs. 9 and S1 the corrected cpx REE concentrations can be better fit by Eq. (10). This indicates that the higher heavy REE abundances in cpx from abyssal peridotites more likely result from subsolidus re-equilibration than melting of a garnet peridotite mantle. It is also important to note that the corrected samples show higher extents of melting and lower melt suction rates (Table 1). Thus, one may underestimate the extent of melting and overestimate the melt suction rate by using the measured REE abundances in cpx from residual peridotites without accounting for subsolidus re-equilibration. It is apparent that the degrees of melting for the lower equilibrium temperature (1074 ºC) are about 1 – 3% greater than those for the higher temperature (1183 ºC), but the melt suction 222 rates for the lower temperature are slightly smaller. The significant differences indicate the trade- off between the subsolidus temperature and the melting parameters: the larger the correction for subsolidus re-equilibration (due to a lower temperature), the greater the extent of melting and the smaller the melt suction rate obtained from the corrected data. To properly correct for the effect of subsolidus re-equilibration, we suggest that one measures REE concentrations in both opx and cpx and use the REE-in-two-pyroxene thermometer of Liang et al. (2013) to determine the equilibrium or apparent temperature of REE in the peridotite. 6. Summary and Further Discussion Based on parameterized lattice strain models for mineral-melt REE partitioning for mantle minerals (olivine, pyroxenes and garnet), we have developed mineral-mineral partitioning models for REE between pairs of mantle minerals. These models reproduce the mineral-mineral REE partition coefficients for well-equilibrated mantle peridotites and eclogites reported in the literature, demonstrating the internal consistencies of the models and their applicability under subsolidus conditions. The temperature, pressure and composition dependent lattice strain parameters enable us to assess the effects of temperature, pressure and mineral composition on mineral-mineral REE partitioning. During subsolidus re-equilibration, major element compositions (and to a lesser extent mineral proportions) in a given sample also vary systematically as a function of temperature and pressure. This temperature- and pressure-induced composition effect, which has not been considered in the present study, may also play an important role in affecting mineral-mineral REE partitioning. Applying the new mineral-mineral REE partitioning models to different types of mantle peridotites, we have demonstrated that subsolidus re-equilibration results in significant redistribution of REE abundances in olivine, opx, garnet and perhaps cpx, in the order of decreasing variability. The extent of REE redistribution in cpx is insignificant when cpx modal abundances are high in residual peridotites or eclogites. We showed that the “garnet signature” — 223 high heavy REE abundances in the cpx could be an indicator of subsolidus equilibration of REEs due to the low cpx modal abundances in abyssal peridotites. Through nonlinear least squares analysis of the corrected REE concentrations in cpx from abyssal peridotites, we have inverted the melting parameters using a steady-state melting model. The inversion results show that the degree of melting can be overestimated and the melt suction rate can be underestimated for abyssal peridotites. Hence, correction for subsolidus re- equilibration is required to better interpret the melting processes through REE abundances in cpx from peridotites. Acknowledgements We thank Cin-Ty Lee for his constructive review that helped to improve this manuscript. This work was supported in part by NSF grant EAR-1220076 and NASA grant NNX13AH07G. References Anders, E., Grevesse, N., 1989. Abundances of the elements: Meteoritic and solar. 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The geochemistry of the volatile trace elements As, Cd, Ga, In and Sn in the Earth’s mantle: New evidence from in situ analyses of mantle xenoliths. Geochimica et Cosmochimica Acta 73(6), 1755-1778. Wood, B. J., Banno, S., 1973. Garnet-orthopyroxene and orthopyroxene-clinopyroxene relationships in simple and complex systems. Contributions to Mineralogy and Petrology, 42(2), 109-124. Wood, B. J., Blundy, J. D., 2002. The effect of H2O on crystal- melt partitioning of trace elements. Geochimica et Cosmochimica Acta 66(20), 3647-3656. Wood, B.J., Blundy, J.D., 2003. Trace element partitioning under crustal and uppermost mantle conditions: the influences of ionic radius, cation charge, pressure and temperature, in Treatise on Geochemistry, vol. 2, The Mantle and Core, edited by Carlson, R.W., Holland, H.D., and Turekian, K.K., pp. 392–424, Elsevier, New York. Workman, R.K., Hart, S.R., 2005. Major and trace element composition of the depleted MORB 228 mantle (DMM). Earth and Planetary Science Letters 231(1), 53-72. Yao, L., Sun, C., Liang, Y., 2012. A parameterized model for REE distribution between low-Ca pyroxene and basaltic melts with applications to REE partitioning in low-Ca pyroxene along a mantle adiabat and during pyroxenite-derived melt and peridotite interaction. Contributions to Mineralogy and Petrology 164(2), 261-280. Figure Captions Figure 4-1 Onuma diagrams showing predicted and measured orthopyroxene-clinopyroxene REE partition coefficients as a function of ionic radii for a well-equilibrated spinel harzburgite (MM766; a) from Witt-Eickschen and O’Neill (2005) and a well-equilibrated spinel lherzolite (DW196A; b) from Witt-Eickschen et al. (2009). The predicted values are shown as solid curves and are calculated using the models of Witt-Eickschen and O’Neill (2005), Lee et al. (2007) and Liang et al. (2013). Figure 4-2 Quadrilateral and ternary diagrams showing compositions of pyroxenes (a) and garnets (b) used in the clinopyroxene-melt REE partitioning model (Sun and Liang, 2012), the low-Ca pyroxene-melt REE partitioning model (Yao et al., 2012) and the garnet-melt REE partitioning model (Sun and Liang, 2013a). Di, En, Hd and Fs denote pyroxene end-members, diopside, enstatite, hedenbergite, and ferrosilite, respectively. Py, Alm, and Spess represent garnet end-members, pyrope, almandine, and spessartine, respectively. Figure 4-3 Comparisons of model-derived and measured REE partition coefficients for orthopyroxene-clinopyroxene (a), olivine-clinopyroxene (b), and garnet-clinopyroxene (c) from well-equilibrated spinel peridotites or eclogites. The peridotite samples are from cratonic lithospheric mantle (Witt-Eickschen and O’Neill, 2005; Witt-Eickschen et al., 2009), while the 229 eclogite samples are Type II eclogites collected from kimberlite pipes in South Africa (Harte and Kirkley, 1997; Huang et al., 2012). Solid blue lines are 1:1 lines, and dashed lines are 1:2 and 2:1 lines. Figure 4-4 Onuma diagrams showing the temperature, pressure and composition dependent REE partition coefficients for olivine-clinopyroxene (a), orthopyroxene-clinopyroxene (b), garnet- clinopyroxene (c-d). Red, green, and blue curves in Figs. 4a-c denote the partition coefficients at 1300 ºC, 1000 ºC and 700 ºC, respectively. Black, magenta, light blue curves in Fig. 4d represent the partition coefficients at 14 GPa, 8 GPa and 2 GPa, respectively. We assumed a pressure of 1 GPa for Fig. 4a, a pressure of 2 GPa for Fig. 4c, and a temperature of 1000 ºC for Fig. 4d. Solid and dashed curves show partition coefficients for different mineral compositions from spinel peridotites and eclogites. Figure 4-5 Onuma diagrams showing the temperature, pressure and composition dependent REE partition coefficients for olivine-garnet (a, c), orthopyroxene-garnet (b, d). The legends for the line colors are the same as those in Fig. 4. We assumed a pressure of 2 GPa for Figs. 5a-b, and a temperature of 1000 ºC for Figs. 5c-d. Solid and dashed curves show partition coefficients for different mineral compositions from two garnet peridotite samples. Figure 4-6 Re-distribution of REEs among clinopyroxene, orthopyroxene and olivine in a spinel lherzolite and a spinel harzburgite at selected temperatures and 1 GPa. We normalized mineral REE concentrations by their respective values at 1300ºC. The proportions and compositions of minerals are listed in supplementary Table S1. Figure 4-7 Re-distribution of REEs among clinopyroxene, garnet, and orthopyroxene in a garnet lherzolite and a garnet harzburgite at selected temperatures along the 42 mW/m2 conductive 230 geotherm. We normalized mineral REE concentrations by their respective values at 1300ºC. The conductive geotherm is from Chapman and Pollack (1977). The proportions and compositions of minerals are listed in supplementary Table S1. The normalized REE concentrations in olivine are similar to those in Fig. 6 and are not shown here. Figure 4-8 Variations of YbN and (Sm/Yb)N in clinopyroxene from abyssal peridotites. The subscript N denotes that Sm and Yb abundances are normalized by CI chondrite of Anders and Grevesse (1989). The grey filed shows the compilation of global abyssal peridotites in Hellebrand et al. (2002; see their Fig. 8). Red curve shows the calculation results of near fractional melting ( R = 0.95 ) of a spinel lherzolite mantle using Eq. (10). Curves marked with temperatures (1200ºC, 1000ºC, and 800ºC) represent results of subsolidus corrections through Eq. (9). To calculate REE abundances in residual clinopyroxene during near fractional melting, we used the same initial mineral proportions in the starting mantle as those in Liang and Peng (2010; 53% olivine + 27% opx + 17% cpx + 3% spinel), the melting reaction from Kinzler and Grove (1992; 35 opx + 59 cpx + 5 sp = 22 ol + 78 melt), mineral-melt partition coefficients of Kelemen et al. (2003), and the depleted MORB mantle in Workman and Hart (2005) as the starting mantle composition. To conduct the subsolidus correction, we used the mineral compositions derived from pMELTS (Ghiorso et al., 2002) by near fractional melting of the same starting mantle composition along the 1350ºC adiabat. Figure 4-9 Comparisons of the measured and corrected REE concentrations in clinopyroxene from an abyssal peridotite (ANTP89-15) along the Central Indian Ridge. The abyssal peridotite data are from Hellebrand et al. (2002) and have heavy REE concentrations in clinopyroxene higher than those derived from the nonlinear least squares inversion to Eq. (10). The corrected REE concentrations in clinopyroxene are calculated according to three subsolidus temperatures (1074 ºC, 1183 ºC, and 1281 ºC). Black (dashed) and red (solid) curves are the nonlinear least 231 squares fits to the measured and the corrected REE abundances in clinopyroxene, respectively. For clarity, data for 1074 ºC were reduced by a factor of 5, whereas data for 1281 ºC were increased by a factor of 5. To conduct the inversion, we used the same initial mineral proportions, starting mantle composition, and mineral-melt partition coefficients as those listed the caption of Fig. 8. We normalized the REE concentrations in clinopyroxene by CI chondrite reported in Anders and Grevesse (1989). For inversions of other samples listed in Table 1, interested readers are referred to supplementary Fig. S1. Figure 4-S1 Comparisons of the measured and corrected REE abundances in clinopyroxene from abyssal peridotites along the Central Indian Ridge. The abyssal peridotite data are all from Hellebrand et al. (2002) and have heavy REE abundances in clinopyroxene higher than those derived from the best fits of nonlinear least squares inversion to Eq. (10). See the caption of Fig. 8 for the legends. Figure 4-S2 Onuma diagrams showing olivine-clinopyroxene REE partition coefficients (a) and olivine-garnet REE partition coefficients (b) as a function of ionic radii. The roughness results from the lattice strain parameters in olivine-melt REE partitioning model that were calibrated based on six-fold coordinated ionic radii. Solid and dashed curves in (a) are the same as those in Fig. 4a, while those in (b) are the same as those in Fig. 5a. Figure 4-S3 Comparisons between experimentally determined olivine-melt REE+Y+Sc partition coefficients and the model predicted values by the models of Sun and Liang (2013a; a) and this study (Eq. A1; b). Sun and Liang’s original model was calibrated based on six-fold ionic radii, while the model of this study was a re-calibration of Sun and Liang’s model with eight-fold ionic radii. χ p is the Pearson’s Chi-square to evaluate the goodness of the model, defined in Eq. (S1). 2 232 Figures Figure 4-1 Lu Yb (a) Spinel harzburgite Lu Yb (b) Spinel lherzolite 10 Er Y 10 Er Y Ho Ho Tb Liang et al. Dy Dy Gd Dopx-cpx Dopx-cpx Witt-Eickschen Sm REE REE Gd Eu La Eu Witt-Eickschen Nd 10 Sm Ce Nd 10 Ce La 10 1 1.05 1.1 1.15 1 1.05 1.1 1.15 Ionic radius (Å) Ionic radius (Å) 233 Figure 4-2 Di Hd pigeonite En Fs 50 50 30 30 10 10 Py 50 Alm+ Spess 234 Figure 4-3 0 10 10 Huang et al. (2012) 10 Harte & Kirkley (1997) 1 10 10 10 0 10 235 10 10 10 10 10 0 10 0 1 10 10 10 10 10 10 10 10 10 10 10 10 10 Figure 4-4 Lu Tm Dy Eu Sm Nd Pr Ce La Lu Tm Dy Eu Sm Nd Pr Ce La 10 Orthopyroxene-Clinopyroxene (a) (b) 10 Olivine-Clinopyroxene 10 10 10 Ha 00 rz ºC Lh bu 10 er rg 00 10 zo ite ºC 10 lite 10 Lh Ha er 10 zo 10 rz lite P = 1 GPa bu Spinel Peridotite Spinel Peridotite rg ite 10 1 1.05 1.1 1.15 1 1.05 1.1 1.15 Ionic radius (Å) Ionic radius (Å) Lu Tm Dy Eu Sm Nd Pr Ce La Lu Tm Dy Eu Sm Nd Pr Ce La 10 10 (c) Ec (d) Ec log log Garnet-Clinopyroxene Garnet-Clinopyroxene ite ite 1 10 (hi 1 10 (h gh igh Ec -C Ec -C lo lo aG gi a gi arn te Ga te 0 et) 0 (lo 8 rn (lo 10 10 w- G et Pa ) w- 10 Ca Ca 00 G ar G ºC ne ar 10 10 t) ne t) 10 10 T = 1000 ºC Eclogite Eclogite 1 1.05 1.1 1.15 1 1.05 1.1 1.15 Ionic radius (Å) Ionic radius (Å) 236 Figure 4-5 Lu Tm Dy Eu Sm Nd Pr Ce La Lu Tm Dy Eu Sm Nd Pr Ce La 10 10 Garnet Peridotite ite Orthopyroxene-Garnet urg rzb Ha Olivine-Garnet 1000 te 10 ºC Harzburgite z oli er Lherz olite Lh 10 ºC 00 10 700 ºC 10 ºC 0 70 Garnet Peridotite (a) (b) 10 10 1 1.05 1.1 1.15 1 1.05 1.1 1.15 Ionic radius (Å) Ionic radius (Å) Lu Tm Dy Eu Sm Nd Pr Ce La Lu Tm Dy Eu Sm Nd Pr Ce La 10 0 10 T = 1000 ºC Garnet Peridotite Orthopyroxene-Garnet 8 GPa Olivine-Garnet Harzburgite 10 te u rgi 10 rzb 8G Pa Ha ite Lhe r zol rzo Lhe lite 10 T = 1000 ºC Garnet Peridotite (c) (d) 10 10 1 1.05 1.1 1.15 1 1.05 1.1 1.15 Ionic radius (Å) Ionic radius (Å) 237 Figure 4-6 Cpx in Spinel Lherzolite Opx in Spinel Lherzolite Olivine in Spinel Lherzolite 2 1300oC 0 10 1200oC 63% olivine 0 10 1.8 1100oC 21% opx o 1000 C 14% cpx o ) o ) C o ) 1300 C C o 900 C ) / (C1300 1.6 3% spinel ) / (C1300 10 opx ) / (Ccpx o 800 C ol 1.4 (Copx (Ccpx (Col T 10 T T 10 1.2 1 10 LaCe Nd Sm Eu Tb Ho Tm Lu La Ce Nd Sm Eu Tb Ho Tm Lu La Ce Nd Sm Eu Tb Ho Tm Lu 238 Cpx in Spinel Harzburgite Opx in Spinel Harzburgite Olivine in Spinel Harzburgite 4 0 10 0 3.5 10 84% olivine o ) o ) 3 13% opx 1300 C o ) 1300 C 1300 C 2% cpx 10 ) / (Copx ) / (Ccpx ) / (Col 2.5 1% spinel (Copx (Ccpx 2 (Col T 10 T T 10 1.5 1 10 La Ce Nd Sm Eu Tb Ho Tm Lu La Ce Nd Sm Eu Tb Ho Tm Lu La Ce Nd Sm Eu Tb Ho Tm Lu Figure 4-7 Garnet in Garnet Lherzolite Cpx in Garnet Lherzolite Opx in Garnet Lherzolite 4 o 1300 C 0 10 3.5 1200oC 57% olivine 0 10 1100oC 27.5% opx o 1000 C 6.5% cpx o ) o ) 3 o ) C 1300 C 1300 C o 900 C 9% garnet ) / (C1300 opx ) / (Ccpx o 800 C ) / (Cgrt 2.5 2 (Copx (Ccpx (Cgrt 10 10 T T T 1.5 1 La Ce Nd SmEu Tb Ho Tm Lu La Ce Nd SmEu Tb Ho Tm Lu La Ce Nd SmEu Tb Ho Tm Lu 239 Garnet in Garnet Harzburgite Cpx in Garnet Harzburgite Opx in Garnet Harzburgite 5 0 10 4.5 56% olivine 0 10 4 39% opx 0.7% cpx o ) o ) o ) C C 1300 C 3.5 ) / (C1300 ) / (C1300 4.3% garnet opx cpx (CTgrt) / (Cgrt 3 2.5 (Copx (Ccpx 10 10 T T 2 1.5 1 La Ce Nd SmEu Tb Ho Tm Lu La Ce Nd SmEu Tb Ho Tm Lu La Ce Nd SmEu Tb Ho Tm Lu Figure 4-8 1 10 Global abyssal peridotites (Sm/Yb)N in cpx 0 10 lting 10 Me 0ºC ºC 00 80 10 Subso lidus e quilibr ation 10 0 1 10 10 Yb in cpx N 240 Figure 4-9 10 5x Concentration normalized by CI 1 10 1x 0 10 1281ºC 0.2x 10 1074ºC 1183ºC 10 Measured 10 Corrected Inversions 10 La Pr Sm Gd Dy Er Yb Ce Nd Eu Tb Ho Tm Lu 241 Figure 4-S1 10 5x 5x 1 10 Concentration normalized by CI 1x 1x 1281ºC 1281ºC 0 0.2x 10 0.2x 10 1074ºC 1074ºC 1183ºC 1183ºC 10 Measured 10 Corrected Inversions 10 10 5x 5x 1 10 Concentration normalized by CI 1x 1x 0 10 0.2x 0.2x 1281ºC 1281ºC 10 1074ºC 1074ºC 1183ºC 1183ºC 10 10 10 10 5x 5x 1 10 Concentration normalized by CI 1x 1x 0 10 1281ºC 0.2x 1281ºC 0.2x 10 1074ºC 1074ºC 1183ºC 1183ºC 10 10 10 La Ce Pr Nd Sm Eu Gd Tb Dy Ho Er Tm Yb Lu La Ce Pr Nd Sm Eu Gd Tb Dy Ho Er Tm Yb Lu 242 Figure 4-S2 Lu Tm Dy Eu Sm Nd Pr Ce La 10 13 (a) 10 00 Olivine-Clinopyroxene ºC 10 00 ºC 10 70 0 10 ºC 10 10 P = 1 GPa 10 1 1.05 1.1 1.15 Lu Tm Dy Eu Sm Nd Pr Ce La 10 (b) 1300 ºC Olivine-Garnet 10 1000 ºC 10 700 ºC P = 2 GPa 10 1 1.05 1.1 1.15 Ionic radius (8-fold) (Å) 243 Figure 4-S3 0 10 (a) Six-fold ionic radii 10 10 10 10 10 2 p 10 0 10 (b) Eight-fold ionic radii 10 10 10 10 10 2 p 10 0 10 10 10 10 10 10 10 244 Tables Table 4-1 Melting parameters obtained by the nonlinear least squares inversion method for abyssal peridotites from the Central Indian Ridge Sample name Fm (%) Rm F1 (%) R1 F2 (%) R2 Circe93-4 16.0 ± 1.8 0.76 ± 0.05 19.5 ± 1.6 0.71 ± 0.04 22.2 ± 1.6 0.68 ± 0.03 ANTP89-1 9.0 ± 0.6 0.94 ± 0.03 12.3 ± 0.4 0.86 ± 0.01 15.1 ± 0.5 0.82 ± 0.01 ANTP89-2 12.2 ± 1.6 0.89 ± 0.05 14.3 ± 1.2 0.85 ± 0.03 15.7 ± 1.1 0.83 ± 0.03 ANTP89-5 9.4 ± 0.9 0.97 ± 0.03 10.3 ± 0.5 0.94 ± 0.02 10.9 ± 0.4 0.93 ± 0.01 ANTP89-8 9.8 ± 1.0 0.95 ± 0.04 11.0 ± 0.6 0.92 ± 0.02 11.8 ± 0.5 0.90 ± 0.02 ANTP89-15 9.6 ± 0.7 0.94 ± 0.03 12.9 ± 0.3 0.86 ± 0.01 15.5 ± 0.8 0.81 ± 0.02 All these samples are from Hellebrand et al. (2002) with high heavy REE abundances in clinopyroxene. Fm and R m are the melting parameters inverted from the measured REE abundances (excluding La) in clinopyroxene. F1 and R1 are the melting parameters inverted from the REE abundances (excluding La) in clinopyroxene corrected by subsolidus equilibration for an equilibrium temperature of 1183 ºC, whereas F2 and R 2 are those for an equilibrium temperature of 1074 ºC. The standard errors are derived from the nonlinear least squares inversion. 245 Table 4-S1 Mineral compositions and proportions in four representative mantle peridotites. Sample name: MM1213 Mo22 Rock type: Spinel Harzburgite Spinel Lharzolite Reference: Witt-Eickschen & O'Neill (2005) Witt-Eickschen & O'Neill (2005) Mineral Olivine Opx Cpx Spinel Olivine Opx Cpx Spinel Proportion (%) 84 13 2 1 63 21 14 3 SiO2 (wt%) 41.91 55.42 53.37 - 40.85 54.59 51.85 - TiO2 0 0.04 0.07 0.15 0.01 0.15 0.51 0.2 Al2O3 0.05 3.83 4.3 30.43 0 5.55 6.93 57.85 Cr2O3 0.07 1.17 1.67 37.27 0.02 0.48 0.86 10.4 FeO 7.78 4.98 3.01 13.78 10.05 6.17 3.58 10.68 MnO 0.12 0.12 0.1 0.18 0 0.13 0 - NiO 0.42 0.12 0.07 0.24 0.39 0.11 0.05 0.46 MgO 50.79 32.86 18.61 17.34 48.8 31.75 15.45 21.38 CaO 0.16 1.68 18.44 - 0.09 0.99 18.7 - Na2O - 0.1 0.73 - - 0 1.53 - K 2O - - - - - - - - La (ppm) - 0.011 0.773 - - 0.012 3.202 - Ce - 0.039 2.221 - - 0.061 9.823 - Pr - - - - - - - - Nd - 0.043 1.502 - - 0.087 8.16 - Sm - 0.018 0.491 - - 0.05 2.546 - Eu - 0.011 0.202 - - 0.024 0.943 - Gd - 0.051 0.787 - - 0.094 3.019 - Tb - - - - - - - - Dy - 0.116 1.055 - - 0.193 3.301 - Ho 0.0014 0.033 0.227 - 0.0019 0.049 0.677 - Er 0.008 0.108 0.637 - 0.0104 0.186 1.926 - Tm - - - - - - - - Yb 0.0139 0.153 0.567 - 0.0235 0.275 1.688 - Lu 0.0027 0.026 0.075 - 0.0058 0.049 0.246 - 246 ! (Continued) Sample name: F-5 F-16 Rock type: Garnet Harzburgite Garnet Lharzolite Reference: Lazarov et al. (2012) Lazarov et al. (2012) Mineral Olivine Opx Cpx Garnet Olivine Opx Cpx Garnet Proportion (%) 56 39 0.70 4.30 57 27.5 6.50 9.00 SiO2 (wt%) 41.48 58.53 55.55 42.27 40.78 57.58 54.9 42.32 TiO2 - 0.01 0.01 0.08 - 0.01 0.03 0.07 Al2O3 - 0.56 1.16 19.03 - 0.64 2.09 21.94 Cr2O3 - 0.3 1.21 6.36 - 0.15 0.86 2.07 FeO 7.06 4.43 2.07 6.35 8.15 5.05 2.56 7.13 MnO 0.09 0.11 0.09 0.32 0.1 0.12 0.09 0.3 NiO 0.41 0.12 0.08 0.01 0.4 0.12 0.06 0.02 MgO 51.08 36.4 18.59 21.08 50.23 35.57 17.95 21.87 CaO 0.03 0.64 20.77 5.75 0.03 0.66 19.14 4.23 Na2O - 0.09 0.99 0.02 - 0.13 1.52 0.03 K 2O - - - - - - - - La (ppm) 0.0017 0.0062 1.43 0.019 0.0024 0.005 1.68 0.013 Ce 0.0025 0.028 6.47 0.377 0.0098 0.02 7.54 0.167 Pr - - 1.29 0.169 - - 1.26 0.065 Nd 0.0018 0.035 6.03 1.74 0.0024 0.018 5.79 0.653 Sm - 0.011 0.988 1.09 0.0008 0.0069 0.735 0.334 Eu 0.0001 0.0023 0.201 0.364 0.0003 0.0015 0.164 0.124 Gd - 0.008 0.445 1.11 0.0008 0.0047 0.419 0.519 Tb 0.0001 0.0009 0.042 0.152 - - 0.053 0.138 Dy 0.0007 0.0026 0.063 0.728 0.0006 0.006 0.32 1.49 Ho - 0.0006 0.0044 0.123 - - 0.061 0.433 Er 0.0002 0.0006 0.0054 0.288 0.001 0.0032 0.143 1.55 Tm - 0.0003 - 0.04 - - 0.015 0.259 Yb - 0.0014 0.0058 0.276 0.0013 0.0047 0.079 2.07 Lu - 0.0001 - 0.043 0.0002 0.0007 0.011 0.33 247 Supplementary Material S1. Recalibration of the olivine model The original olivine model of Sun and Liang (2013a) was calibrated based on six-fold coordinated ionic radii, which is a standard practice in the literature. However, the partitioning models for clinopyroxene (cpx), low-Ca pyroxene and garnet were calibrated based on eight-fold coordinated ionic radii. Such differences in ionic radii result in a kink around Pr in the Onuma diagram (partition coefficients vs. ionic radii, Onuma et al., 1968) for the calculated olivine-cpx or olivine-garnet REE partition coefficients (supplementary Fig. S2). This kink is not physically meaningful and likely due to the uncertainties in estimation of the six-fold ionic radius of Pr (see discussion in Yao et al., 2012). Therefore, we followed the same procedure as described in Sun and Liang (2013a) for the original olivine model, and re-calibrated the model for REE partitioning between olivine and basaltic melt using eight-fold coordinated ionic radii. The re- calibrated olivine model is listed in Section S2. To evaluate the goodness of the model, we defined the Pearson’s Chi-square as (D − D ) 2 N m χ 2p = ∑ j j (S1) j=1 Dj where D j is the model predicted olivine-melt partition coefficient for element j; D jm is the measured partition coefficient for element j; N is the total number of measured partitioning data used in the fit to the lattice strain model. A better predictive model should provide partition coefficients closer to measured values and thus has a smaller χ p . The comparable values of χ p 2 2 indicate that the new olivine model ( χ 2p = 2.36 ) is equivalent to the original model ( χ 2p = 2.29 ) in terms of reproducing experimental partitioning data (supplementary Fig. S3). 248 S2. Parameterized lattice strain models for REE partitioning between mantle minerals and basaltic melts The following equations summarize the parameters used in the lattice strain models (Eq. 5a) for REE partitioning between mantle minerals (olivine, pyroxene, and garnet) and basaltic melts: 1. Olivine model (see Appendix B for more discussion) ln D0 = −0.44 ( ±0.30 ) − 0.18 ( ±0.01) P + 123.75( ±13.43) X Al (A1a) − 1.49 ( ±0.28) × 10−2 Fo ( ) r0 Å = 0.809 ( ±0.007 ) (A1b) E ( GPa ) = 298 ( ±11) (A1c) 2. Low-Ca pyroxene model (Yao et al., 2012; Sun and Liang, 2013b) 3.87 ( ±0.74 ) × 104 ln D0 = −5.37 ( ±0.49 ) + + 3.54 ( ±0.61) X Al T RT (A2a) + 3.56 ( ±1.02 ) X Ca M2 − 0.84 ( ±0.22 ) X Timelt ( ) r0 Å = 0.693( ±0.055 ) + 0.432 ( ±0.147 ) XCa M2 + 0.228 ( ±0.056 ) XMg M2 (A2b) E ( GPa ) = ⎡⎣1.85( ±0.52 ) × r0 − 1.37 ( ±0.47 ) − 0.53( ±0.11) X Ca M2 ⎤ × 103 ⎦ (A2c) 3. Clinopyroxene model (Sun and Liang, 2012) 7.19 ( ±0.73) × 10 4 ln D0 = −7.14 ( ±0.53) + + 4.37 ( ±0.47 ) X Al T RT (A3a) + 1.98 ( ±0.36 ) XMg − 0.91( ±0.19 ) XHmelt M2 2O ( ) r0 Å = 1.066 ( ±0.007 ) − 0.104 ( ±0.035 ) X AlM1 − 0.212 ( ±0.033) XMg M2 (A3b) E ( GPa ) = ⎡⎣ 2.27 ( ±0.44 ) r0 − 2.00 ( ±0.44 ) ⎤⎦ × 10 3 (A3c) 249 4. Garnet model (Sun and Liang, 2013a; updated) 9.03( ±0.98) × 104 − 93.02 ( ±17.06 ) P ( 37.78 − P ) ln D0 = −2.01( ±0.70 ) + RT (A4a) − 1.04 ( ±0.44 ) X Ca ( ) r0 Å = 0.785 ( ±0.031) + 0.153( ±0.029 ) XCa (A4b) E ( GPa ) = ⎡⎣ −1.67 ( ±0.45) + 2.35( ±0.51) r0 ⎤⎦ × 103 (A4c) In these equations, numbers in parentheses are 2σ uncertainties estimated directly from the simultaneous inversion; D0 is the partition coefficient for strain-free substitution; r0 is the ionic radius of the “ideal” cation for the strain-free lattice site; E is the apparent Young’s modulus for the lattice site; P is the pressure in GPa; T is the temperature in K; and R is the gas constant (= 8.3145 J mol-1 K-1). In Eq. (A1a), XAl is the Al content in olivine in mole per four-oxygen, and Fo is the forsterite content in olivine [=100 × Mg/(Mg + Fe) in mole]. In Eqs. (A2a-A2c), and Eqs. T M1 (A3a-A3c), X Al is the cation content of the tetrahedral Al in pyroxene per six-oxygen; X Al is M2 M2 the cation content of Al on the M1 site in pyroxene per six-oxygen; X Ca (or X Mg ) is the cation melt content of Ca (or Mg) on the M2 site in pyroxene per six-oxygen; X H 2O is the molar fraction of melt H2O in the melt calculated following Wood and Blundy (2002); and X Ti is the cation fraction of Ti in the melt per six-oxygen. In Eq. (A4), XCa is the cation content of Ca in garnet per 12- oxygen. Pyroxene formulae are calculated by assuming a random distribution of Fe2+ and Mg2+ over the M1 and M2 sites (Wood and Banno 1973) and that all iron is present as ferrous iron. 250 CHAPTER 5 5 A REE-in-Garnet-Clinopyroxene Thermobarometer for Eclogites, Granulites and Garnet Peridotites 251 Abstract We present a REE-in-garnet-clinopyroxene thermobarometer for eclogites, granulites, and garnet peridotites based on the temperature, pressure and mineral composition dependent partitioning of rare earth elements (REEs) between garnet and clinopyroxene. This new thermobarometer is derived from the garnet-clinopyroxene REE partitioning model in Chapter 4 that was calibrated against experimentally determined garnet-melt and clinopyroxene-melt partitioning data. An important advantage of this new thermobarometer is its multi-element nature: it makes use of a group of trace elements that have similar geochemical behaviors at magmatic and subsolidus conditions, which enables us to invert temperature and pressure simultaneously using least squares methods. Application of the REE-in-garnet-clinopyroxene thermobarometer to REE partitioning data from laboratory experiments and field samples (i.e., quartz-bearing, graphite-bearing, and diamond-bearing granulites and eclogites; and well- equilibrated mantle eclogite xenoliths) published in the literature validates its reliability at both magmatic and subsolidus conditions. Application of the new thermobarometer to eclogites, garnet granulites and peridotites from various tectonic settings reveals an intriguing observation: temperatures derived from the REE-based thermobarometer are consistently higher than those derived from the widely used Fe-Mg thermometer of Krogh (1988) for samples that experienced cooling, but systematically lower than temperatures derived from the Fe-Mg thermometer for samples from thermally perturbed tectonic settings. The temperature discrepancies are likely due to the relative differences in diffusion rates between trivalent REEs and divalent Fe-Mg in garnet and clinopyroxene. Temperatures derived from the REE-based thermometer are closely related to closure temperatures for samples that experienced cooling, but are likely equilibrium or apparent re-equilibration temperatures at an early stage of heating for samples from thermally perturbed tectonic environments. The REE-in-garnet-clinopyroxene thermobarometer can shed new light on thermal histories of mafic and ultramafic rocks. 252 1. Introduction The exchange of Fe-Mg between garnet and clinopyroxene has been successfully calibrated as thermometers that can quantitatively determine equilibrium temperatures of eclogites, garnet peridotites, and garnet pyroxenites (e.g., Råheim and Green, 1974; Ellis and Green, 1979; Ganguly, 1979; Saxena, 1979; Powell, 1985; Krogh, 1988; Ai, 1994; Ravna, 2000; Nakamura, 2009). However, all these thermometers require independent estimates of pressures, which need additional phases to constrain (e.g., the garnet-orthopyroxene barometer; Brey et al., 2008). Since a significant fraction of mantle eclogites is bi-mineralic, a reliable garnet- clinopyroxene barometer is a prerequisite for a better constraint of their equilibrium pressures and temperatures. Attempts have been made to calibrate garnet-clinopyroxene barometers through thermodynamic analysis of experimental data (e.g., Brey et al., 1986; Mukhopadhyay, 1991; Simakov and Taylor, 2000; Simakov, 2008), yet these barometers are still not as reliable as the garnet-orthopyroxene barometers (Nimis and Grütter, 2010). Hence, the equilibrium temperatures of bi-mineralic eclogites are often calculated using the garnet-clinopyroxene thermometers at an assumed pressure. Because the garnet-clinopyroxene thermometers are all pressure dependent, temperature estimations can differ by up to 150 ºC if the assumed pressure is off by 2 GPa. This is illustrated in Fig. 5-1. Assuming that the eclogites approach chemical equilibrium at a temperature and pressure defined by the local geotherm, one can estimate the equilibrium pressure and temperature by coupling the local geotherm with the garnet-clinopyroxene thermometers (e.g., Griffin and O’Reilly, 2007). However, the local geotherm derived from garnet peridotite xenoliths can vary by ±1 GPa (Griffin et al., 2003). Thus, uncertainties in the temperature estimations are still significant. Another important source of uncertainties in the garnet-clinopyroxene thermometers is the presence of Fe3+ in garnet and clinopyroxene. Given the reducing conditions imposed by graphite capsules in phase equilibrium experiments, Fe3+ abundances in the minerals are likely very small and thus total Fe is used to represent Fe2+ in the calibration of the garnet-clinopyroxene 253 thermometers. However, a significant amount of Fe3+ may be present in natural minerals. This may result in large errors (> 200ºC) in temperature estimations using the garnet-clinopyroxene Fe-Mg thermometers (e.g., Ravna and Paquin, 2003). Recently, Matjuschkin et al. (2014) experimentally examined the Fe3+ effect on the Fe-Mg exchange thermometers at 1100 – 1400 ºC and 5 GPa. Although they observed substantial amounts of Fe3+ in their experiments (Fe3+/∑Fe = 0.116 – 0.206 in garnet), the temperatures calculated using the garnet-clinopyroxene thermometer of Krogh (1988) are within 25 ºC of the experimental temperatures, except that for the 1400ºC experiment (Fe3+/∑Fe = 0.199 in garnet). Consequently, these authors suggested that the garnet- clinopyroxene Fe-Mg thermometers are insensitive to the presence of Fe3+, which contradicts the study of Ravna and Paquin (2003) on natural eclogite samples. Clearly, detailed experimental and field studies are needed to further address the Fe3+ problem. In this study, we present a new garnet-clinopyroxene thermobarometer based on the exchange of rare earth elements (REEs) between garnet and clinopyroxene. The distribution of trace elements between minerals depends on temperature, pressure, and mineral major element compositions and can be calibrated as thermometers (e.g., Stosch, 1982; Seitz et al., 1999; Witt-Eickschen and O’Neill, 2005; Lee et al., 2007; Liang et al., 2013; Chapter 4). Based on the temperature-dependent REE partitioning between orthopyroxene and clinopyroxene, Liang et al. (2013) developed a REE-in-two-pyroxene thermometer by combining the clinopyroxene-melt and orthopyroxene-melt REE partitioning models (Chapter 1; Yao et al., 2012). This thermometer treats REE as a group in temperature calculation, which helps to reduce analytical uncertainties. Through numerical simulations, Yao and Liang (2014) showed that the temperatures calculated by the REE-in-two-pyroxene thermometer are the closure temperature of REEs in cooling two-pyroxene systems. Because REEs diffusive about two to three orders of magnitude slower than divalent cations (e.g., Ca2+, Mg2+, Fe2+) in pyroxenes (Cherniak and 254 Dimanov, 2010 and references therein), the REE-based thermometers can record higher closure temperatures of mafic and ultramafic rocks during cooling. We have recently developed a parameterized lattice strain model for REE partitioning between garnet and clinopyroxene (Chapter 4). The lattice strain parameters in the model were calibrated by experimentally determined mineral-melt partitioning data. Through the garnet- clinopyroxene REE partitioning model, we found that REE partitioning between garnet and clinopyroxene is very sensitive to temperature and pressure as well as mineral major element composition. Specifically, garnet-clinopyroxene REE partition coefficients decrease by up to two orders of magnitude as temperature decreases from 1300 ºC to 700 ºC, whereas they increase by about one order of magnitude as pressure decreases from 14 GPa to 2 GPa [see Figs. 4c-d in Chapter 4]. Here we expand the idea of the REE-in-two-pyroxene thermometer to garnet- clinopyroxene systems and develop a REE-in-garnet-clinopyroxene thermobarometer using the garnet-clinopyroxene REE partitioning model in Chapter 4. This new thermobarometer enables us to obtain the equilibrium or closure temperature and pressure simultaneously by analyzing REEs and major elements in coexisting garnet and clinopyroxene, and shed new light on thermal histories of mafic and ultramafic rocks. 2. Developing a REE-in-Garnet-Clinopyroxene Thermobarometer 2.1. Theoretical basis In general, thermometers or barometers are based on the temperature- or pressure-sensitive exchange of elements (or components) of interest between two coexisting minerals. The exchange coefficient (or partition coefficient), D, can be described by the thermodynamic expression ΔS ΔH + PΔV ln D = − − ln γ R , (1) R RT where ΔS, ΔH and ΔV is the changes of entropy, enthalpy and volume of the exchange reaction; R is the gas constant; T is the temperature; P is the pressure; and γ R represents the ratio of the 255 activity coefficients of the element (or component) in the two minerals. Eq. (1) can be simplified as B + f (P) ln D = A + , (2) T where A and B are coefficients that depend on mineral major element compositions; f ( P ) is a function of pressure. When the volume change of the exchange reaction is independent of pressure, f ( P ) can be expressed as C × P in which C is a coefficient independent of pressure. From Eq. (2), we can obtain generalized equations for thermometers and barometers: B+C×P T= , (3) ln D − A 1 P= ⎡T ( ln D − A ) − B ⎤⎦ . (4) C⎣ The temperature-pressure-composition dependent partitioning of trace elements between a pair of minerals also takes the simple form of Eq. (2) (e.g., Stosch, 1982; Seitz et al., 1999; Witt- Eickschen and O’Neill, 2005; Lee et al., 2007; Liang et al., 2013). Similar to Eq. (3a) in Liang et al. (2013), we rearrange Eq. (2) in a linear form for a group of geochemically similar elements, such as REEs, Bi = T ( ln Di − Ai ) + f ( P ) , (5) where i is an element in the group. If the partitioning of a group of trace elements is sensitive to both temperature and pressure, we can use Eq. (5) to determine the temperature and pressure simultaneously. In a plot of (lnD-A) vs. B for REEs, Eq. (5) defines a line passing through all REEs in a well-equilibrated sample. The slope of this line provides the equilibrium temperature, whereas the intercept determines the equilibrium pressure. 256 2.2. Garnet-clinopyroxene REE partitioning model The exchange of a REE between garnet and clinopyroxene can be quantify by a parameterized lattice strain model (Chapter 4) D0grt ⎡ 4π N A E grt ⎛ r0grt grt 3⎞ ( ) 1 ( ) 2 grt-cpx DREE = cpx exp ⎢− ⎜ r0 − rREE − r0grt − rREE ⎟ D0 ⎢⎣ RT ⎝ 2 3 ⎠ (6) 4π N A E cpx ⎛ r0cpx cpx 3⎞ ⎤ ( ) ( 1 cpx ) 2 + ⎜ 2 0 r − rREE − r − rREE ⎟ ⎥ RT ⎝ 3 0 ⎠ ⎥⎦ where DREE is the partition coefficient of a given REE; D0 is the partition coefficient for strain- free substitution; E is the apparent Young’s modulus for the lattice site; r0 is the size of the strain- free lattice site; rREE is the ionic radius of the REE; NA is Avogadro’s number; superscripts grt and cpx denote garnet and clinopyroxene. The lattice strain parameters (D0, r0 and E) are the same as those in the mineral-melt lattice strain model of Blundy and Wood (1994). In a mineral- melt system, the lattice strain parameters generally depend upon temperature, pressure and compositions of the mineral and melt (e.g., Blundy and Wood, 1994; Wood and Blundy, 1997, 2002, 2003; Chapter 3). To quantify the distribution of REEs between garnet and clinopyroxene, one can parameterize the lattice strain parameters as functions of temperature, pressure and composition using experimentally determined mineral-melt REE partition coefficients. Because clinopyroxene-melt and garnet-melt REE partition coefficients are important to the interpretation of magmatic processes in the Earth’s mantle, considerable efforts have been devoted to developing parameterized lattice strain models for REE partitioning between clinopyroxene and basaltic melt (Wood and Blundy, 1997, 2002; Chapter 1) and between garnet and basaltic melt (van Westrenen et al., 2001; Wood and Blundy, 2002; van Westrenen and Draper, 2007; Draper and van Westrenen, 2007; Corgne et al., 2012; Chapter 3). In two recent studies, we systematically examined clinopyroxene-melt and garnet-melt REE and Y partition coefficients as functions of temperature, pressure and compositions using the lattice strain model 257 (Chapters 1 and 3). Our new models were calibrated against a carefully selected high quality experimental partitioning dataset through parameter swiping and simultaneous or global nonlinear least squares inversion of all the filtered partitioning data for each mineral-melt system. Fig. 5-2 displays the major element compositions of clinopyroxene and garnet from the compiled experiments. These include 344 clinopyroxene-melt partitioning data (REEs and Y) from 43 experiments (conducted at 1042-1470 °C and 1 atm-4 GPa) and 538 garnet-melt partitioning data (REEs and Y) from 64 experiments (conducted at 1325-2300 °C and 2.4-25 GPa). The clinopyroxenes are rich in magnesium but also include some with jadeite components [Mg# = 54 – 100, and Na2O = 0 - 3.6 %; Mg# = 100 × Mg/(Mg + Fe) in mole], while the garnets are rich in pyrope or majorite components (Mg# = 54-100). The interested reader is referred to Chapters 1-3 for detailed information. The compiled clinopyroxene-melt REE and Y partitioning data can be best fit by a lattice strain model using the following lattice strain parameters (Chapter 1): 7.19 ( ±0.73) × 10 4 ln D0cpx = −7.14 ( ±0.53) + + 4.37 ( ±0.47 ) X Al T RT (7a) + 1.98 ( ±0.36 ) XMg M2 − 0.91( ±0.19 ) XHmelt 2O ( ) r0cpx Å = 1.066 ( ±0.007 ) − 0.104 ( ±0.035 ) X AlM1 − 0.212 ( ±0.033) XMg M2 (7b) E cpx ( GPa ) = ⎡⎣ 2.27 ( ±0.44 ) r0 − 2.00 ( ±0.44 ) ⎤⎦ × 10 3 (7c) where numbers in parentheses are 2σ uncertainties estimated directly from the simultaneous T M1 inversion; X Al is the amount of the tetrahedral Al in pyroxene per six-oxygen; X Al is the M2 amount of Al on the M1 site in pyroxene per six-oxygen; X Mg is the cation content of Mg on the melt M2 site in pyroxene per six-oxygen; and X H 2O is the molar fraction of H2O in the melt per six- oxygen calculated following the procedure of Wood and Blundy (2002). Pyroxene structure 258 formulae are calculated by assuming a random distribution of Fe2+ and Mg2+ over the M1 and M2 sites (Wood and Banno, 1973) and that all iron is present as ferrous iron. The compiled garnet-melt REE and Y partitioning data can be best fit by a lattice strain model using the following lattice strain parameters (Chapter 4): 9.03( ±0.98) × 104 − 93.02 ( ±17.06 ) P ( 37.78 − P ) ln D = −2.01( ±0.70 ) + grt 0 RT (8a) − 1.04 ( ±0.44 ) X grt Ca ( ) r0grt Å = 0.785 ( ±0.031) + 0.153( ±0.029 ) XCa grt (8b) E grt ( GPa ) = ⎡⎣ −1.67 ( ±0.45) + 2.35( ±0.51) r0 ⎤⎦ × 103 (8c) grt where P is the pressure in GPa; XCa is the cation content of Ca in garnet per 12-oxygen. In both clinopyroxene and garnet partitioning models, we used 8-fold coordinated ionic radii of REE and Y from Shannon (1976). Eqs. (7a-c and 8a-c) indicate that temperature, pressure and mineral major element compositions dominate REE and Y partitioning in clinopyroxene and garnet. The effect of water in the melt on clinopyroxene-melt REE partitioning is only significant under very hydrous magmatic conditions. Combining Eqs. (6, 7a-c, and 8a-c), we obtained a generalized lattice strain model for REE and Y partitioning between garnet and clinopyroxene under anhydrous conditions in Chapter 4. We demonstrated that REE partition coefficients calculated using this model agree very well with directly measured values in well-equilibrated mantle eclogite xenoliths (Type II) from the Roberts Victor kimberlite, South Africa reported in Harte and Kirkley (1997) and Huang et al. (2012). To further test the validity of this model, here we compare garnet-clinopyroxene REE and Y partition coefficients predicted by Eqs. (6, 7a-c, and 8a-c) with those derived from mineral-melt partitioning experiments and with those measured in additional well-equilibrated mantle eclogite xenoliths from various locations. The partitioning experiments were conducted at 1100-1900 ºC and 3-12 GPa, and produced clinopyroxene and garnet coexisting with melts (Green et al., 2000; 259 Klemme et al., 2002; Adam and Green, 2006; Tuff and Gibson, 2007; Suzuki et al., 2012). Partitioning data from these experiments have been used to independently calibrate our clinopyroxene-melt and garnet-melt REE partitioning models except the clinopyroxene-melt partitioning data from Tuff and Gibson (2007) and Suzuki et al. (2012). In addition to the well-equilibrated mantle xenoliths from the Roberts Victor kimberlite, South Africa (Type II eclogites; Harte and Kirkley, 1997; Huang et al., 2012), here we further expand our field test by considering well-equilibrated eclogites from the Udachnaya kimberlite, Siberia (Group 2 eclogites; Jacob and Foley, 1999), the Koidu kimberlite complex, West Africa (low-MgO eclogites; Barth et al., 2001), and the Jericho kimberlite, Canada (diamond eclogites; Smart et al., 2009). Note the garnets from these mantle eclogites are more Fe-rich than those used in the model calibrations (Fig. 5-2b). To calculate the garnet-clinopyroxene REE and Y partition coefficients, we used the reported final equilibrium temperatures for the partitioning experiments, and calculated the equilibrium temperatures of the eclogite xenoliths using the garnet- clinopyroxene Fe-Mg thermometer of Krogh (1988) at an assumed pressure of 3 GPa. Figures 5-3a and 5-3b show that the garnet-clinopyroxene REE and Y partition coefficients derived from Eqs. (6, 7a-c, and 8a-c) are generally in good agreement with those measured from the partitioning experiments and well-equilibrated mantle eclogite xenoliths, respectively. The outliers in Fig. 5-3b are light REEs and presumably can be attributed to poor analytical precisions or secondary alterations. Since the lattice strain parameters for REE partitioning in clinopyroxene and garnet were calibrated independently at magmatic conditions, the good agreement not only demonstrates their internal consistencies but also justifies their extrapolation to subsolidus conditions and to more Fe-rich garnet (Fig. 5-2b). 260 2.3. A REE-in-garnet-clinopyroxene thermobarometer Given the garnet-clinopyroxene REE partitioning model (Eqs. 6, 7a-c, and 8a-c), we can develop a REE-in-garnet-clinopyroxene thermobarometer using Eq. (2). The corresponding terms of Eq. (2) now take on the following expressions: A = 5.13− 1.04 X Ca grt − 4.37 X AlT ,cpx − 1.98X Mg M2,cpx , (9a) B = 2.21×103 + 909.85G ( rREE ) , (9b) f ( P ) = −93.02P 2 + 3514.30P , (9c) ⎛ r0cpx cpx 3⎞ G ( rREE ) = E ( ) ( 1 cpx ) 2 cpx ⎜ 2 0 r − rREE − r − rREE ⎟ ⎝ 3 0 ⎠ , (9d) ⎛ r0grt grt 3⎞ ( 1 ) ( ) 2 −E ⎜grt r0 − rREE − r0grt − rREE ⎟ ⎝ 2 3 ⎠ where E and r0 are given by Eqs. (7b-c and 8b-c); A and B are coefficients in Eq. (2); and f(P) replaces the pressure term in Eq. (2). The coefficient A depends strongly on major element compositions of garnet and clinopyroxene, while the coefficient B is a function of mineral major melt element composition and the ionic radii of REEs. Note that the X H 2O term is excluded in Eq. (9a) because it unlikely affects REE partitioning between garnet and clinopyroxene. To calculate the equilibrium temperature and pressure simultaneously for a given sample, we follow the steps similar to those for the REE-in-two-pyroxene thermometer in Liang et al. (2013). First, we calculate the coefficients A and B from Eqs. (9a-b) using major element compositions of garnet and clinopyroxene. Second, we examine the quality of measured REE abundances in garnet and clinopyroxene in a spider diagram and check if REEs define a line in the plot of (lnD – A) vs. B. Finally, we carry out a linear least squares analysis for garnet- clinopyroxene REE partition coefficients in the plot of (lnD – A) vs. B. We obtain the temperature (TREE) from the slope, and calculate the pressure (PREE) from the intercept f(P) through Eq. (9c). 261 From the linear least squares analysis of garnet-clinopyroxene REE and Y partition coefficients in the plot of (lnD – A) vs. B, we can also make estimates on the uncertainties of the calculated temperature and pressure. Figures 5-4a and 5-4b show an example of the temperature and pressure inversion for a well-equilibrated diamond eclogite reported in Smart et al. (2009). In this sample, light REEs are enriched in the clinopyroxene but highly depleted in the garnet, while heavy REEs are depleted in the clinopyroxene but enriched in garnet (Fig. 5-4a). The distribution of REEs between garnet and clinopyroxene generally agree with their partitioning behaviors. Fig. 5-4b shows that all REEs and Y define a straight line in the plot of (lnD – A) vs. B. The slope and intercept of this line provide a temperature of 846 ± 21ºC and a pressure of 4.21 ± 0.38 GPa, respectively. The temperature and pressure places this diamond-bearing eclogite in the diamond stability field and hence can be interpreted as the equilibrium temperature and pressure of this sample. Assuming an equilibrium pressure of 4.21 GPa, we calculated the equilibrium temperature for this eclogite sample using several garnet-clinopyroxene Fe-Mg thermometers (TEG: Ellis and Green, 1979; TK88: Krogh, 1988; TKR: Ravna, 2000; TN09: Nakamura, 2009). The temperature derived from the REE-in-garnet-clinopyroxene thermobarometer is in excellent agreement with that derived from the widely used thermometer of Krogh (1988) but is lower than those derived from other three garnet-clinopyroxene Fe-Mg thermometers (Fig. 5-4b). Because some REEs are highly depleted in garnet or clinopyroxene (e.g., light REEs in garnet and heavy REEs in clinopyroxene), they may be easily affected by secondary alterations or have significant analytical errors. One of the advantages of the REE-based thermobarometer is that one can eliminate the outliers using a robust linear least squares regression method (Figs. 5- 4(c-d)). Alternatively, one can manually exclude the outliers and obtain the temperature and pressure using a linear least squares regression. However, when all REEs and Y in the plot of (lnD – A) vs. B become continuously curved, the garnet and clinopyroxene may be strongly 262 perturbed by secondary processes. It is then impossible to obtain a meaningful temperature and pressure (Fig. 5-S1). 3. Validation of the REE-in-Garnet-Clinopyroxene Thermobarometer 3.1. Experimental test To assess the validity of the REE-in-garnet-clinopyroxene thermobarometer, we apply the new thermobarometer to partitioning experiments that have coexisting garnet, clinopyroxene and melts. We compiled 14 experiments reported in the literature (Green et al., 2000; Adam and Green, 2006; Tuff and Gibson, 2007; Suzuki et al., 2012). These experiments are the same as those used in Fig. 5-3a while excluding the experiment in an Fe-free system from Klemme et al. (2002). Four experiments from Green et al. (2000) and Adam and Green (2006) were conducted at 1100 – 1200 ºC and 3 – 4 GPa for 22.5 – 48 hrs under hydrous conditions (10.91 – 17.35 wt% water in the melt). Four experiments from Tuff and Gibson (2007) were conducted at 1425 – 1750 ºC and 3 – 7 GPa for 4 – 25 hrs under anhydrous conditions. Six experiments from Suzuki et al. (2012) were conducted at 1550 – 1900 ºC and 3 – 12 GPa for 1 – 2 hrs under anhydrous conditions. All these experiments used basaltic starting compositions and produced garnets and clinopyroxenes with relatively large variations in compositions (e.g., Mg# = 66 – 77 for garnet, and Mg# = 76 – 86 for clinopyroxene). The clinopyroxenes from the experiments in Tuff and Gibson (2007) are on the boundary of augite and sub-calcium augite. Application of the REE-in- garnet-clinopyroxene thermobarometer to these clinopyroxenes may involve a significant extrapolation. Following the procedure described in Section 2.3, we calculated the temperatures and pressures for the 14 experiments using the REE-in-garnet-clinopyroxene thermobarometer (Figs. 5-5 and 5-S2). The temperatures and pressures calculated using the REE-in-garnet-clinopyroxene thermobarometer agree very well with the experimental temperatures (Texp) and pressures (Pexp) 263 (Fig. 5-5). Except for one experiment from Suzuki et al. (2012, 1900°C and 12 GPa), the absolute differences between the calculated temperatures and experimental temperatures are generally within 100ºC (6 – 129ºC; Fig. 5-5a). Interestingly, the larger temperature difference (174ºC) in the 1900°C run of Suzuki et al. (2012) is comparable to the thermal gradient (~150 ºC) near hot spots in the very high temperature multi-anvil experiments (van Westrenen et al., 2003). The differences between the calculated pressures and the experimental pressures are within 1 GPa (0.08 – 0.76 GPa) for 8 of 14 experiments (Fig. 5-5b). The calculated pressures for three experiments from Suzuki et al. (2012) and one experiment from Tuff and Gibson (2007) are 2.2 – 2.9 GPa greater than the experimental pressures, while that for the 8 GPa experiment from Suzuki et al. (2012) is 1.5 GPa smaller than the experimental pressure. The significant differences in temperatures and pressures could be attributed to potential disequilibrium in these partitioning experiments, analytical uncertainties (due in part to very small crystal size), and/or limitations of the REE-in-garnet-clinopyroxene thermobarometer. For instance, curvatures in the plot of (lnD – A) vs. B for the garnet-clinopyroxene REE partition coefficients from the 1900 ºC experiment in Suzuki et al. (2012) (Fig. 5-S2) may result from disequilibrium between garnet and clinopyroxene and/or melt contamination during trace element analysis. The aforementioned partitioning experiments with coexisting garnet and clinopyroxene also enable us to compare the accuracy between the REE-in-garnet-clinopyroxene thermobarometer and the major element-based garnet-clinopyroxene thermobarometers. The conventional garnet-clinopyroxene thermometers were all calibrated based on the Fe-Mg exchange between garnet and clinopyroxene. Garnet-clinopyroxene barometers were based on Ca-Mg exchange between garnet and clinopyroxene (Brey et al., 1986) or Ca-Tschermak (CaTs) solubility in clinopyroxene coexisting with garnet (e.g., Mukhopadhyay, 1991; Simakov and Taylor, 2000; Simakov, 2008). To assess the accuracy of different thermobarometers, we calculated the Pearson’s Chi-squares using the expression 264 (M ) 2 N − Ej χ =∑ 2 j p (10) j=1 Ej where N is the total number of samples used in the comparison; Mj is the temperature (or pressure) measured for sample j; Ej is the temperature (or pressure) estimated using different thermometers for sample j. A smaller χ p indicates that the thermobarometer is more accurate to reproduce the 2 experimental temperatures (or pressures). We calculated equilibrium temperatures for the 14 experiments using four garnet- clinopyroxene Fe-Mg thermometers (Ellis and Green, 1979; Krogh, 1988, Ravna, 2000; Nakamura, 2009) and equilibrium pressures using the recent garnet-clinopyroxene barometer of Simakov (2008). The thermometers of Ellis and Green (1979), Krogh (1988) and Ravna (2000) have been widely applied to garnet- and clinopyroxene-bearing rocks. The thermometer of Nakamura (2009) was recently calibrated by adopting a subregular-solution model for garnet. The experimental pressures were used in these thermometers to estimate temperatures, while the experimental temperatures and the garnet-clinopyroxene thermometer of Krogh (1988) were used in the barometer of Simakov (2008). Figure 5-6 displays the comparisons between the calculated temperatures with the experimental run temperatures. The four thermometers consistently provide temperatures about 265 – 568 ºC greater than the run temperatures of two experiments from Green et al. (2000). The overestimates for the two experimental temperatures may be due to significant amounts of Fe3+ in garnet and clinopyroxene, potential effects of water on garnet-clinopyroxene Fe-Mg exchange, and/or disequilibrium of Fe-Mg between garnet and clinopyroxene. Although the thermometer of Ellis and Green (1979) seems to best reproduce the experimental temperatures among the four thermometers, its χ p (= 268) remains significantly greater than that of the REE-in-garnet- 2 clinopyroxene thermobarometer ( χ p = 63 ). Excluding the two experiments (Runs 1798 and 2 265 1807) from Green et al. (2000), the thermometer of Krogh (1988) best reproduces the 12 experimental temperatures with the smallest χ p (= 43), which is similar to that of the REE-in- 2 garnet-clinopyroxene thermobarometer ( χ p = 49 ). 2 Figure 5-7 shows the comparisons between the calculated pressures using the barometer of Simakov (2008, designated as PS08) and the experimental pressures. For the low-pressure experiments (< 5 GPa), the barometer of Simakov (2008) reproduces the experimental pressures to within 0.01 – 1.14 GPa using the experimental temperatures; however, for the high-pressure experiments (> 5 GPa), the barometer of Simakov (2008) reproduces the experimental pressures to within 1.53 – 2.37 GPa (Fig. 5-7a). Combining with the thermometer of Krogh (1988), the barometer of Simakov (2008) produces larger errors particularly for the two experiments from Green et al. (2000), and has greater χ p (= 8; Fig. 5-7b) than that ( χ p = 3 ; Fig. 5-7a) using the 2 2 experimental temperatures. Excluding the two experiments from Green et al. (2000) in Fig. 5-7b reduces χ p for Simakov’s barometer to 5, comparable to that in Fig. 5-7a. The barometer of 2 Simakov (2008) generally gives rise to χ p values similar to that ( χ p = 5 ; Fig. 5-5b) derived 2 2 from the REE-in-garnet-clinopyroxene thermobarometer. It is important to bear in mind that the experimental test of the REE-in-garnet- clinopyroxene thermobarometer is based on a rather limited laboratory partitioning dataset. To further test and validate the REE-in-garnet-clinopyroxene thermobarometer, we turn to field data. 3.2. Field test Because the diamond-graphite phase boundary and the quartz-coesite transformation have been well-constrained (e.g., Kennedy and Kennedy, 1976; Bohlen and Boettcher, 1982; Day, 2012), diamond-, graphite-, coesite- and quartz-bearing eclogites, lherzolites and granulites are excellent candidates to test the reliability of a garnet-clinopyroxene thermobarometer. Here we 266 use the REE-in-garnet-clinopyroxene thermobarometer to calculate equilibrium temperatures and pressures for three types of samples (9 diamond-bearing eclogites, 2 graphite-bearing eclogites, and 12 quartz-bearing eclogites or granulites) with major and trace element compositions of garnet and clinopyroxene reported in the literature. The 9 diamond-bearing eclogites include 1 sample from Udachnaya kimberlite pipe in Siberia (Shatsky et al., 2008) and 8 samples from the Jericho Kimberlite in the northern Slave craton (Smart et al., 2009; up to 20% diamond); the 2 graphite-bearing eclogites are from the West Africa Craton (Barth et al., 2001); the 12 quartz- bearing samples contain 7 eclogites from Dabie-Sulu terrane (Tang et al., 2007), 1 granulite from Central Finland (Nehring et al., 2010), and 4 granulites from Udachnaya and Komsomolskaya Kimberlite Pipes in Siberia (Koreshkova et al., 2011). The individual temperature and pressure inversions for these samples can be found in Fig. 5-S3. For comparison, we also calculate the equilibrium temperatures and pressures for these samples using the barometer of Simakov (2008) and the thermometer of Krogh (1988). The REE-in-garnet-clinopyroxene thermobarometer generates reasonable temperatures and pressures for the three types of samples except pressures for two diamond-bearing eclogites (0.2 – 0.5 GPa lower than the diamond-graphite boundary; Fig. 5-8a). Because the barometer of Simakov (2008) does not work for clinopyroxene without CaTs or enstatite components, the combination of the barometer of Simakov (2008) and the thermometer of Krogh (1988) only produces temperatures and pressures for 12 samples (5 diamond-bearing, 1 graphite-bearing, and 6 quartz-bearing). However, the pressures of the 12 samples are highly problematic (Fig. 5-8b). Combining with other garnet-clinopyroxene thermometers (e.g., Ellis and Green, 1979; Ravna, 2000; Nakamura, 2009) or using temperatures derived from the REE-in-garnet-clinopyroxene thermobarometer would not significantly improve the pressures derived from the barometer of Simakov (2008) for these field samples. To further examine the accuracy and reliability of our REE-in-garnet-clinopyroxene thermobarometer, we compare the equilibrium temperatures of well-equilibrated mantle eclogites 267 calculated using our REE-based thermobarometer with those calculated using the Fe-Mg thermometers of Ellis and Green (1979), Krogh (1988), Ravna (2000), and Nakamura (2009) at equilibrium pressures derived from the REE-in-garnet-clinopyroxene thermobarometer (Fig. 5-9). We compiled 35 mantle eclogite xenoliths with mineral major and trace element compositions reported in the literature that most likely approach equilibrium in the mantle. These eclogites were used in Section 2.2 and Fig. 5-3b to justify our garnet-clinopyroxene REE partitioning model. They include 14 Type II eclogites from the Kaapvaal Craton (Harte and Kirkley, 1997; Huang et al., 2012), 2 Group 2 eclogites from the Siberian Craton (Jacob and Foley, 1999), 11 low-MgO eclogites from the West African Craton (Barth et al., 2001), and 8 diamond eclogites from the Slave Craton (Smart et al., 2009). To facilitate comparisons between thermometers, we calculate the Pearson’s Chi-squares ( χ p ) using Eq. (10) and replace the measured temperatures 2 (Mj in Eq. 10) by those derived from the REE-in-garnet-clinopyroxene thermobarometer. The smaller χ p value, the better agreement between the REE and Fe-Mg thermometer is. For the 35 2 well-equilibrated mantle eclogites, the widely used garnet-clinopyroxene Fe-Mg thermometers of Ellis and Green (1979), Krogh (1988) and Ravna (2000) provide temperatures generally within 100ºC (dashed lines) of those calculated using the REE-in-garnet-clinopyroxene thermobarometer (Figs. 5-9(a-c)). Note that the 100ºC temperature differences are comparable to the uncertainties of the garnet-clinopyroxene Fe-Mg thermometers. However, the recent Fe-Mg thermometer of Nakamura (2009) generates temperatures for many samples significantly (up to 341 ºC) higher than those derived from our REE-based thermobarometer (Fig. 5-9d). Overall, for the well- equilibrated samples, temperature estimations by Krogh’s thermometer (1988) are in excellent agreement with those of the REE-in-garnet-clinopyroxene thermobarometer ( χ p = 299 ). 2 In summary, the 14 partitioning experiments demonstrate that the REE-in-garnet- clinopyroxene thermobarometer generally better reproduces the experimental temperatures than 268 the garnet-clinopyroxene Fe-Mg thermometers, and has a good reproducibility for the experimental pressures, comparable to that of the barometer of Simakov (2008). Application to diamond-, graphite-, and quartz-bearing field samples further validate the reliability of the REE- in-garnet-clinopyroxene thermobarometer. In addition, the excellent agreement in temperatures derived from the REE-in-garnet-clinopyroxene thermobarometer and the widely used thermometer of Krogh (1988) for the 35 well-equilibrated mantle eclogites proves the accuracy of the REE-in-garnet-clinopyroxene thermobarometer for field samples at subsolidus conditions. 4. Geological Applications There is a large body of work on major and trace element abundances in garnet- and clinopyroxene-bearing rocks from active tectonic environments in the Earth’s mantle and lower crust (e.g., high pressure and ultra-high pressure terranes, subducted oceanic lithosphere, and thermally eroded lithospheric mantle). Because garnet- and clinopyroxene-bearing rocks from active tectonic settings have complex thermal histories, major and trace elements in the garnet and clinopyroxene may depart from chemical equilibrium at the local geotherm during exhumation, subduction or thermal erosion processes. Applying the REE-in-two-pyroxene thermometer to abyssal peridotites and mafic cumulates, Liang et al. (2013) demonstrated that the REE-in-two-pyroxene thermometer records higher closure temperatures than the major element- based two-pyroxene thermometers for mafic and ultramafic rocks that experienced cooling. This raises two important questions for the REE-in-garnet-clinopyroxene thermobarometer. (1) Are there any differences in temperatures derived from the REE-in-garnet-clinopyroxene thermobarometer and the garnet-clinopyroxene Fe-Mg thermometers for garnet- and clinopyroxene-bearing rocks from different tectonic environments? (2) Can the REE-in-garnet- clinopyroxene thermobarometer be used to study thermal histories of these rocks? In this section, we first discuss the physical meaning of temperatures and pressures derived from the REE-in- garnet-clinopyroxene thermobarometer, and then apply the REE-in-garnet-clinopyroxene 269 thermobarometer to garnet- and clinopyroxene-bearing rocks from tectonic settings that experienced cooling or heating processes. For comparison, we also calculate temperatures using the garnet-clinopyroxene Fe-Mg thermometer of Krogh (1988) at pressures derived from the REE-in-garnet-clinopyroxene thermobarometer. 4.1. Physical meaning of calculated temperature and pressure Diffusive re-distribution of REEs between a pair of minerals during subsolidus re- equilibration depends on the diffusion rates of REEs in the minerals, the partition coefficients of REEs between this pair of minerals, grain sizes of the minerals and relative mineral proportions (Liang, 2014). The diffusion rates of REEs in clinopyroxene decrease systematically with their ionic radii (Van Orman et al., 2001), whereas those in garnet are insensitive to their ionic radii (Van Orman et al., 2002; Fig. 5-10a). As demonstrated in Section 2.2, the partition coefficients of REEs between garnet and clinopyroxene also depend on their ionic radii. In general, light REEs are highly compatible in clinopyroxene relative to garnet, while heavy REEs are very compatible in garnet relative to clinopyroxene (Fig. 5-10b). To assess the dominant factors determining the diffusive re-distribution of REEs, we use the following equation to calculate the time scales of diffusive re-equilibration for REEs in garnet-clinopyroxene bi-mineralic systems (Liang, 2014) ⎛ φcpx ⎞ L2grt ⎛ φgrt k ⎞ L2cpx tD = ⎜ ⎟ +⎜ ⎟ (11) ⎝ φgrt k + φcpx ⎠ β Dgrt ⎝ φgrt k + φcpx ⎠ β Dcpx where φcpx, and φgrt are the volume proportions of clinopyroxene and garnet, respectively; k is the partition coefficient of a trace element between garnet and clinopyroxene; Dgrt and Dcpx are the diffusivities of the trace element in garnet and clinopyroxene, respectively; β is a geometric factor, and is 1, 4, or 5 for plane sheet of half length L, cylinder or sphere of radius L, respectively. For the purpose of demonstration, here we consider garnet-clinopyroxene aggregates with a uniform spherical grain size (Lgrt = Lcpx = 0.25 mm; β = 5). 270 Figure 5-10c compares the diffusive re-equilibration times for REEs in garnet- clinopyroxene aggregates for three choices of mineral proportions (φcpx = 20%, 50%, and 80%) at 1200ºC and 1000ºC. Because of their smaller diffusion rates in clinopyroxene and large garnet- clinopyroxene partition coefficients [cf. Figs. 5-10(a-b) and Eq. (11)], heavy REEs in clinopyroxene determine their diffusive re-equilibration times in garnet-clinopyroxene aggregates. However, the diffusive re-equilibration times for light REEs are results of a combination of partition coefficients, diffusion rates, and mineral proportions. For garnet-clinopyroxene aggregates with less than 20% clinopyroxene, light REEs in clinopyroxene dominate their diffusive re-equilibration times. As the clinopyroxene proportion increases, light REEs in garnet become more important to affecting their diffusive re-equilibration times in garnet-clinopyroxene aggregates, which leads to comparable diffusive re-equilibration times for light and heavy REEs. Because the REE-in-garnet-clinopyroxene thermobarometer are based on the temperature and pressure dependent garnet-clinopyroxene REE exchange, for a garnet- and clinopyroxene-bearing rock that experienced cooling, temperatures (and pressures) derived from this thermobarometer is thus closely related to the average closure temperature (and pressure) of REEs in garnet- clinopyroxene bi-mineralic systems, and may be affected by the relative mineral proportions. To further examine the physical meaning of temperatures (and pressures) derived from the REE-in-garnet-clinopyroxene thermobarometer for thermally perturbed samples, we compare the “diffusive opening” temperatures of Fe-Mg with those of REEs in garnet and clinopyroxene. Using the garnet Fe-Mg diffusion data from Freer and Edwards (1999) and the garnet Ce diffusion data from Van Orman et al. (2002), we calculated the “diffusive opening” temperatures of Fe-Mg and Ce in a garnet (1 mm diameter) with a linear heating rate (200ºC/Ma) using the simple equation developed by Watson and Cherniak (2013). We found that the 50% retention level for Fe-Mg in garnet is reached at 677 ºC while that for Ce in garnet is reached at 1049 ºC. Similarly, we also calculated the “diffusive opening” temperatures of Fe-Mg and Yb in a 271 clinopyroxene (1 mm diameter) using the clinopyroxene Fe-Mg diffusion data from Ganguly and Tazzoli (1994) and the clinopyroxene Yb diffusion data from Van Orman et al. (2001). The 50% retention level for Fe-Mg in clinopyroxene is reached at 801 ºC while that for Yb in clinopyroxene is reached at 1037 ºC. The “diffusive opening” temperatures of Fe-Mg in garnet and clinopyroxene (677 – 801 ºC) are significantly lower than those of REEs (1037 – 1049 ºC). Therefore, for a garnet- and clinopyroxene-bearing rock that underwent heating, temperatures (and pressures) estimated by the REE-in-garnet-clinopyroxene thermobarometer are likely the equilibrium temperature (and pressure) before heating or an average re-equilibration temperature (and pressure) of REEs in garnet-clinopyroxene bi-mineralic systems at an early stage of heating. In the succeeding discussion, we will further demonstrate this through field data. 4.2. Granulites, eclogites and peridotites from cooling tectonic settings We compiled 27 samples with major and trace element compositions of garnet and clinopyroxene reported in the literatures from cooling tectonic environments. These samples include 8 granulite xenoliths from Siberia (Koreshkova et al., 2011), 6 granulites from granulite blocks in Central Finland (Nehring et al., 2010), 8 eclogites from Dabie-Sulu ultra-high pressure terrane (Tang et al., 2007), 3 garnet peridotites from the orogenic peridotite massif in the Western Gneiss Region in Norway (Spengler et al., 2006), and 2 garnet peridotite xenoliths from the arc lithosphere in Sierra Nevada (Chin et al., 2013). Based on the decrease of Mg# in the rims of garnet grains, Koreshkova et al. (2011) suggest that the granulites from Siberia experienced subsequent cooling and decompression following the last granulite metamorphic event. A similar cooling and decompression process was also inferred from the thermobarometry and metamorphic reactions for the granulites from Finland (Hölttä and Paavola, 2000; Nehring et al., 2010). The 8 eclogites from Dabie-Sulu and the 3 garnet peridotites from Norway were exhumed to the surface presumably associated with cooling. Based on the low equilibrium temperatures (< 800 ºC at ~ 3 GPa) derived from the pyroxene thermobarometer, Chin et al. (2013) suggested that 272 the garnet peridotite xenoliths from Sierra Nevada underwent compression and cooling after melt depletion at shallow depth. For the aforementioned samples, the temperatures derived from the REE-in-garnet- clinopyroxene thermobarometer are systematically higher than those calculated using the garnet- clinopyroxene Fe-Mg thermometer of Krogh (1988) (Fig. 5-11a; see also Fig. 5-S3 for individual temperature and pressure inversions). One exception is an eclogite from Dabie-Sulu with a higher Fe-Mg temperature. The higher REE temperature is a common feature for samples experienced cooling processes. Because REEs diffuse significantly slower than Fe and Mg in garnet and clinopyroxene (e.g., Van Orman et al., 2002; Cherniak and Dimanov 2010 and references therein), the REE-in-garnet-clinopyroxene thermobarometer records temperatures at the early stage of cooling (i.e., higher closure temperatures). For retrograde granulites or eclogites, it would be particularly useful to reveal peak metamorphic conditions. Therefore, the pressures and temperatures derived from the REE-in-garnet-clinopyroxene thermobarometer may be used to define exhumation trajectories for the garnet and clinopyroxene-bearing rocks (Fig. 5-11b). It may be possible to estimate cooling or exhumation histories of these rocks by coupling the Sm- Nd isotope ages and the REE-in-garnet-clinopyroxene thermobarometer. 4.3. Eclogites, garnet pyroxenites and peridotites from thermally perturbed settings We compiled 37 garnet- and clinopyroxene-bearing rocks with mineral major and trace element compositions reported in the literature from thermally perturbed tectonic settings. The 37 samples contain 4 eclogite xenoliths from the Siberia craton (3 Group 1 eclogites: Jacob and Foley, 1999; 1 diamond-bearing eclogite: Shatsky et al., 2008), 17 eclogite xenoliths from Kimberley, South Africa (Jacob et al., 2009), 2 eclogite xenoliths from Jericho in the Slave Craton (Group B and Group C eclogites; Smart et al., 2009), 4 M3 garnets from the Western Gneiss Region in Norway (Scambelluri et al., 2008), 4 Type-IV garnet pyroxenites from the Beni 273 Bousera massif in Morocco (Gysi et al., 2011), and 6 garnet peridotite xenoliths from Prahuaniyeu, South America (Bjerg et al., 2009). The diamond-bearing eclogite from Siberia displays light carbon isotope composition in diamond, indicating that it derived from subducted oceanic or continental lithosphere (Shatsky et al., 2008). The Group 1 eclogite xenoliths from Siberia show elevated oxygen isotope ratios than the mantle values, suggesting a low-temperature altered upper crust origin (Jacob and Foley, 1999). Although the eclogite xenoliths from Kimberley were metasomatized with a significant amount of phlogotites, they retained the lighter oxygen isotope compositions derived from their protoliths, seawater altered oceanic cumulates (Jacob et al., 2009). The Group B and Group C eclogites from the Slave Craton have been interpreted as remnants of subducted oceanic crust mainly based on the U-Pb ages of zircon and rutile in the eclogites (Heaman et al., 2002). The formation of the M3 majoritic garnets from Norway also involved deep subduction during the orogenic process according to the phase assemblages in the M3 minerals (e.g., Scambelluri et al., 2008). The preserved magmatic plagioclase and prograde metamorphic phase assemblages indicate that the Type-IV pyroxenites from Morocco originated from delaminated crustal cumulates (Gysi et al., 2011). Finally, the apparent Sm-Nd isotope ages and high equilibrium temperatures suggest that the mantle sources of the garnet peridotite xenoliths from Prahuaniyeu have been thermally perturbed by a high-temperature event (Bjerg et al., 2009). Figure 5-11c shows that temperatures derived from the REE-in-garnet-clinopyroxene thermobarometer are systematically lower than those calculated using the garnet-clinopyroxene Fe-Mg thermometer of Krogh (1988) for these samples (see Fig. 5-S3 for individual temperature and pressure inversions). (One possible exception is the Group B eclogite from the Slave Craton). This further demonstrates that the Fe-Mg exchange thermometer can be easily reset to the high ambient temperature during heating, while the REE-based thermometer potentially records former low temperatures at an early stage of heating or perhaps before heating. The temperature differences between the REE and the Fe-Mg thermometers therefore may be used to infer thermal 274 histories (i.e., cooling and heating) of mafic and ultramafic rocks from various tectonic settings. For subduction-derived eclogites and peridotites, temperatures and pressures calculated using the REE-in-garnet-clinopyroxene thermobarometer may be used to deduce subduction trajectories (Fig. 5-11d). When coupled with Sm-Nd isotope ages, the REE-in-garnet-clinopyroxene thermobarometer may be used to constrain the rates of subduction, delamination, or heating. Thus, the REE-in-garnet-clinopyroxene thermobarometer would be particularly useful to study large- scale tectonic processes. 5. Summary and Further Discussion We have developed a REE-in-garnet-clinopyroxene thermobarometer for garnet- and clinopyroxene-bearing mafic and ultramafic rocks. This new thermobarometer is based on the temperature- and pressure-dependent REE and Y partitioning between garnet and clinopyroxene, and is tested against measured partition coefficients from experimentally determined mineral-melt partition coefficients and from field samples, including eclogites and granulites with quartz, graphite and diamond, and well-equilibrated mantle eclogite xenoliths. Taken collectively, these experimental and field data establishes the accuracy and reliability of the REE-in-garnet- clinopyroxene thermobarometer at magmatic and subsolidus conditions. Applications of the REE- in-garnet-clinopyroxene thermobarometer to garnet- and clinopyroxene-bearing mafic and ultramafic rocks from active tectonic environments demonstrate that the REE-based thermobarometer records temperatures higher than those from the Fe-Mg thermometer for samples from cooling tectonic settings, but lower than those from the Fe-Mg thermometer for samples from thermally perturbed settings. We attribute the systematic temperature differences to the differences in diffusion rates, and hence closure temperatures, between the trivalent REEs and divalent Fe-Mg in garnet and clinopyroxene. Thus, the REE-in-garnet-clinopyroxene thermobarometer is capable of revealing thermal histories of garnet- and clinopyroxene-bearing rocks. Because garnet and clinopyroxene used in our model calibrations are mostly Mg-rich, 275 cautions should be exercised when applying the REE-in-garnet-clinopyroxene thermobarometer to field samples with grossular-rich garnet or Fe-rich garnet and clinopyroxene (e.g., Mg# < 40, and > 50% grossular in garnet). Additional REE partitioning experiments with coexisting garnet and clinopyroxene in more mafic systems are needed to further test and calibrate the REE-in- garnet-clinopyroxene thermobarometer in the future. The distribution of Fe2+-Mg2+ in the M2 and M1 sites in clinopyroxene becomes highly ordered at lower temperatures (e.g., McCallister et al., 1976; Dal Negro et al., 1982; Ganguly, 1982; Brizi et al., 2000). In our parameterized lattice model, REE partitioning in clinopyroxene M2 depends on X Mg which was calculated by assuming random distribution of Fe2+-Mg2+ in clinopyroxene (Eq. 7a). The ordering of Fe2+-Mg2+ over the M1 and M2 sites in clinopyroxene may lead to significant uncertainties in the temperature estimation for field samples. Here, we assessed the effect of Fe2+-Mg2+ ordering in clinopyroxene on temperatures derived from the REE-based thermobarometer using the relation between temperature and Fe2+-Mg2+ distribution in clinopyroxene quantified by Brizi et al. (2000; their Eq. 4). We first calculated the amount of Mg in the M2 site of clinopyroxene from the experiments compiled in Chapter 1, and re- calibrated the lattice strain parameters in Eqs. (7a-c). The updated coefficients differ from those in Eqs. (7a-c) within the 2σ errors, but slightly decrease the model reproducibility for the compiled clinopyroxene-melt REE and Y partitioning data. Provided the ordering distribution of Fe2+-Mg2+ in clinopyroxene, we then re-calculated temperatures for the 35 well-equilibrated mantle eclogite xenoliths using the updated lattice strain parameters for clinopyroxene. The temperatures marginally increase by 1 – 20 ºC (Supplementary Fig. 5-S4), indicating negligible influence of the ordering of Fe2+-Mg2+ in clinopyroxene. The small effect of Fe2+-Mg2+ ordering M2 in clinopyroxene can be understood by the small coefficient of X Mg in Eq. (7a) and low abundance of Mg in the M2 site in clinopyroxene. 276 Another important source of uncertainties is the trade-off between the temperature and pressure in the garnet-clinopyroxene REE partitioning model (Eq. 2). Through Monte Carlo simulations, we found that the inverted temperatures and pressures show a weak but positive correlation (Fig. 5-S5). The accuracy of the REE-in-garnet-clinopyroxene thermobarometer also depends on analytical errors in major element and REE compositions of garnet and clinopyroxene. Analytical errors in major element concentrations of garnet and clinopyroxene are typically small, i.e., less than 1% errors in electron microprobe analysis, while those in REE abundances of garnet and clinopyroxene may be up to 20% or perhaps greater by the Laser Ablation Inductively Coupled Plasma Mass Spectrometry (LA-ICP-MS) analysis. The effects of analytical errors on the accuracy of the REE-in-garnet-clinopyroxene thermobarometer can also be illustrated through Monte Carlo simulations. For example, 1% relative errors in major element compositions of garnet and clinopyroxene result in less than 15 ºC uncertainties in the inverted temperature and less than 0.25 GPa uncertainties in the calculated pressure. These uncertainties are comparable to those from 10% analytical error in REEs in garnet and clinopyroxene (Fig. 5-12). The uncertainties in the estimated temperatures and pressures increase with the analytical errors in the REE abundances, while the uncertainties in the estimated temperature also increase with the equilibrium temperature (Fig. 5-12). The number of REEs used in the inversion is also an important factor. When all REEs are included in the inversion, a 20% analytical error in REEs results in less than 50 ºC uncertainties in temperature and 0.5 GPa uncertainties in pressures. When certain REEs are below detection limits or altered by secondary processes (e.g., light REE enrichments), one has to exclude them to obtain a reliable temperature and pressure (Figs. 5-4(c-d)). 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A parameterized model for REE distribution between low- Ca pyroxene and basaltic melts with applications to REE partitioning in low-Ca pyroxene along a mantle adiabat and during pyroxenite-derived melt and peridotite interaction. Contributions to Mineralogy and Petrology, 164(2), 261-280. 285 Figure Captions Figure 5-1 Temperature variations as functions of pressure derived from different garnet- clinopyroxene Fe-Mg thermometers. Major element compositions of garnet and clinopyroxene are from Huang et al. (2012; RV07-12). Figure 5-2 Quadrilateral and ternary diagrams showing compositions of clinopyroxenes (a) and garnets (b) used in the clinopyroxene–melt REE partitioning model (Chapter 1), and the garnet– melt REE partitioning model (Chapter 3). Di, En, Hd and Fs denote pyroxene end-members, diopside, enstatite, hedenbergite, and ferrosilite, respectively. Py, Gross, and Alm+ represent garnet end-members, pyrope, grossular, almandine (+spessartine), respectively. Gray areas denote the clinopyroxene and garnet compositions from well-equilibrated mantle eclogite xenoliths. See text for details of the mantle eclogites. Figure 5-3 Comparisons of model-derived and measured REE and Y partition coefficients between garnet and clinopyroxene for partitioning experiments (a) and well-equilibrated mantle eclogite xenoliths (b). The experimental data are from Green et al. (2000), Klemme et al. (2002), Adam and Green (2006), Tuff and Gibson (2007), and Suzuki et al. (2012), while the mantle eclogite xenoliths are from the Roberts Victor kimberlite, South Africa (Type II eclogites; Harte and Kirkley, 1997; Huang et al., 2012), the Udachnaya kimberlite, Siberia (Group 2 eclogites; Jacob and Foley, 1999), the Koidu kimberlite complex, West Africa (low-MgO eclogites; Barth et al., 2001), and the Jericho kimberlite, Canada (Diamond eclogites; Smart et al., 2009). Solid blue lines are 1:1 lines, and dashed lines are 1:2 and 2:1 lines. Figure 5-4 Inversions of temperatures and pressures from REE abundances in garnet and clinopyroxene for a well-equilibrated diamond eclogite (a, b) and a light REE-altered eclogite (c, d). The mineral compositions of the diamond eclogite are from Smart et al. (2009) and those of 286 the light REE-altered eclogite are from Huang et al. (2012). (a, c) display the primitive mantle normalized REE abundances in garnet and clinopyroxene, and (b, d) show the inversions of the temperature and pressure through linear least squares regression analysis. The coefficients A and B are calculated using Eqs. (9b-c). Primitive mantle compositions are from Hofmann (1988). Symbols with light blue colors highlight the REEs that may be altered and were excluded in the temperature and pressure inversion. Figure 5-5 Comparisons of the temperatures and pressures derived from the REE-in-garnet- clinopyroxene thermobarometer and those from the experimental runs. Solid blue lines are 1:1 lines, and dashed lines denote ±100 ºC in (a) and ±1 GPa in (b). The χ p value in (a) becomes 49 2 when the two experiments (Runs 1798 and 1807) from Green et al. (2000) were excluded. Figure 5-6 Comparisons of the calculated temperatures by the garnet-clinopyroxene Fe-Mg thermometers and the experimental temperatures. The thermometers are from Ellis and Green (1979; a), Ravna (2000; b), Krogh (1988; c) and Nakamura (2009; d). Pressures used in the thermometers were the experimental pressures. χ p values in the circled regions were calculated 2 by excluding the two experimental data within the circled regions [Runs 1798 and 1807 from Green et al. (2000)]. Figure 5-7 Comparisons of the estimated pressures and the experimental pressures. To calculate pressures, the experimental temperatures (a) and the thermometer of Krogh (1988; b) were used in the garnet-clinopyroxene barometer of Simakov (2008). Figure 5-8 Temperatures and pressures for eclogites and granulites with quartz, graphite and diamond estimated by the REE-in-garnet-clinopyroxene thermobarometer (a) and the major 287 element-based garnet-clinopyroxene thermometer and barometer of Krogh (1988) and Simakov (2008) (b). The graphite-diamond phase boundary is from Day (2012), and the quartz-coesite phase boundary is from Bohlen and Boettcher (1982). Figure 5-9 Comparisons of the temperatures derived from the REE-in-garnet-clinopyroxene thermobarometer and those calculated by the Fe-Mg thermometers of Ellis and Green (1979; a), Ravna (2000; b), Krogh (1988; c) and Nakamura (2009; d) for well-equilibrated mantle eclogite xenoliths. The pressures used in the Fe-Mg thermometers were calculated by the REE-in-garnet- clinopyroxene thermobarometer. Details of these eclogites samples are in the text and in Fig. 5-3. Figure 5-10 (a) Diffusion coefficients of REEs in clinopyroxene and garnet as a function of temperature (Van Orman et al., 2001, 2002). (b) Partition coefficients of REEs between garnet and clinopyroxene at 1200ºC, 1000ºC, 800ºC and 2.8 GPa. (c) Diffusive re-equilibration times for REEs in garnet-clinopyroxene aggregates at 1200ºC and 1000ºC for three choices of clinopyroxene proportions (20%, 50%, 80%). Figure 5-11 Calculated temperatures and pressures for garnet and clinopyroxene-bearing rocks from cooling (a, b) and thermally perturbed (c, d) tectonic settings. (a, c) show the systematic temperature differences between the REE-in-garnet-clinopyroxene thermobarometer and the garnet-clinopyroxene Fe-Mg thermometer of Krogh (1988). (b, d) display the calculated pressures and temperatures by the REE-in-garnet-clinopyroxene thermobarometer. In the legend, P, E, G and Pxn represent peridotites, eclogites, granulites and pyroxenites. Eclogites from Siberia include the Group 1 eclogites from Jacob and Foley (1999; squares) and the diamond-bearing eclogite from Shatsky et al. (2008; triangle). Details of other samples are in the text. 288 Figure 5-12 Uncertainties in the calculated temperatures and pressures using the REE-in-garnet- clinopyroxene thermobarometer arising from analytical errors of REEs in garnet and clinopyroxene. Here we consider analytical uncertainties in REE compositions from two eclogites [RV07-12 from Huang et al. (2012); JDE 07 from Smart et al. (2009)] with different equilibrium temperatures and pressures (RV07-12: 1015 ºC, 2.4 GPa, dashed curves; JDE07: 801 ºC, 3.8 GPa, solid curves). The temperature and pressure uncertainties are standard errors calculated from Monte Carlo simulation results for 1000 sets of garnet-clinopyroxene REE partition coefficients with normally distributed random noise as the analytical error. Figure 5-S1 Inversion of the temperature and pressure from REE abundances in garnet and clinopyroxene for an eclogite with REEs in disequilibrium. The mineral compositions of the eclogite are from Doucet et al. (2013). (a) shows the primitive mantle normalized REE abundances in garnet and clinopyroxene, and (b) shows the inversion of the temperature and pressure through linear least squares regression analysis. Figure 5-S2 Inversions of the temperatures and pressures from REE abundances in garnet and clinopyroxene for the individual partitioning experiments from the literature. Figure 5-S3 Inversions of the temperatures and pressures from REE abundances in garnet and clinopyroxene for the individual field samples from the literature. Figure 5-S4 The differences in temperatures calculated using the REE-in-garnet-clinopyroxene thermometers with ordering versus random distribution of Fe2+-Mg2+ in clinopyroxene as a function of equilibrium temperatures for well-equilibrated mantle eclogite xenoliths. The xenoliths are the same as those used in Fig. 5-9. 289 Figure 5-S5 Results of Monte Carlo simulations showing the correlation between temperatures and pressures derived from the REE-in-garnet-clinopyroxene thermobarometer for 1000 sets of synthetic garnet-clinopyroxene REE partition coefficients with 10% normally distributed random noise. The mineral compositions of the eclogite are from Huang et al. (2012; RV07-12). 290 Figures Figure 5-1 1150 1100 Temperature (°C) 1050 ) 09 0) 20 79) r a( 20 0 n (19 mu a ( Gree 1000 ka n s& Na av Elli R 950 ) (1 988 Krogh 900 850 2.5 3 3.5 4 4.5 5 5.5 6 Pressure (GPa) 291 Figure 5-2 (a) Di Hd Mantle eclogites En Fs Gro (b) 50 50 30 30 Mantle 10 eclogites 10 Pyr 50 Alm+ 292 Figure 5-3 10 10 1 1 10 10 0 0 10 10 10 10 10 10 0 1 0 1 10 10 10 10 10 10 10 10 10 10 293 Figure 5-4 10 o (a) TREE ± C (b) Garnet PREE ± Primitive Mantle Normalized 1 10 o Tm T C Ho o Clinopyroxene T C Tb 0 o Gd 10 TEG C o T C Eu Sm Nd 10 Pr La 10 La Pr Sm Gd Dy Ho Tm Lu Ce Nd Eu Tb Y Er Yb o TREE ± C (d) PREE ± Primitive Mantle Normalized Garnet o T C Tm T o C Ho o Tb TEG C Gd o Eu T C Sm Clinopyroxene Nd La Pr Sm Gd Dy Ho Tm Lu Ce Nd Eu Tb Y Er Yb 294 Figure 5-5 2200 15 Suzuki et al. (2012) 2 Adam and Green (2006) p =5 2000 Tuff and Gibson (2007) Green et al. (2000) 1800 10 PREE (GPa) ( C) o 1600 REE T 2 1400 p = 49 5 2 p = 63 1200 (a) (b) 1000 0 1000 1200 1400 1600 1800 2000 0 5 10 15 T (oC) Pexp (GPa) exp 295 Figure 5-6 2200 2200 2 2 (a) p = 268 (c) p = 307 2000 P = Pexp 2000 P = Pexp 1800 1800 TK88 (oC) TEG (oC) 2 1600 1600 p = 43 2 p = 103 1400 1400 Suzuki et al. (2012) 1200 Adam and Green (2006) 1200 Tuff and Gibson (2007) Green et al. (2000) 1000 1000 1000 1200 1400 1600 1800 2000 2200 1000 1200 1400 1600 1800 2000 2200 Texp (oC) Texp (oC) 2400 2200 2 2 (b) p = 414 (d) p= 374 2200 2000 P = Pexp P = Pexp 2000 1800 TN09 (oC) TK00 (oC) 1800 1600 2 = 126 p 1600 2 p = 190 1400 1400 1200 1200 1000 1000 1000 1200 1400 1600 1800 2000 2200 1000 1200 1400 1600 1800 2000 2200 o Texp ( C) Texp (oC) 296 Figure 5-7 15 15 (a) 2 =3 (b) 2 =8 p p T = Texp T = TK88 10 10 PS08 (GPa) PS08 (GPa) 5 5 Suzuki et al. (2012) Adam and Green (2006) Tuff and Gibson (2007) Green et al. (2000) 0 0 0 5 10 15 0 5 10 15 Pexp (GPa) Pexp (GPa) 297 Figure 5-8 0 1 0 2 (GPa) PS08 (GPa) 2 3 REE 4 P 4 5 6 (a) 6 8 600 800 1000 1200 1400 600 800 1000 1200 TREE (oC) TK88 (oC) 298 Figure 5-9 1400 1400 Huang et al. (2012) Harte & Kirkley (1997) (c) 1300 1300 Jacob and Foley (1999) 1200 Smart et al. (2009) 1200 Barth et al. (2001) 1100 1100 TREE (oC) TREE (oC) (a) 1000 1000 900 900 800 800 P = PREE P = PREE 700 2 700 2 p= 435 p= 299 600 600 600 800 1000 1200 1400 600 800 1000 1200 1400 TEG (oC) TK88 (oC) 1400 1400 1300 (b) 1300 (d) 1200 1200 1100 1100 TREE (oC) TREE ( C) o 1000 1000 900 900 800 800 P = PREE P = PREE 700 2 700 2 p= 458 p= 865 600 600 600 800 1000 1200 1400 600 800 1000 1200 1400 TK00 (oC) TN09 (oC) 299 Figure 5-10 10 10 10 (a) (b) (c) 10 10 10 0% 1 10 cpx Diffusion Coefficient (m /s) 10 cpx ºC 10 20% 0 00 cpx 10 12 50 % 10 Yb cpx 300 in RE 1 80% cp Ei 0ºC 10 1000ºC x ng 10 rt 1 00 Dy 10 100% grt in 0 cp 10 100 x x %c 10 20% cp px ºC Nd px 1200ºC 0 c 80 in cp 10 50% La x 10 cpx 10 80% in 100% grt cp x 10 10 10 6 6.5 7 7.5 8 La Ce Pr Nd SmEu Gd Tb Dy Ho Er Tm Yb Lu La Ce Pr Nd SmEu Gd Tb Dy Ho Er Tm Yb Lu 10000/T (K ) Figure 5-11 301 Figure 5-12 2 300 801 ºC 1015 ºC 3.8 GPa 2.4 GPa All REEs All REEs 250 No HREEs No HREEs No LREEs 1.5 No LREEs 200 P (GPa) T (oC) 150 1 100 0.5 50 (a) (b) 0 0 0 10 20 30 40 50 0 10 20 30 40 50 Errors in REE analysis (%) Errors in REE analysis (%) 302 Figure 5-S1 1 10 o TREE ± C Lu PREE ± Primitive Mantle Normalized 0 10 0 Tm o T C Ho Garnet o TK00 C Tb B/1000 o Gd 10 TEG C o Eu T C Sm Nd Clinopyroxene 10 Pr La 10 La Pr Sm Gd Dy Ho Tm Lu 0 Ce Nd Eu Tb Y Er Yb 303 Figure 5-S2 Figure S2(1) 3 10 4 Suzuki et al. (2012) Suzuki et al. (2012) Sample: S1678 o 2 Sample: S1678 TREE = 1658±41 C Texp = 1550oC 0 2 PREE = 5.33±0.39GPa 10 Pexp = 3GPa Ho −2 Tb Gd Eu −4 Sm 1 Nd −6 10 Pr −8 Garnet −10 Cpx 0 10 −12 3 10 4 Suzuki et al. (2012) Suzuki et al. (2012) Sample: U236 Sample: U236 o 2 Texp = 1580oC TREE = 1641±44 C Concentration (ppm) 2 10 Pexp = 5GPa PREE = 7.15±0.56GPa Lu 0 Tm Ho −2 Tb B/1000 1 Gd 10 Eu −4 Sm Nd −6 0 Pr 10 −8 La −10 −1 10 −12 3 10 4 Suzuki et al. (2012) Suzuki et al. (2012) Sample: U206 Sample: U206 o 2 Texp = 1580oC TREE = 1624±55 C 2 10 Pexp = 5GPa PREE = 7.75±0.57GPa 0 Ho −2 Tb 1 Gd 10 Eu −4 Sm −6 0 10 −8 −10 −1 10 −12 La Ce Pr NdSmEuGd Tb Dy Y Ho Er TmYb Lu −10 −5 0 ln(D)−A 304 Figure S2(2) 3 10 4 Suzuki et al. (2012) Suzuki et al. (2012) Sample: U279 o 2 Sample: U279 TREE = 1732±39 C Texp = 1650oC Lu Tm 0 2 PREE = 6.54±0.41GPa 10 Pexp = 8GPa Ho Tb −2 Gd Eu Sm −4 1 Nd −6 10 Pr −8 Garnet La −10 Cpx 0 10 −12 3 10 4 Suzuki et al. (2012) Suzuki et al. (2012) Sample: U196 o 2 Sample: U196 TREE = 1900±65 C Texp = 1850oC Concentration (ppm) Lu 0 2 PREE = 9.92±0.98GPa Tm 10 Pexp = 10GPa Ho Tb −2 B/1000 Gd Eu −4 Sm 1 Nd −6 10 Pr −8 La −10 0 10 −12 3 10 4 Suzuki et al. (2012) Suzuki et al. (2012) Sample: U312 o 2 Sample: U312 TREE = 2074±116 C Texp = 1900oC Lu Tm 0 PREE = 11.17±1.95GPa 10 2 Pexp = 12GPa Ho Tb −2 Gd Eu Sm −4 1 Nd −6 10 Pr −8 La −10 0 10 −12 La Ce Pr NdSmEuGd Tb Dy Y Ho Er TmYb Lu −10 −5 0 ln(D)−A 305 Figure S2(3) 1 10 4 Adam and Green (2006) Adam and Green (2006) Sample: 1956 Sample: 1956 o 2 Texp = 1180oC TREE = 1088±63 C 0 10 Pexp = 4GPa PREE = 3.62±0.81GPa Lu 0 Ho −2 −1 Tb 10 −4 Sm −6 −2 Nd 10 −8 Garnet La −10 Cpx −3 10 −12 1 10 4 Mineral−Melt Partition Coefficient Tuff and Gibson (2007) Tuff and Gibson (2007) Sample: P−511 Sample: P−511 o 2 Texp = 1475oC TREE = 1466±111 C 0 10 Pexp = 3GPa PREE = 2.35±0.58GPa 0 Lu Ho −2 B/1000 Tb 10 −1 Gd −4 Eu Sm −6 −2 10 −8 −10 −3 10 −12 1 10 4 Tuff and Gibson (2007) Tuff and Gibson (2007) Sample: P−529 Sample: P−529 o 2 Texp = 1425oC TREE = 1392±155 C 0 10 Pexp = 3GPa PREE = 3.76±1.05GPa 0 Lu Ho −2 −1 Tb 10 Gd −4 Eu Sm −6 −2 10 −8 −10 −3 10 −12 La Ce Pr NdSmEuGd Tb Dy Y Ho Er TmYb Lu −10 −5 0 ln(D)−A 306 Figure S2(4) 1 10 4 Tuff and Gibson (2007) Tuff and Gibson (2007) Sample: S−1295 Sample: S−1295o 2 Texp = 1500oC TREE = 1519±83 C 0 10 Pexp = 5GPa PREE = 7.30±1.23GPa 0 Ho −2 −1 Tb 10 Gd −4 Eu Sm −6 Nd −2 Pr 10 −8 Garnet −10 Cpx −3 10 −12 1 10 4 Mineral−Melt Partition Coefficient Tuff and Gibson (2007) Tuff and Gibson (2007) Sample: S−1330 Sample: S−1330 o 2 Texp = 1750oC TREE = 1718±169 C 0 10 Pexp = 7GPa PREE = 9.90±3.00GPa 0 Ho −2 B/1000 −1 Tb 10 Gd −4 Sm −6 Nd −2 Pr 10 −8 −10 −3 10 −12 1 10 4 Green et al. (2000) Green et al. (2000) Sample: 1787 Sample: 1787 o 2 Texp = 1200oC TREE = 1098±44 C 10 0 Lu 0 Pexp = 3GPa PREE = 2.53±0.47GPa Ho −2 Tb 10 −1 Gd −4 Eu Sm −6 Nd −2 10 Pr −8 La −10 −3 10 −12 La Ce Pr NdSmEuGd Tb Dy Y Ho Er TmYb Lu −10 −5 0 ln(D)−A 307 10 1 Sample: 1798 Sample: 1798 o 10 Texp = 1100oC TREE ±91 C PREE ± 0 Pexp Ho 0 Tb 10 Gd Eu Sm 10 10 Garnet Cpx 10 10 1 10 Sample: 1807 o Sample: 1807 o Texp C TREE ± C PREE ± Ho 0 0 Pexp 10 Tb Gd B/1000 Eu 10 Nd 10 Pr 10 La 10 La Ce Pr NdSmEuGd Tb Dy Y Ho Er TmYb Lu 0 308 Figure 5-S3 10 1 10 TREE = 907± C PREE ± 0 Tb 0 10 Sm 10 Pr 10 Cpx 10 10 1 10 TREE ± C PREE = 1.57± 0 0 10 B/1000 10 Sm 10 10 10 1 10 TREE = 910± C PREE ± 0 0 10 Tb Sm 10 Pr 10 10 Ce Pr Sm Tb Dy Y Er TmYb 0 309 10 1 10 TREE ±17 C Tm PREE ±0.17GPa 0 Tb 0 10 Sm 10 Pr 10 Cpx 10 10 1 10 TREE ± C PREE ± 0 0 10 B/1000 Sm 10 10 10 10 1 10 TREE ± C PREE ± 0 0 10 Sm 10 10 10 Ce Pr Sm Tb Dy Y Er TmYb 0 310 10 ±15oC 1 10 TREE Tm PREE ±0.11GPa 0 Tb 0 10 Sm 10 Pr 10 Cpx 10 10 1 o 10 TREE ± C PREE = 1.51± Tm 0 0 10 Tb B/1000 Sm 10 Pr 10 La 10 10 1 o 10 TREE ± C PREE ± 0 0 10 10 Sm 10 La 10 La Ce Pr Sm Tb Dy Y Er TmYb 0 311 10 ±50oC 1 10 TREE PREE = 0.86± 0 0 10 Sm 10 Nd 10 Cpx 10 10 1 o 10 TREE = 819± C PREE ± 0 0 10 B/1000 10 Sm Nd 10 10 10 TREE = 1106±15oC 1 10 PREE ± 0 Tm 0 10 Ho 10 Sm Nd Pr 10 La 10 La Ce Pr NdSm Dy Y Ho Er Tm 0 312 10 1 Sample: Pra70 10 TREE ± C PREE ± 0 Tm 0 10 Tb Gd 10 Sm Nd Pr 10 Cpx 10 10 1 10 TREE ± C PREE ± 0 Tm 0 10 B/1000 Tb Gd 10 Sm Nd 10 10 10 1 10 TREE ± C PREE ± 0 Tm 0 10 Tb Gd 10 Sm Nd Pr 10 10 Ce Pr NdSm Gd Tb Y Er TmYb 0 313 10 1 10 TREE ± C PREE ± 0 Tm 0 10 Tb Gd 10 Sm Nd Pr 10 Cpx 10 10 1 10 TREE ± C PREE ± 0 Tm 0 10 B/1000 Tb Gd 10 Sm Nd Pr 10 10 10 1 10 TREE ± C PREE ± 0 0 10 Tb Gd 10 Sm Nd 10 Pr 10 Ce Pr NdSm Gd Tb Y Er TmYb 0 314 10 1 o 10 TREE ± C PREE ± 0 0 10 Ho Tb Gd Eu 10 Sm Nd 10 Pr Gt Peridotite Garnet Location: Sierra Nevada La Cpx 10 10 Primitive Mantle Normalized ±101oC 1 10 TREE PREE ±0.98GPa 0 0 Ho 10 B/1000 Tb Gd Eu 10 Sm Nd 10 Garnet Pyroxenite Location: N Morocco 10 10 1 o 10 TREE ± C PREE ± 0 0 10 Ho Tb Gd Eu 10 10 Garnet Pyroxenite Location: N Morocco 10 La Ce Pr NdSmEuGd Tb Dy Y Ho Er TmYb Lu 0 315 10 4 ±109oC 1 10 TREE PREE ±1.06GPa 0 0 Ho 10 Tb Gd Eu 10 Sm Nd 10 Garnet Pyroxenite Garnet Location: N Morocco Cpx 10 10 4 Primitive Mantle Normalized ±47oC 1 10 TREE PREE = 1.17±0.49GPa 0 0 10 Ho B/1000 Tb Gd Eu 10 Sm Nd 10 Garnet Pyroxenite Location: N Morocco 10 10 4 TREE = 779± oC 1 10 PREE = 4.06±0.41GPa 0 0 10 Ho Tb Eu 10 Sm Nd 10 Eclogite La Location: Kaapvaal 10 La Ce Pr NdSmEuGd Tb Dy Y Ho Er TmYb Lu 0 316 10 Harte & Kirkley (1997) 1 o 10 TREE ± C PREE ± 0 0 10 Ho Tb Eu 10 Sm Harte & Kirkley (1997) Nd 10 Eclogite Location: Kaapvaal La Cpx 10 10 Harte & Kirkley (1997) Primitive Mantle Normalized 1 o 10 TREE ± C PREE ± 0 0 10 Ho B/1000 Tb Eu 10 Sm Harte & Kirkley (1997) Nd 10 Eclogite Location: Kaapvaal La 10 10 Harte & Kirkley (1997) 1 o 10 TREE ± C PREE ± 0 Ho 0 10 Tb Eu Sm 10 Nd Harte & Kirkley (1997) 10 Eclogite Location: Kaapvaal 10 La Ce Pr NdSmEu Tb Dy Y Ho Er TmYb Lu 0 317 10 Harte & Kirkley (1997) Sample: HRV175 ± oC 1 10 TREE PREE ± 0 Ho 0 Tb 10 Eu Sm 10 Nd Harte & Kirkley (1997) Sample: HRV175(II) 10 Eclogite Location: Kaapvaal Cpx 10 10 Primitive Mantle Normalized TREE = 1015±15oC 1 10 PREE ± 0 Tm 0 Ho 10 B/1000 Tb Eu 10 Sm Nd 10 Pr Eclogite Location: Kaapvaal 10 10 1 o 10 TREE ± C PREE ± 0 Tm 0 10 Ho Tb Eu 10 Sm Nd 10 Eclogite Location: Kaapvaal 10 La Ce Pr NdSmEu Tb Dy Y Ho Er TmYb Lu 0 318 10 1 o 10 TREE ± C PREE ± 0 Tm 0 10 Ho Tb Eu 10 Sm Eclogite Nd Location: Kaapvaal 10 Pr Cpx 10 10 Primitive Mantle Normalized 1 o 10 TREE ± C PREE ± 0 Lu Tm 0 10 Ho B/1000 Tb Eu 10 Sm Nd 10 Eclogite Location: Kaapvaal 10 10 1 o 10 TREE ± C PREE ± 0 Tm 0 10 Ho Tb Eu 10 Sm Nd 10 Eclogite Location: Kaapvaal 10 La Ce Pr NdSmEu Tb Dy Y Ho Er TmYb Lu 0 319 10 1 o 10 Eclogite TREE = 1115± C Location: Kaapvaal PREE ± 0 Tm 0 Ho 10 Tb Eu Sm 10 10 Cpx 10 10 ±55oC 1 10 TREE Lu PREE = 1.77± 0 Ho 0 10 Tb Eu Sm 10 10 Eclogite Location: Kaapvaal 10 10 1 o 10 TREE = 975± C PREE ± Tb 0 Eu 0 Sm 10 Pr 10 10 Eclogite Location: Kaapvaal 10 La Ce Pr SmEu Tb Dy Y Ho Er TmYb Lu 0 320 10 1 o 10 Eclogite TREE ± C PREE = 1.05± Ho 0 0 10 Eu Sm Nd 10 10 Location: Kaapvaal Cpx 10 10 Primitive Mantle Normalized 1 Sample: 55 o 10 TREE ± C PREE ± 0 0 10 Tb Eu 10 Sm Nd Pr 10 Eclogite La Location: Siberia 10 10 1 Sample: 77 o 10 TREE ± C PREE ± 0 Lu 0 Tm 10 Ho Tb Eu 10 Sm Nd Pr 10 La Eclogite Location: Siberia 10 La Ce Pr NdSmEu Tb Dy Y Ho Er TmYb Lu 0 321 Figure S3(14) 2 10 4 Jacob and Foley (1999) Sample: 91 2 TREE = 778±26oC 1 10 PREE = 3.78±0.41GPa 0 Lu Tm 10 0 −2 Ho Tb Gd −4 Eu 10 −1 Sm −6 Nd Jacob and Foley (1999) Pr −2 Sample: 91(I) −8 10 La Eclogite Garnet −10 Location: Siberia Cpx −3 10 −12 2 10 4 Jacob and Foley (1999) Primitive Mantle Normalized Sample: 29 2 TREE = 1043±35oC 1 10 Tm 0 PREE = 2.45±0.35GPa Ho 0 Tb −2 10 Gd B/1000 Eu Sm −4 −1 10 Nd −6 Pr Jacob and Foley (1999) −2 Sample: 29(II) −8 10 La Eclogite −10 Location: Siberia −3 10 −12 2 10 4 Jacob and Foley (1999) Sample: 43 2 10 1 TREE = 1041±49oC Lu Tm PREE = 2.18±0.40GPa Ho 0 Tb 0 Gd −2 10 Eu Sm −4 −1 Nd 10 −6 Pr Jacob and Foley (1999) −2 Sample: 43(II) −8 10 La Eclogite −10 Location: Siberia −3 10 −12 La Ce Pr NdSmEuGd Tb Dy Y Ho Er TmYb Lu −10 −5 0 ln(D)−A 322 Figure S3(15) 2 10 4 Jacob et al. (2009) Sample: DJ0220o 2 1 Lu 10 TREE = 1059±14 C Tm PREE = 4.80±0.18GPa 0 Ho 0 Tb −2 10 Gd Eu Sm −4 −1 10 −6 Nd Jacob et al. (2009) Pr −2 Sample: DJ0220() −8 10 Eclogite La Garnet −10 Location: Kimberley Cpx −3 10 −12 2 10 4 Jacob et al. (2009) Primitive Mantle Normalized Sample: DJ0295o 2 10 1 TREE = 1025±16 C Lu Tm 0 PREE = 4.17±0.21GPa Ho 10 0 Tb −2 B/1000 Gd Eu −4 Sm −1 10 −6 Nd Jacob et al. (2009) Pr −8 −2 Sample: DJ0295() 10 Eclogite La −10 Location: Kimberley −3 10 −12 2 10 4 Jacob et al. (2009) Sample: DJ0296 2 TREE = 867±9oC 1 10 Lu PREE = 3.52±0.14GPa 0 Tm 0 Ho −2 10 Tb Gd −4 −1 Eu 10 Sm −6 Jacob et al. (2009) Nd −2 Sample: DJ0296() −8 10 Pr Eclogite −10 Location: Kimberley La −3 10 −12 La Ce Pr NdSmEuGd Tb Dy Y Ho Er TmYb Lu −10 −5 0 ln(D)−A 323 Figure S3(16) 2 10 4 Jacob et al. (2009) Sample: KimE−1 2 TREE = 889±28oC 1 10 Lu 0 PREE = 2.78±0.37GPa Tm 0 Ho −2 10 Tb Gd −4 −1 Eu 10 Sm −6 Jacob et al. (2009) Nd −2 Sample: KimE−1() −8 10 Pr Eclogite Garnet −10 Location: Kimberley Cpx −3 10 −12 2 10 4 Jacob et al. (2009) Primitive Mantle Normalized Sample: K3−V1 o Lu 2 1 Tm 10 TREE = 1114±13 C Ho 0 PREE = 5.56±0.15GPa Tb 0 Gd −2 10 Eu B/1000 Sm −4 −1 Nd 10 −6 Pr Jacob et al. (2009) −2 Sample: K3−V1() −8 10 La Eclogite −10 Location: Kimberley −3 10 −12 2 10 4 Jacob et al. (2009) Sample: XM1−122 2 TREE = 987±16oC 1 10 Lu 0 PREE = 3.12±0.22GPa Tm 10 0 Ho −2 Tb Gd −4 −1 Eu 10 Sm −6 Jacob et al. (2009) Nd −2 Sample: XM1−122() −8 10 Pr Eclogite −10 Location: Kimberley La −3 10 −12 La Ce Pr NdSmEuGd Tb Dy Y Ho Er TmYb Lu −10 −5 0 ln(D)−A 324 Figure S3(17) 2 10 4 Jacob et al. (2009) Sample: XM1−254 2 TREE = 908±14oC 1 10 PREE = 5.17±0.25GPa Lu 0 Tm 10 0 Ho −2 Tb −4 Gd −1 Eu 10 Sm −6 Jacob et al. (2009) Nd −2 Sample: XM1−254() Pr −8 10 Eclogite Garnet La −10 Location: Kimberley Cpx −3 10 −12 2 10 4 Jacob et al. (2009) Primitive Mantle Normalized Sample: XM1−676 2 Lu TREE = 951±14oC 1 10 Tm PREE = 3.00±0.14GPa Ho 0 Tb 0 Gd −2 10 Eu B/1000 Sm −4 −1 Nd 10 −6 Pr Jacob et al. (2009) −2 Sample: XM1−676() −8 10 La Eclogite −10 Location: Kimberley −3 10 −12 2 10 4 Jacob et al. (2009) Sample: XM1−677 2 TREE = 943±51oC 1 10 Lu 0 PREE = 4.02±0.82GPa Tm 10 0 Ho −2 Tb Gd −4 −1 Eu 10 Sm −6 Jacob et al. (2009) Nd −8 −2 Sample: XM1−677() Pr 10 Eclogite −10 Location: Kimberley La −3 10 −12 La Ce Pr NdSmEuGd Tb Dy Y Ho Er TmYb Lu −10 −5 0 ln(D)−A 325 Figure S3(18) 2 10 4 Jacob et al. (2009) Sample: XM1−724 2 TREE = 809±13oC 1 10 Lu 0 PREE = 1.83±0.17GPa Tm 10 0 Ho −2 Tb Gd −4 −1 Eu 10 Sm −6 Jacob et al. (2009) Nd −2 Sample: XM1−724() −8 10 Pr Eclogite Garnet −10 Location: Kimberley La Cpx −3 10 −12 2 10 4 Jacob et al. (2009) Primitive Mantle Normalized Sample: XM1−725 2 TREE = 1013±32oC 1 10 PREE = 5.08±0.52GPa Lu 0 Tm 10 0 Ho −2 B/1000 Tb −4 Gd −1 Eu 10 Sm −6 Jacob et al. (2009) Nd −2 Sample: XM1−725() Pr −8 10 Eclogite La −10 Location: Kimberley −3 10 −12 2 10 4 Jacob et al. (2009) Sample: XM2−35 Lu 2 TREE = 983±9oC 1 10 Tm PREE = 3.03±0.09GPa Ho 0 Tb 10 0 Gd −2 Eu Sm −4 −1 10 Nd −6 Pr Jacob et al. (2009) −2 Sample: XM2−35() −8 10 La Eclogite −10 Location: Kimberley −3 10 −12 La Ce Pr NdSmEuGd Tb Dy Y Ho Er TmYb Lu −10 −5 0 ln(D)−A 326 Figure S3(19) 2 10 4 Jacob et al. (2009) Sample: XM2−38 2 TREE = 674±20oC 1 10 Lu 0 PREE = 2.50±0.32GPa Tm 10 0 Ho −2 Tb −4 Gd 10 −1 Eu Sm −6 Jacob et al. (2009) Nd −2 Sample: XM2−38() −8 10 Pr Eclogite Garnet −10 Location: Kimberley La Cpx −3 10 −12 2 10 4 Jacob et al. (2009) Primitive Mantle Normalized Sample: XM2−39 2 TREE = 792±12oC 1 10 PREE = 2.56±0.19GPa Lu 0 Tm 10 0 Ho −2 B/1000 Tb −4 Gd −1 Eu 10 Sm −6 Jacob et al. (2009) Nd Sample: XM2−39() −8 10 −2 Pr Eclogite La −10 Location: Kimberley −3 10 −12 2 10 4 Jacob et al. (2009) Sample: XM1−727 2 TREE = 716±19oC 1 10 Lu 0 PREE = 3.67±0.35GPa Tm 10 0 Ho −2 Tb −4 Gd 10 −1 Eu Sm −6 Jacob et al. (2009) Nd −2 Sample: XM1−727() −8 10 Pr Eclogite −10 Location: Kimberley La −3 10 −12 La Ce Pr NdSmEuGd Tb Dy Y Ho Er TmYb Lu −10 −5 0 ln(D)−A 327 Figure S3(20) 2 10 4 Jacob et al. (2009) Sample: K8−49o 2 1 10 TREE = 854±34 C PREE = 4.05±0.33GPa Eu 0 Sm 10 0 Nd −2 Pr −4 10 −1 La −6 Jacob et al. (2009) −2 Sample: K8−49() −8 10 Eclogite Garnet −10 Location: Kimberley Cpx −3 10 −12 2 10 4 Jacob et al. (2009) Primitive Mantle Normalized Sample: XM1−723 2 TREE = 825±15oC 1 10 PREE = 4.44±0.26GPa Lu 0 Tm 10 0 Ho −2 B/1000 Tb −4 Gd −1 Eu 10 Sm −6 Jacob et al. (2009) Nd −2 Sample: XM1−723() −8 10 Pr Eclogite La −10 Location: Kimberley −3 10 −12 2 10 4 Koreshkova et al. (2011) Sample: Uk1 o 2 1 10 TREE = 962±47 C PREE = 2.47±0.60GPa 0 0 Ho −2 10 Tb Gd −4 −1 Eu 10 Sm −6 Koreshkova et al. (2011) Nd −8 −2 Sample: Uk1(avg) 10 Pr Granulite −10 Location: Siberia −3 10 −12 La Ce Pr NdSmEuGd Tb Dy Y Ho Er TmYb Lu −10 −5 0 ln(D)−A 328 Figure S3(21) 2 10 4 Koreshkova et al. (2011) Sample: Uk37 o 2 10 1 TREE = 890±22 C Lu Tm 0 PREE = 1.38±0.27GPa Ho 10 0 −2 Tb Gd −4 −1 Eu 10 Sm −6 Koreshkova et al. (2011) Nd −8 −2 Sample: Uk37(avg) 10 Pr Granulite Garnet −10 Location: Siberia Cpx La −3 10 −12 2 10 4 Koreshkova et al. (2011) Primitive Mantle Normalized Sample: Uk21o 2 1 10 TREE = 886±7 C Lu PREE = 1.30±0.09GPa Tm 0 0 Ho −2 10 B/1000 Tb Gd −4 −1 Eu 10 Sm −6 Koreshkova et al. (2011) Nd −8 −2 Sample: Uk21(avg) 10 Pr Granulite −10 Location: Siberia −3 La 10 −12 2 10 4 Koreshkova et al. (2011) Sample: Y6 o 2 1 10 TREE = 922±32 C PREE = 2.00±0.39GPa Tm 0 Ho 10 0 −2 Tb Gd −4 −1 Eu 10 Sm −6 Koreshkova et al. (2011) Nd −8 −2 Sample: Y6(avg) 10 Pr Granulite −10 Location: Siberia −3 10 −12 La Ce Pr NdSmEuGd Tb Dy Y Ho Er TmYb Lu −10 −5 0 ln(D)−A 329 Figure S3(22) 2 10 4 Koreshkova et al. (2011) Sample: Uk5 o 2 1 10 TREE = 909±49 C PREE = 2.55±0.72GPa 0 Ho 10 0 −2 Tb Gd −4 −1 Eu 10 Sm −6 Koreshkova et al. (2011) Nd −8 −2 Sample: Uk5(avg) 10 Pr Granulite Garnet −10 Location: Siberia Cpx La −3 10 −12 2 10 4 Koreshkova et al. (2011) Primitive Mantle Normalized Sample: Y7 o 2 1 10 TREE = 832±14 C Lu PREE = 1.53±0.19GPa Tm 0 0 Ho −2 10 B/1000 Tb Gd −4 −1 Eu 10 Sm −6 Koreshkova et al. (2011) Nd −8 −2 Sample: Y7(avg) 10 Pr Granulite −10 Location: Siberia −3 La 10 −12 2 10 4 Koreshkova et al. (2011) Sample: Y53 o 2 1 10 TREE = 856±13 C Lu PREE = 1.54±0.17GPa Tm 0 Ho 10 0 −2 Tb Gd −4 −1 Eu 10 Sm −6 Koreshkova et al. (2011) Nd −2 Sample: Y53(avg) −8 10 Pr Granulite −10 Location: Siberia −3 La 10 −12 La Ce Pr NdSmEuGd Tb Dy Y Ho Er TmYb Lu −10 −5 0 ln(D)−A 330 Figure S3(23) 2 10 4 Koreshkova et al. (2011) Sample: Uk35 o 2 1 10 TREE = 864±13 C Lu PREE = 1.92±0.17GPa 0 Tm 0 Ho −2 10 Tb Gd −4 −1 Eu 10 Sm −6 Koreshkova et al. (2011) Nd −2 Sample: Uk35(avg) −8 10 Pr Granulite Garnet −10 Location: Siberia Cpx −3 10 −12 2 10 4 Nehring et al. (2010) Primitive Mantle Normalized Sample: 02M2 o 2 1 10 TREE = 916±28 C PREE = 2.47±0.24GPa 0 10 0 −2 Gd B/1000 Eu Sm −4 −1 10 −6 Nd Nehring et al. (2010) −2 Sample: 02M2() −8 10 Granulite −10 Location: Central Finland −3 10 −12 2 10 4 Nehring et al. (2010) Sample: 36M1 o 2 1 10 TREE = 945±25 C Lu PREE = 2.05±0.26GPa 0 10 0 −2 Gd −4 −1 Eu 10 Sm −6 Nehring et al. (2010) Nd −2 Sample: 36M1(1) −8 10 Granulite −10 Location: Central Finland −3 10 −12 La Ce Pr NdSmEuGd Tb Dy Y Ho Er TmYb Lu −10 −5 0 ln(D)−A 331 10 4 1 Sample: 140M o Lu 10 TREE ± C PREE = 0.75± 0 0 10 Gd Eu Sm 10 Nd 10 Granulite Garnet Location: Central Finland Cpx 10 10 4 Primitive Mantle Normalized 1 o 10 TREE ± C PREE ± 0 0 10 B/1000 Gd Eu 10 Sm Nd 10 Granulite Location: Central Finland La 10 10 4 1 Sample: 49M o 10 TREE ±17 C Lu PREE ±0.19GPa 0 0 10 Gd Eu 10 Sm Nd 10 Granulite Location: Central Finland 10 La Ce Pr NdSmEuGd Tb Dy Y Ho Er TmYb Lu 0 332 Figure S3(25) 2 10 4 Nehring et al. (2010) Sample: 76M1 o 2 1 10 TREE = 836±29 C PREE = 0.35±0.32GPa 0 10 0 −2 Gd −4 Eu −1 10 Sm −6 Nehring et al. (2010) Nd −2 Sample: 76M1() −8 10 Granulite Garnet −10 Location: Central Finland Cpx −3 10 −12 2 10 4 Scambelluri et al. (2008) Primitive Mantle Normalized Sample: M3−grain bd 2 TREE = 871±23oC 1 10 PREE = 2.65±0.38GPa 0 10 0 −2 B/1000 Tb Gd −4 10 −1 Eu Sm −6 Scambelluri et al. (2008) −2 Sample: M3−grain bd() Nd −8 10 Pr Gt Peridotite −10 Location: W. Norway La −3 10 −12 2 10 4 Scambelluri et al. (2008) Sample: M3−vein 2 TREE = 924±49oC 1 10 PREE = 3.19±0.81GPa 0 10 0 −2 Tb Gd −4 10 −1 Eu Sm −6 Scambelluri et al. (2008) −2 Sample: M3−vein() Nd −8 10 Pr Gt Peridotite −10 Location: W. Norway La −3 10 −12 La Ce Pr NdSmEuGd Tb Dy Y Ho Er TmYb Lu −10 −5 0 ln(D)−A 333 10 1 o 10 TREE ± C PREE ± 0 0 10 Tb Gd 10 Eu Sm Nd 10 Pr Gt Peridotite Garnet Location: W. Norway La 10 10 Primitive Mantle Normalized 1 o 10 TREE ± C PREE ± 0 0 10 B/1000 Tb Gd 10 Eu Sm Nd 10 Pr Gt Peridotite Location: W. Norway La 10 10 1 Sample: o 10 TREE ± C PREE ± 0 0 10 Gd Eu 10 Sm Nd 10 Location: Siberia La 10 La Ce Pr NdSmEuGd Tb Dy Y Ho Er TmYb Lu 0 334 Figure S3(27) 2 10 4 Smart et al. (2009) Sample: JDE 01 2 TREE = 768±12oC 1 10 PREE = 3.26±0.21GPa Lu 0 Tm 10 0 Ho −2 Tb −4 Gd −1 Eu 10 Sm −6 Smart et al. (2009) Nd Sample: JDE 01(Diamond) −8 10 −2 Pr Eclogite Garnet La −10 Location: Slave Cpx −3 10 −12 2 10 4 Smart et al. (2009) Primitive Mantle Normalized Sample: JDE 02 2 TREE = 861±34oC 1 10 PREE = 4.01±0.38GPa Lu 0 Tm 10 0 Ho −2 B/1000 Tb −4 Gd −1 Eu 10 Sm −6 Smart et al. (2009) −2 Sample: JDE 02(Diamond) −8 10 Eclogite −10 Location: Slave −3 10 −12 2 10 4 Smart et al. (2009) Sample: JDE 03 2 TREE = 834±13oC 1 10 PREE = 4.46±0.24GPa Lu 0 Tm 10 0 Ho −2 Tb −4 Gd −1 Eu 10 Sm −6 Smart et al. (2009) Nd −2 Sample: JDE 03(Diamond) Pr −8 10 Eclogite La −10 Location: Slave −3 10 −12 La Ce Pr NdSmEuGd Tb Dy Y Ho Er TmYb Lu −10 −5 0 ln(D)−A 335 Figure S3(28) 2 10 4 Smart et al. (2009) Sample: JDE 07 2 TREE = 801±10oC 1 10 PREE = 3.81±0.18GPa Lu 0 Tm 10 0 Ho −2 Tb −4 Gd −1 Eu 10 Sm −6 Smart et al. (2009) Nd −2 Sample: JDE 07(Diamond) Pr −8 10 Eclogite Garnet La −10 Location: Slave Cpx −3 10 −12 2 10 4 Smart et al. (2009) Primitive Mantle Normalized Sample: JDE 17 2 TREE = 767±18oC 1 10 PREE = 3.02±0.27GPa Lu 0 Tm 10 0 Ho −2 B/1000 Tb −4 Gd −1 Eu 10 Sm −6 Smart et al. (2009) Nd −2 Sample: JDE 17(Diamond) Pr −8 10 Eclogite −10 Location: Slave −3 10 −12 2 10 4 Smart et al. (2009) Sample: JDE 19 2 TREE = 918±52oC 1 10 PREE = 4.41±0.60GPa 0 Tm 10 0 Ho −2 Tb −4 Gd −1 Eu 10 Sm −6 Smart et al. (2009) −2 Sample: JDE 19(Diamond) −8 10 Eclogite −10 Location: Slave −3 10 −12 La Ce Pr NdSmEuGd Tb Dy Y Ho Er TmYb Lu −10 −5 0 ln(D)−A 336 Figure S3(29) 2 10 4 Smart et al. (2009) Sample: JDE 22 2 TREE = 846±21oC 1 10 PREE = 4.21±0.38GPa 0 Tm 10 0 Ho −2 Tb −4 Gd −1 Eu 10 Sm −6 Smart et al. (2009) Nd −2 Sample: JDE 22(Diamond) Pr −8 10 Eclogite Garnet La −10 Location: Slave Cpx −3 10 −12 2 10 4 Smart et al. (2009) Primitive Mantle Normalized Sample: JDE 23 2 TREE = 907±44oC 1 10 PREE = 4.15±0.48GPa Lu 0 Tm 10 0 Ho −2 B/1000 Tb −4 Gd −1 Eu 10 Sm −6 Smart et al. (2009) −2 Sample: JDE 23(Diamond) −8 10 Eclogite −10 Location: Slave −3 10 −12 2 10 4 Smart et al. (2009) Sample: 44−9 o 2 1 10 TREE = 817±26 C PREE = 1.93±0.36GPa Lu 0 Tm 10 0 Ho −2 Tb −4 Gd −1 Eu 10 Sm −6 Smart et al. (2009) Nd Sample: 44−9(No Diamond) −8 10 −2 Pr Eclogite La −10 Location: Slave −3 10 −12 La Ce Pr NdSmEuGd Tb Dy Y Ho Er TmYb Lu −10 −5 0 ln(D)−A 337 10 1 Sample: GroupoB 10 TREE ± C Lu PREE ± Tm 0 Ho 0 10 Tb Gd Eu Sm 10 Nd Pr 10 Eclogite Garnet La Location: Slave Cpx 10 10 Primitive Mantle Normalized 1 o 10 TREE ± C PREE ± 0 0 10 B/1000 Gd Eu 10 Sm Nd 10 Gt Peridotite Location: W Norway La 10 10 1 o 10 TREE ± C PREE ± 0 0 10 Gd 10 Eu Sm Nd 10 Gt Peridotite Location: W Norway 10 La Ce Pr NdSmEuGd Tb Dy Y Ho Er TmYb Lu 0 338 10 1 o 10 Gt Peridotite TREE ± C Location: W Norway PREE ± 0 0 10 Gd 10 Eu Sm Nd 10 Garnet Cpx 10 10 Primitive Mantle Normalized Sample: DB10 Lu 1 o Tm 10 TREE ± C PREE ± Ho 0 Tb 0 Gd 10 B/1000 Eu Sm 10 Nd Pr 10 Eclogite 10 10 1 Sample: DB11 o 10 TREE ±10 C Ho 0 PREE ± Tb 0 Gd 10 Eu Sm Nd 10 Pr 10 Eclogite 10 La Ce Pr NdSmEuGd Tb Dy Y Ho Er TmYb Lu 0 339 Figure S3(32) 2 10 4 Tang et al. (2007) Sample: DB13−2o 2 1 10 TREE = 1006±56 C PREE = 0.59±0.45GPa 0 Ho 10 0 −2 Tb Gd Eu −4 −1 Sm 10 −6 Tang et al. (2007) Nd −2 Sample: DB13−2(UHP) Pr −8 10 Eclogite Garnet −10 Location: Dabie−Sulu Cpx −3 10 −12 2 10 4 Tang et al. (2007) Primitive Mantle Normalized Sample: SL6−1o 2 1 10 TREE = 913±80 C Lu Tm 0 PREE = 0.61±0.50GPa Ho 10 0 Tb −2 Gd B/1000 Eu Sm −4 −1 10 −6 Nd Tang et al. (2007) Pr −2 Sample: SL6−1(UHP) −8 10 Eclogite −10 Location: Dabie−Sulu −3 10 −12 2 10 4 Tang et al. (2007) Sample: SL7−1o 2 1 10 TREE = 861±19 C Ho 0 PREE = 0.58±0.11GPa Tb 0 Gd −2 10 Eu Sm −4 −1 Nd 10 Pr −6 Tang et al. (2007) −2 Sample: SL7−1(UHP) −8 10 Eclogite −10 Location: Dabie−Sulu −3 10 −12 La Ce Pr NdSmEuGd Tb Dy Y Ho Er TmYb Lu −10 −5 0 ln(D)−A 340 10 1 o 10 TREE ± C ± 0 REE 0 Tb 10 Sm 10 Nd 10 Eclogite Cpx 10 10 1 o 10 TREE ± C ± 0 REE Tb 0 10 Sm B/1000 Nd 10 10 Eclogite 10 10 1 o 10 TREE ± C ± Tm 0 REE 0 10 Tb Sm 10 Nd 10 Eclogite 10 La Ce NdSm Tb Dy Y TmYb 0 341 Figure 5-S4 20 (ºC) random REE 10 Tordering REE 0 600 700 800 900 1000 1100 1200 random TREE (ºC) 342 Figure 5-S5 1040 1020 Temperature (°C) 1000 980 960 940 920 900 880 2.5 3 3.5 4 4.5 5 5.5 6 Pressure (GPa) 343 CHAPTER 6 6 A REE-in-Plagioclase-Clinopyroxene Thermometer for Mafic and Ultramafic Rocks 344 Abstract A REE-in-plagioclase-clinopyroxene thermometer has been developed for plagioclase- and clinopyroxene-bearing mafic and ultramafic rocks. This new thermometer is based on the temperature-dependent REE partitioning between plagioclase and clinopyroxene, and is calibrated against experimentally determined plagioclase-melt and clinopyroxene-melt partition coefficients. Application of the REE-in-plagioclase-clinopyroxene thermometer to mafic and ultramafic rocks from the Bushveld complex shows that temperatures derived from the REE-in- plagioclase-clinopyroxene thermometer agree well with the crystallization temperatures calculated using the empirical thermometer of Thy et al. (2013). Due to the slow diffusion rates of REEs in plagioclase and clinopyroxene, the REE-in-plagioclase-clinopyroxene thermometer likely records (near) crystallization temperatures of mafic and ultramafic cumulate rocks. This REE-based thermometer can be used to study the thermal and magmatic history of mafic and ultramafic rocks from the Earth, Moon and other planetary bodies. Coupling with the radiogenic isotopes, the REE-in-plagioclase-clinopyroxene thermometer can provide additional constrains on the magma chamber processes of layered intrusions. 345 1. Introduction Plagioclase and clinopyroxene are common rock-forming minerals in mafic and ultra- mafic rocks. Quantitative determination of equilibrium (or crystallization) temperatures for plagioclase-bearing rocks is important to elucidate magmatic processes. Many thermometers have been developed to quantify the plagioclase crystallization temperatures based on the temperature- dependent saturation of plagioclase in silicate melts (e.g., Kudo and Weill 1970; Mathez 1973; Glazner 1984; Marsh et al. 1990; Putrika, 2005; Lange et al., 2009). However, application of these thermometers requires the composition of melt in equilibrium with plagioclase, which is often absent in natural samples (e.g., cumulate rocks in layered intrusions). As the anorthite content in plagioclase generally increase with the equilibrium temperature (e.g., Kudo and Weill 1970; Mathez 1973; Glazner 1984; Marsh et al. 1990; Putrika, 2005; Lange et al., 2009), simple empirical thermometers have also been developed for selected ranges of melt compositions by calibrating the equilibrium temperature solely as a function of anorthite content in plagioclase (e.g., Morse, 2008, 2013; Thy et al., 2009, 2013). Because anorthite content in plagioclase also varies with the equilibrium pressure and the melt composition (e.g., Takagi et al., 2005; Lange et al., 2009), significant uncertainties may be involved in these empirical thermometers when applied to plagioclases and melts out of the calibration ranges. Recently, Faak et al. (2013) found that the exchange of Mg between plagioclase and clinopyroxene strongly depends on temperature, the anorthite content in plagioclase and the activity of SiO2 in the system, and they experimentally calibrated a plagioclase-clinopyroxene Mg-exchange thermometer. Applying to mafic cumulates in the Bushveld Complex from Godel et al. (2011) and Vantongeren and Mathez (2013), the Mg-exchange thermometer generates temperatures (651 – 830 ºC) significantly lower than the possible crystallization temperatures (1105 – 1183 ºC) calculated by the empirical thermometer of Thy et al. (2013). Provided the fast diffusion rate of Mg in plagioclase (e.g., about three orders of magnitude faster than Nd; 346 Cherniak, 2010), the temperatures derived from the Mg-exchange thermometer of Faak et al. (2013) are likely subsolidus or Mg closure temperatures of these mafic cumulates. It has been long recognized that the distribution of rare earth elements (REEs) between two coexisting minerals depends on temperature, pressure and mineral compositions (e.g., Stosch, 1982; Seitz et al., 1999; Witt-Eickschen and O’Neill, 2005; Lee et al., 2007; Liang et al., 2013; Chapter 4). Based on the temperature dependent REE partitioning between two pyroxenes and between garnet and clinopyroxene, we have developed a REE-in-two-pyroxene thermometer and a REE-in-garnet-clinopyroxene thermobarometer that can provide equilibrium temperatures or closure temperatures for mafic and ultramafic rocks (Liang et al., 2013; Chapter 5). Because the diffusion rates of trivalent REEs are significantly greater than those of divalent Ca, Mg, and Fe in minerals, the REE-based thermometer can potentially record thermal events more close to magmatic temperatures for mafic and ultramafic rocks during cooling. In this study, we further expand the idea of REE-based thermometers and develop a REE-in-plagioclase-clinopyroxene thermometer. We show that this new thermometer can be applied to a wide range of mafic and ultramafic rocks from the Earth, Moon and other planetary bodies. The REE-in-plagioclase- clinopyroxene thermometer is particularly useful to deciphering the magma chamber processes in layered intrusions. 2. Developing a REE-in-Plagioclase-Clinopyroxene Thermometer The general theoretical basis of REE-based thermometers and barometers is summarized in Liang et al. (2013) and Chapter 5. Combining the independently calibrated lattice strain parameters for REE partitioning in plagioclase and clinopyroxene, we can formulate a lattice strain model for REE partitioning between plagioclase and clinopyroxene. Finally, we can obtain a REE-in-plagioclase-clinopyroxene thermometer from the plagioclase-clinopyroxene REE partitioning model. Here we first develop a parameterized lattice strain model for REE 347 partitioning between plagioclase and basaltic melts based on partitioning data from our experiments and those from literatures. 2.1. A plagioclase-melt REE partitioning model Several models have been developed to quantify REE partitioning between plagioclase and silicate melts (e.g., Bindeman et al., 1998; Wood and Blundy, 2003; Bédard, 2006; Tepley et al., 2010; Hui et al., 2011). Typically, these models (e.g., Bindeman et al., 1998;Tepley et al., 2010; Hui et al., 2011) were calibrated against experimental partitioning data following the simple linear expression of Blundy and Wood (1991) RT ln D plg-melt j = a × An + b (1) where D plg-melt j is the plagioclase-melt partition coefficient of element j; R is the gas constant; An is the anorthite content in plagioclase [An = 100 × Ca/(Ca + Na) in mole]; T is the temperature in K; and a and b are constant coefficients. The model of Bédard (2006) also follows Eq. (1), but was calibrated against partitioning data from the laboratory and natural samples. However, these models fail to reproduce a large number of REE partition coefficients from recent partitioning experiments (Figs. 6-1). Because REE3+, Ca2+ and Na+ have similar ionic radii (REE3+: 0.977–1.16 Å; Ca2+: 1.12 Å; Na+: 1.18 Å; VIII-fold coordination; Shannon 1976), REEs enter the M site in plagioclase by substituting for Ca2+ or Na+. This substitution is likely charge balanced by Na+ replacing Ca2+ in the M site, or Al3+ replacing Si4+ in the tetrahedral site (Kneip and Liebau, 1994). The coordination number of the M site varies from 7 to 9 with the cation radii in the M site. Here, we adopted the assumption in Wood and Blundy (2003) that REEs and Y are VIII-fold coordinated in the M site. The partition coefficients of REEs and Y from a given plagioclase-melt partitioning experiment vary systematically as a function of their ionic radii, and can be quantitatively described by the lattice strain model (Brice, 1975; Blundy and Wood, 1994) 348 ⎡ −4π EN A ⎛ r0 3⎞ ⎤ ( ) 1 ( ) 2 D plg-melt = D0 exp ⎢ ⎜ r0 − rj − r0 − rj ⎟ ⎥ (2) ⎣ RT ⎝ 2 ⎠⎦ j 3 where D0 is the partition coefficient for strain-free substitution; r0 is the ionic radius of the “ideal” cation for the strain-free lattice site; rj is the ionic radius of element j; E is the apparent Young’s modulus for the lattice site; NA is Avogadro’s number. In general, the lattice strain parameters (D0, r0, and E) are functions of pressure, temperature and composition and may be quantified using (empirical) parameterized models. Wood and Blundy (2003) proposed a preliminary lattice strain model for plagioclase-melt REE partitioning. Because experimentally determined plagioclase- melt REE partition coefficients were rather limited before 2003, it was unlikely for them to directly obtain a generalized lattice strain model by calibrating the lattice strain parameters as functions of temperature, pressure and composition. Instead, Wood and Blundy (2003) eliminated the strain-free partition coefficient (D0) in the lattice strain model using La partition coefficient as a reference. Based on the experimental REE partitioning data from Bindeman et al. (1998) and Bindeman and Davis (2000), they found that E is constant and that r0 decreases linearly with An. Using the La partitioning model from Bindeman et al. (1998), they obtained a generalized lattice strain model for REE partitioning between plagioclase and melt. However, their model significantly overestimates the recent experimental plagioclase-melt REE partition coefficients by up to one order of magnitude (Fig. 6-1b). Combining with a recently calibrated La partitioning model from Hui et al. (2011), the Wood and Blundy’s model can generally reproduce the experimental partitioning data to within the 1:2 and 2:1 lines (Fig. 6-2a). This indicates that the accuracy of the Wood and Blundy’s model strongly relies on that of the La partitioning model. Nevertheless, an accurate, generalized lattice strain model for plagioclase-melt REE partitioning is still needed to develop the REE-in-plagioclase-clinopyroxene thermometer. To further expand the trace element partitioning database, we conducted piston-cylinder experiments to determine trace element partitioning between anorthitic plagioclase and lunar basaltic melts. We obtained two preliminary experiments (Run An-Red-2 at 1400 ºC and 0.6 GPa; 349 Run An-Red-3 at 1350 ºC and 0.8 GPa) with anorthite (An = 98) coexisting with lunar basaltic melts [Mg# = 50; TiO2 = 6.4 wt% and 9.8 wt%; Mg# = 100*Mg/(Mg+Fe) in mole]. The experimental results have been presented in Graff et al. (2013). We compiled 42 plagioclase-melt partitioning experiments from Blundy (1997), Bindeman et al. (1998), Bindeman and Davis (2000), Aigner-Torres et al. (2007), and Tepley et al. (2010). However, plagioclase-melt REE partition coefficients from 21 of the 42 experiments do not follow parabola in the Onuma diagram (partition coefficients vs. ionic radii; Onuma et al., 1968), indicating possible poor analytical quality, melt contamination during analysis, or disequilibrium between plagioclase and melt. After filtering these 21 experiments, we obtained 23 partitioning experiments including two from this study and 21 experiments (conducted at 1127 – 1299 ºC and an atmospheric pressure) from the aforementioned studies. Plagioclases and melts generated in these experiments cover a wide range of compositions (An = 53 –98 in plagioclase, Mg# = 49 – 100 in melt). Eu was excluded in the model calibration because it is heterovalent in plagioclase. Some elements were also excluded when they significantly deviate from the parabola in the Onuma diagram defined by other REEs. Finally, we obtained 137 REE and Y partition coefficients between plagioclase and basaltic melts. Following the procedures described in Chapters 1-3, we parameterized the lattice strain parameters (D0, r0 and E in Eq. 2) as functions of temperature, pressure and compositions of plagioclase and melt through parameter swiping and simultaneous or global nonlinear least squares inversion of all the filtered partitioning data. We found that D0 is negatively correlated with Ca abundance in plagioclase and temperature, and that r0 and E can be treated as constants. The global fit to the 137 plagioclase-melt REE and Y partition coefficients generates the following expressions for the lattice strain parameters: 17.52 ( ±2.27 ) ×104 = 14.03( ±1.89 ) − ( ) − 4.77 ( ±0.40 ) X Ca 3 plg plg ln D0 (3a) RT 350 ( ) r0plg Å = 1.235 ( ±0.074 ) (3b) E plg ( GPa ) = 132 ( ±62 ) (3c) plg where XCa is the cation content of Ca in plagioclase per 8-oxygen; numbers in parentheses are 2σ uncertainties estimated directly from the simultaneous inversion. The decrease of D0 with Ca abundance in plagioclase is consistent with the negative correlation between partition coefficients and An in plagioclase (Eq. 1). It is interesting that the constant r0 for trivalent REE partitioning in plagioclase in Eq. (3b) is very close to that for divalent cations partitioning in plagioclase (r0 = 1.227 Å; Miller et al., 2006), indicating that they all partitioning into the large M site in plagioclase. Replacing the lattice strain parameters in Eq. (2) by Eqs. (3a-c), we obtained a generalized lattice strain model for REE and Y partitioning between plagioclase and basaltic melt. To assess the goodness of fit and to compare with previous models in a simple way, we calculated the Pearson's Chi-square ( χ p ) after the inversion using the expression 2 (D − D ) 2 N m χ =∑ 2 j j p (4) j=1 Dj m where N (= 137) is the total number of plagioclase-melt partitioning data used; D j is the measured partition coefficients for element j; Dj is the model predicted partition coefficient. A smaller χ p indicates a better predictive model. Fig. 6-2b shows that the partition coefficients 2 predicted by our new model (Eqs. 2, 3a-c) are in excellent agreement with those determined experimentally. The χ p value derived from our model ( χ p = 0.70 ) is about three to six times 2 2 smaller than those calculated using the previous models ( χ p = 1.99 − 4.46 ; Figs. 6-1(a-d) and 6- 2 2a). The number (= 5) of coefficients in this model is equal to those in the models of Wood and 351 Blundy (2003, or revised version), but is much fewer than those (= 30) in previous models based on Eq. (1). This demonstrates that our new model is a significant improvement over the previous models in quantifying plagioclase-melt REE and Y partitioning. 2.2. A REE-in-plagioclase-clinopyroxene thermometer The exchange of a trace element between plagioclase and clinopyroxene can also be quantified by the lattice strain model in Chapter 4 if the lattice strain parameters are independent of melt composition ⎡ 4π N A E plg ⎛ r0plg plg 3⎞ D0plg ( ) − 13 ( r ) 2 D plg-cpx j = cpx exp ⎢ − ⎜ 2 r0 − rj 0 plg − rj ⎟ D0 ⎢⎣ RT ⎝ ⎠ (5) 4π N A E cpx ⎛ r0cpx cpx ⎞⎤ ( ) − 13 ( r ) 2 3 + ⎜ 2 r0 − rj 0 cpx − rj ⎟⎥ RT ⎝ ⎠ ⎥⎦ plg-cpx where D j is the partition coefficient of element j between plagioclase and clinopyroxene. Combining with the lattice strain parameters for REE partitioning in plagioclase (Eqs. 3a-c) and clinopyroxene [Eqs. (8-10) in Chapter 1], Eq. (5) allow us to quantitatively determine the distribution of REEs between plagioclase and clinopyroxene. To examine the effect of temperature and mineral composition, we calculated plagioclase-clinopyroxene REE partition coefficients using Eq (5) and mineral major element composition from a lunar ferroan anorthosites (FANs; 60025,702,C from Floss et al., 1998) and a gabbronorite (B06-064 from VanTongeren and Mathez, 2013) for three temperatures (700 ºC, 1000 ºC and 1300 ºC). Fig. 6-3 shows that plagioclase-clinopyroxene REE partition coefficients increase systematically with the ionic radius, temperature and An. As temperature increases from 700 ºC to 1300 ºC, plagioclase- clinopyroxene REE partition coefficients increase by five to six orders of magnitude. As An increases by 27, the plagioclase-clinopyroxene REE partition coefficients increase by one order of magnitude (Fig. 6-3). 352 Given the striking temperature effect on plagioclase-clinopyroxene REE partitioning, we can develop a REE-in-plagioclase-clinopyroxene thermometer in a form similar to Eq. (6a) in Chapter 5: ( B j = T ln D plg-cpx j −A , ) (6a) where A is a coefficient dependent strongly on major element compositions of plagioclase and clinopyroxene; B is a coefficient that depends on mineral major element composition and the ionic radii of REEs. From Eq. (5), we can derive expressions to calculate A and B, viz., ( ) 3 A = 21.17 − 4.77 X Ca plg − 4.37 X Al T ,cpx − 1.98X Mg M2,cpx , (6b) B j = 2.97 × 104 + 909.85G rj , () (6c) ⎛ r cpx 3⎞ ( ) ( ) − 13 ( r ) 2 G rj = E cpx ⎜ 0 r0cpx − rj 0 cpx − rj ⎟ ⎝ 2 ⎠ , (6d) ⎛ r0plg plg 3⎞ ( ) 1 ( ) 2 −E ⎜ plg r0 − rj − r0plg − rj ⎟ ⎝ 2 3 ⎠ Following steps similar to those for the REE-in-two-pyroxene thermometer in Liang et al. (2013), one can calculate the temperature for a mafic or ultramafic rock with coexisting plagioclase and clinopyroxene. Here we briefly summarized these steps: (1) calculate coefficients A and B using Eqs. (6b-d) and mineral major element composition; (2) examine plagioclase-clinopyroxene REE partition coefficients in a spider diagram and check if REEs define a line passing through the origin in a plot of (lnD – A) vs. B (D denotes D plg-cpx j hereafter); (3) perform linear least square regression analysis of plagioclase-clinopyroxene REE partition coefficients in the plot of (lnD – A) vs. B to determine the slope of the line, i.e., the temperature. The uncertainties of the estimated temperature can be obtained through the linear least squares analysis. Figure 6-4 shows an example of the temperature inversion for a gabbronorite (B06-064) from the Bushveld Complex reported in VanTongeren and Mathez (2013). In this sample, REEs 353 are enriched in clinopyroxene but are depleted in plagioclase (Fig. 6-4a). Since middle and heavy REEs are strongly incompatible in plagioclase, their abundances in plagioclase are close to detection limits (Fig. 6-4a). In the temperature inversion diagram (Fig. 6-4b), REEs define a straight line passing through the origin. Eu was excluded in the temperature inversion because it is mainly divalent in plagioclase and is systematically apart from other REEs. Several middle and heavy REEs (Dy, Gd and Y) slightly deviate from the line most likely due to their large analytical uncertainties, and were also excluded in the temperature inversion. The slope of this line gives a temperature of 1181 ± 5 ºC. This temperature agrees very well with the crystallization temperature (1161 ºC) of plagioclase calculated using the empirical thermometer of Thy et al. [2013; T (ºC) = 895 + 3.8*An (±19 ºC)]. We then applied the REE-in-plagioclase-clinopyroxene thermometer to 26 mafic and ultramafic rocks from the Lower Zone, Lower Critical Zone and Main Zone in the Bushveld complex with major elements and REEs in plagioclase and clinopyroxene reported in Godel et al. (2011) and VanTongeren and Mathez (2013). These samples have relatively high An (= 55 – 76) in plagioclase and high Mg# (= 65 – 91) in clinopyroxene. Surprisingly, the temperatures derived from the REE-in-plagioclase-clinopyroxene thermometer are in excellent agreement with those calculated using Thy et al.’s empirical thermometer (Fig. 6-5). Note that the temperatures derived from Thy et al.’s empirical thermometer are systematically higher than those calculated using the REE-based thermometer for low An plagioclase but are systematically lower for high An plagioclase, though the differences in temperatures between these two thermometers are generally within 20 ºC (Fig. 6-5). As demonstrated by Lange et al. (2009; see their Fig. 7), the relationship between An and temperature becomes highly nonlinear for plagioclase with low (< 50) and high An (> 70), and can be strongly affected by melt composition. For a given An, temperatures differ by 100 ºC between basaltic and andesitic melts (Lange et al., 2009). This suggests that the differences in temperatures between the REE-based and the An-based thermometers for 354 plagioclase with low and high An are likely due to the uncertainties in the empirical linear relationship between temperature and An [T (ºC) = 895 + 3.8*An (±19 ºC); Thy et al., 2013]. In general, the excellent agreement in temperatures between the REE-in-plagioclase- clinopyroxene thermometer and the An-based thermometer of Thy et al. (2013) indicates that this REE-based thermometer likely records the crystallization temperatures of plagioclase (or their approximate values) for cumulate rocks. This inspires a broader application of the REE-in- plagioclase-clinopyroxene thermometer to lunar FANs and Mg-suite rocks, eucrites, and refractory inclusions in chondrites (CAI: Ca-Al-rich inclusions; POI: plagioclase-olivine-rich inclusions), which we will present in the next section. 3. Geological Applications 3.1. Applications to planetary materials We compiled 10 FANs, two Mg-suite rocks, three eucrites, one CAI, and one POI with major elements and REEs in plagioclase and clinopyroxene reported in the literature. REEs in plagioclase (An = 95 – 98) and clinopyroxene (Mg# = 70 – 86) from the 10 FANs were reported in Floss et al. (1998) and James et al. (2002), while major elements in the minerals were published in McGee (1993). The two Mg-suite rocks are anorthosite and troctolite with major elements and REEs in plagioclase (An = 95) and clinopyroxene (Mg# = 89 – 93) reported in Shervais and McGee (1998). The three eucrites were reported in Pun and Papike (1995) with major elements and REEs in plagioclase (An = 91 – 99) and clinopyroxene (Mg# = 61 – 76). The CAI sample is Type-B1 CAI in the Allende meteorite, and was reported in Meeker (1995) with major elements and REEs in primary plagioclase (An = 99) and clinopyroxene (Mg# = 100). The POI sample is an unusual basaltic inclusion in the Allende meteorite reported in Kennedy and Hutcheon (1992) with major elements and REEs in plagioclase (An = 93) and clinopyroxene (Mg# = 99). Plagioclase and clinopyroxene from these samples have major element composition 355 generally within the calibration range of our REE-in-plagioclase-clinopyroxene thermometer. Fig. 6-6 displays the temperatures calculated using the REE-in-plagioclase-clinopyroxene thermometer for these samples. The temperatures for the 10 FAN samples vary within a small range (1279 – 1358 ºC), and are about 50 – 100 ºC higher than the MAGFOX-derived plagioclase crystallization temperatures (1235 – 1261 ºC) in a lunar magma ocean (LMO) model (Longhi, 2003). The small temperature range for all the FAN samples suggests that the high temperatures derived from the REE-based thermometer is a global feature for the lunar highland crust. If the high temperatures are the crystallization temperatures of FANs in the LMO, it indicates that anorthite becomes saturated in the LMO earlier than that predicted by MAGFOX. The early saturation of anorthite may result from more complicated LMO crystallization processes than that assumed in MAGFOX calculation or from a difference in initial LMO composition. Alternatively, the high temperatures may indicate a global thermal perturbation in the lunar highland crust, which reset the apparent temperature recorded in the REE-in-plagioclase-clinopyroxene thermometer. The temperatures of the two Mg-suite rocks are 1297 ºC and 1375 ºC and overlap with those of FANs (1279 – 1358 ºC). The temperatures of the three eucrites (1250 – 1357 ºC) are also very similar to those of the Mg-suite rocks and FANs, and support the igneous differentiation origin of the eucrites. The temperature of the Type-B CAI is 1462 ºC, and is significantly greater than the crystallization temperature of anorthite (1260 ºC; Stolper, 1982) in a liquid with a bulk CAI composition. The temperature of the POI (1339 ºC) is lower than that of the CAI but greater than that possible crystallization temperature of plagioclase in a melt with a POI-like composition (Kennedy and Hutcheon, 1992). Therefore, the REE-in-plagioclase-clinopyroxene thermometer is promising to reveal the formation of these plagioclase- and clinopyroxene-bearing rocks as well as thermal evolutions of their parent bodies. However, more work is still required to examine how robust this thermometer can be applied to these compositional spaces. 356 3.2. Applications to the Bushveld layered intrusions The Bushveld Complex is the world’s largest layered mafic intrusion, and has served as a benchmark for understanding magma chamber processes. Extensive petrologic and geochemical studies have documented the systematic variations of major, minor, and trace elements and isotopes with stratigraphic height across the Bushveld Complex. Spatial variations in chemical fractionation indices such as Mg# in mafic minerals and An in plagioclase have revealed important magma chamber processes involving magma-wall rock interaction, magma recharge and fractional crystallization. Yet the origin and evolution of the Bushveld Complex remain an enigma. To shed new light on the dynamic processes that contribute to magma chamber build-up, we calculate crystallization temperatures appropriate for portions of the Bushveld complex using the REE-in-plagioclase-pyroxene thermometer. We obtained 15 gabbronorites from the Lower Main Zone of the Bushveld complex. Major elements in plagioclase and clinopyroxene of these samples were reported in Roelofse and Ashwal (2012), and trace compositions in plagioclase and clinopyroxene were analyzed in situ using the LA-ICP-MS at Brown University. Details of the analytical procedures and results are in the Supplementary Material. We also compiled 19 gabbronorites from the Upper Zone and Upper Main Zone (VanTongeren and Mathez, 2013), and 6 pyroxenites and 1 harzburgite from the Lower Zone and Lower Critical Zone (Godel et al., 2011). The 26 samples were reported with major elements and REEs in plagioclase (An = 55 – 76) and clinopyroxene (Mg# = 65 – 91). Generally, the 41 samples cover the stratigraphic section of the Bushveld Complex. Since detailed isotope studies have not been conducted for the 41 samples, here we compiled 119 Sr isotope data along the stratigraphic section of the Bushveld Complex from Sharpe et al. (1985), Kruger et al. (1987), Cawthorn et al. (1991), Tegner et al. (2006), and Maier et al. (2013). Application of the REE-in-plagioclase-clinopyroxene thermometer to these samples reveals systematic temperature variations along stratigraphic height and strong correlations 87 between the temperatures and the published initial Sr/86Sr in bulk samples and between the 357 temperatures and An (Fig. 6-7). In the Lower and Critical zones, temperatures show a positive 87 correlation with initial Sr/86Sr and An, suggesting that the magma chamber process was dominated by magma-wall rock assimilation and fractional crystallization with possibly increasing magma influx in the lower critical zone. In the Lower Main Zone, temperatures 87 continuously increase from the bottom up while the initial Sr/86Sr remains constant with clustered An. This indicates continuous magma inputs in the magma chamber of the Lower Main Zone and these magmas likely came from a similar source. Note that this process does not systematically change An. From the bottom to the top of the pyroxenite marker, temperatures shift up ~170ºC with the initial 87Sr/86Sr decreasing from 0.708 to 0.707 and An increasing from 57 to 76, consistent with a large influx of new magmas. In the Upper Zone, temperatures decrease with 87 An from the bottom up but the initial Sr/86Sr appears constant, suggesting that fractional crystallization and crystal settling largely controlled the magma chamber processes. These initial results are encouraging and demand more detailed studies with higher spatial resolution along stratigraphic height. Variations in (near) magmatic temperatures and their correlations with isotopes and chemical fractionation indices may offer new insights into the magma chamber processes in layered intrusions. Acknowledgements We wish to thank Lewis Ashwal and Frederick Roelofse for generously providing 15 samples from the Lower Main Zone of the Bushveld Complex, Jill VanTongenren for sharing her published data and useful discussion, Christian Tegner for useful discussion, Reed Mershon and Boda Liu for their help with thin sections, and Soumen Mallick for setting up the LA-ICP-MS. One of the preliminary plagioclase-melt partitioning experiments was conducted by Michelle Graff for her senior thesis research, and is greatly appreciated. This work was supported in part by the NSF grant EAR-1220076 and NASA grant NNX13AH07G. 358 References Aigner-Torres, M., Blundy, J., Ulmer, P., & Pettke, T. (2007). 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Thy, P., Tegner, C., & Lesher, C. E. (2009). Liquidus temperatures of the Skaergaard magma. American Mineralogist, 94(10), 1371-1376. Vantongeren, J. A., & Mathez, E. A. (2013). Incoming Magma Composition and Style of Recharge below the Pyroxenite Marker, Eastern Bushveld Complex, South Africa. Journal of Petrology, 54(8), 1585-1605. Witt-Eickschen, G., & O'Neill, H. S. C. (2005). The effect of temperature on the equilibrium distribution of trace elements between clinopyroxene, orthopyroxene, olivine and spinel in upper mantle peridotite. Chemical Geology, 221(1), 65-101. Wood, B. J., & Blundy, J. D. (2003). Trace element partitioning under crustal and uppermost 363 mantle conditions: the influences of ionic radius, cation charge, pressure and temperature, in Treatise on Geochemistry, vol. 2, The Mantle and Core, edited by R. W. Carlson, H. D. Holland, and K. K. Turekian, pp. 392–424, Elsevier, New York. Figure Captions Figure 6-1 Comparisons between experimentally determined plagioclase-melt REE+Y partition coefficients (D) and those predicted by models from Bindeman et al. (1998; a), Wood and Blundy (2003; b), Bédard (2006; c) and Hui et al. (2011; d). Solid blue lines are 1:1 lines, and dashed lines are 1:2 and 2:1 lines. Error bars are 1σ errors of measured partitioning data from the experiments. χ p is the Pearson’s Chi-square for the compiled plagioclase-melt partitioning data, 2 as defined by Eq. (4) to aid model evaluation. Figure 6-2 Comparisons between experimentally determined plagioclase-melt REE+Y partition coefficients and those predicted by the revised model of Wood and Blundy (2003; a), and the model from this study (Eqs. 2, 3a-c). We updated the original model of Wood and Blundy (2003) using a recent plagioclase-melt partitioning model for La from Hui et al. (2011). Figure 6-3 Onuma diagrams showing the temperature and composition dependent plagioclase- clinopyroxene REE partition coefficients. The partition coefficients were calculated using Eq. (5) for three temperatures (1300 ºC, 1000 ºC, 700 ºC) and two compositions. Dashed curves represent the calculated partition coefficients for a lunar ferroan anorthosite (FANs: 60025,702,C) from Floss et al. (1998), and solid curves show the calculated partition coefficients for a gabbronorite (B06-064) from the Bushveld Complex (VanTongeren and Mathez, 2013). 364 Figure 6-4 Inversions of temperatures from REE abundances in plagioclase and clinopyroxene for a gabbronorite (B06-064) from the Bushveld Complex (VanTongeren and Mathez, 2013). The coefficients A and B were calculated using Eqs. (6b-c). Primitive mantle compositions are from Hofmann (1988). Symbols with light blue colors show the low quality data for REEs and Eu that were excluded in the temperature inversion. TREE is the temperature calculated using the REE-in- plagioclase-clinopyroxene thermometer. TAn is the temperature derived from the empirical thermometer of Thy et al. [2013; T (ºC) = 895 + 3.8*An (±19 ºC)]. Figure 6-5 Comparisons between temperatures derived from the REE-in-plagioclase- clinopyroxene thermometer and those calculated using the An-based thermometer of Thy et al. (2013) for mafic and ultramafic cumulate rocks from the Bushveld Complex. Note the dashed lines denote the 1σ errors of temperatures derived from the An-based thermometer. Figure 6-6 Temperatures calculated using the REE-in-plagioclase-clinopyroxene thermometer for lunar FANs, Mg-suite rocks, eucrites, CAI and POI reported in the literature. See text for details. Figure 6-7 Composite initial Sr isotope ratios, temperatures, and An along the stratigraphic height in the Bushveld Complex. Figure 6-S1 Comparisons of measured plagioclase-melt partitioning data (circles) and those predicted by the model from this study (red lines) for individual experiments. Markers with light blue color represent partitioning data excluded in our model calibration. Figure 6-S2 Primitive mantle normalized REE abundances in plagioclase and clinopyroxene from the Lower Main Zone of the Bushveld Complex. Primitive mantle compositions are from Hofmann (1988). 365 Figures Figure 6-1 0 0 10 10 (a) Bindeman et al. (1998) 10 10 Predicted D Predicted D 10 10 2 2 p = 3.94 p = 5.15 10 0 10 0 10 10 10 10 10 10 10 10 Observed D Observed D 0 0 10 10 10 10 Predicted D Predicted D 10 10 2 2 p = 2.14 p = 3.07 10 0 10 0 10 10 10 10 10 10 10 10 Observed D Observed D 366 Figure 6-2 0 0 10 10 (a) Wood & Blundy (b) This study 10 10 Predicted D Predicted D 10 10 p p = 0.71 10 0 10 0 10 10 10 10 10 10 10 10 Observed D Observed D 367 Figure 6-3 0 Yb Er Dy Eu Sm Nd Pr Ce La 10 10 Plagioclase-clinopyroxene 10 7) =9 N (An 10 FA 10 7 0) n= (A ri te 10 no bbro Ga 10 10 1 1.05 1.1 1.15 Ionic radius (Å) 368 Figure 6-4 1 10 Primitive Mantle Normalized Clinopyroxene o TREE ± C La 0 o 10 T ±19 C Ce B/1000 Pr Pla gio Nd cla se Sm 10 Gd Eu Dy Y Vantongeren & (a) (b) 10 La Pr Sm Gd Dy Ho Tm Lu Ce Nd Eu Tb Y Er Yb 369 Figure 6-5 1300 Vantongeren & Mathez (2013) Godel et al. (2011) 1250 1200 TREE (oC) 1150 1100 1050 1000 1000 1050 1100 1150 1200 1250 1300 TAn (oC) 370 Figure 6-6 Moore County Serra de Mage Eucrite Moama Binda POI 3529Z CAI 14321,1273 14305,301 Mg-suite 67215,6,603 67635,8 64435,270 64435,268,M 64435,268,L FAN 60025,699 60025,702,M 60025,702,C 62255,42,C 60055,5 1100 1200 1300 o 1400 1500 TREE ( C) 371 Figure 6-7 This Study 6000 Godel et al. (2011) VanTongeren & Upper Zone Upper Zone Mathez (2013) Upper Zone Fra cti on 5000 ati on Stratigraphic Height (m) 4000 Magma Influx Magma Influx Fr ac Main Zone Main Zone Main Zone tio na tio n? 3000 Magma Influx 372 2000 Critical Zone Critical Zone Zone Critical Zone 1000 Magma Influx Magma Influx Lower Zone Lower 0 0.704 0.706 0.708 0.71 1050 1100 1150 1200 50 60 70 80 87 86 T (oC) An# Initial Sr/ Sr REE Figure 6-S1 Supplementary Fig. 6-S1a 0 Run# 16 Run# 35 Run# 34 10 Eu Eu P = 0.00 GPa P = 0.00 GPa P = 0.00 GPa T = 1220 oC T = 1180 oC T = 1180 oC An = 76 An = 77 An = 74 Duration = 99 h Duration = 97 h Duration = 97 h 10 Eu La Pr La Lu Pr La Ce Sm Ce Nd Nd Ce Gd Pr Ho Nd Tb Dy 10 Y Y Y 0 10 Partition Coefficient La La La Pr Pr Ce Eu Ce Pr Eu Ce 10 Sm Nd Nd Eu Sm Y Gd Y Dy Y Er P = 0.00 GPa P = 0.00 GPa P = 0.00 GPa 10 T = 1187 oC T = 1187 oC T = 1187 oC An = 55 An = 54 An = 54 0 10 La La La Nd Nd Pr Sm Ce Nd 10 Ce Ce Pr Eu Eu Pr Eu Sm Dy Y Y Y Er P = 0.00 GPa P = 0.00 GPa P = 0.00 GPa Lu 10 T = 1187 oC T = 1257 oC T = 1257 oC Lu An = 53 An = 68 An = 70 1 1.4 1 1.4 1 1.4 Ionic Radius (Å) 373 Supplementary Fig. 6-S1b 0 10 Ce La La Pr Eu Nd La Sm Ce 10 Sm Nd Ce Sm Pr Eu Nd Pr Y Dy Y Er Y P = 0.00 GPa P = 0.00 GPa P = 0.00 GPa 10 Lu o C o C o C An = 73 An = 76 0 10 Run# NP5 Run# SDP Eu Eu P = 0.00 GPa P = 0.00 GPa T = 1176 oC o C Partition Coefficient La An = 76 An = 73 Eu Pr Ce Sm La 10 Nd Ce La Y Nd Nd Ce Sm P = 0.00 GPa Er 10 o C Yb An = 77 Er 0 Run# DAD1 Run# SDD 10 P = 0.00 GPa P = 0.00 GPa P = 0.00 GPa o o o C C C 10 La La La Nd Nd Nd Eu Eu Eu Sm 10 Sm Sm Er Er Yb Er 1 1 1 Ionic Radius (Å) 374 Supplementary Fig. 6-S1c 0 Eu 10 P = 0.00 GPa P = 0.60 GPa P = 0.80 GPa Eu o C Eu T = 1400 oC T = 1350 oC Partition Coefficient An = 69 An = 98 An = 98 Duration = 115 h Duration = 30 h Duration = 48 h 10 La Nd La Nd Sm Ce Sm La Gd Nd Sm Gd Y 10 Yb Dy Lu Ho Er Yb Lu 1 1.4 1 1.4 1 1.4 Ionic Radius (Å) 375 Figure 6-S2 10 Clinopyroxene Primitive Mantle Normalized 1 10 0 10 Plagioclase 10 10 La Ce Pr Nd Sm Eu Gd Dy Ho Y Yb Lu 376 Supplementary Material S1. Trace element contents in plagioclase and clinopyroxene from the Lower Main Zone of the Bushveld Complex We analyzed trace element abundances in plagioclase and clinopyroxene in 15 samples from the Lower Main Zone of the Bushveld Complex using a Thermo X-Series 2 quadrupole ICP-MS in conjunction with an Ultra-short 193 nm wavelength excimer laser ablation system Analyte G2 at Brown University. The analytical method is similar to that used in Chapter 2. Samples were ablated with a 65 – 80 µm beam, a 60% output energy and a frequency of 10 Hz. Counting times were 30 s for background and 60 s for measurement of the spot. Analyses were calibrated using the external standards BCR-2g, BHVO-2g, BIR-1g and the internal standard CaO reported in Roelofse and Ashwal (2013). The trace element compositions of plagioclase and clinopyroxene are reported in Table S1. Figure 6-S2 displays the primitive mantle normalized REE abundances in plagioclase and clinopyroxene from the 15 samples. In general, REEs are enriched in clinopyroxene, but are depleted systematically in plagioclase from light to heavy REEs. Since heavy REE contents in plagioclase are very close to detection limits, the slight enrichments of Yb and Lu in plagioclase are likely due to analytical uncertainties. 377 Table 6-S1 Trace element composition of clinopyroxene and plagioclase from the Lower Main Zone of the Bushveld Complex Sample 966 780 436.95 664 1219 392.81 1005.88 122.41 147.28 416.28 544.5 832.74 244.38 305.3 357.65 Clinopyroxene P (ppm) 47.025 31.105 42.948 38.811 38.893 40.936 31.253 30.398 39.649 30.926 43.251 38.451 37.013 36.467 49.308 sd 9.362 6.489 8.580 3.218 6.686 5.611 6.421 6.478 2.807 3.147 8.046 9.780 5.826 3.032 23.308 Li 11.975 9.372 9.664 15.951 8.164 9.259 10.524 7.713 8.214 10.542 8.944 9.839 9.025 8.946 10.142 sd 1.979 1.374 0.914 2.372 0.566 0.564 0.719 0.738 0.745 0.846 1.099 1.302 0.979 1.717 0.787 Sc 107.994 91.766 71.655 91.704 75.803 100.238 78.781 84.304 90.428 85.967 94.147 91.227 78.882 95.664 93.524 sd 2.753 4.511 3.638 1.979 4.159 5.143 4.354 6.377 3.770 7.221 3.127 2.674 2.384 4.785 6.422 Ti 2985.584 2534.564 2435.454 2450.560 2063.315 2002.216 1993.168 2177.885 2659.157 1956.053 2570.779 2430.502 2438.698 2483.774 2433.628 sd 479.359 308.677 350.128 440.446 395.960 795.566 581.156 524.756 256.624 415.611 654.185 745.115 352.513 507.780 747.617 V 597.906 446.187 361.000 414.574 359.121 422.277 393.761 391.476 426.135 376.214 400.069 427.258 407.899 488.408 416.490 sd 36.062 53.699 20.054 18.716 32.027 53.923 48.240 44.472 13.064 33.466 37.003 47.748 18.227 22.205 45.790 Cr 158.266 424.297 222.043 320.010 881.687 143.112 1046.525 144.721 160.197 198.689 286.514 475.986 276.186 222.303 233.159 sd 45.856 182.863 16.451 26.483 374.337 45.141 107.259 34.399 7.470 64.885 22.036 165.738 13.808 19.909 58.820 Co 76.356 65.554 51.536 53.723 49.693 57.541 55.169 61.404 57.875 55.630 55.062 53.271 56.231 62.191 58.634 sd 8.265 6.580 4.122 2.399 5.574 3.757 5.347 5.185 2.254 5.701 7.382 6.745 3.288 3.213 7.597 Ni 287.809 242.124 272.283 303.183 258.198 295.711 318.435 316.733 272.020 296.035 324.301 267.049 273.719 247.652 305.908 sd 25.021 19.031 22.981 12.027 28.718 20.876 28.688 25.000 9.469 21.098 34.684 40.251 21.464 20.230 47.451 Ga sd Rb 0.372 0.867 0.230 0.210 0.285 0.154 0.109 0.615 0.287 0.481 sd 0.126 0.034 0.106 0.033 0.532 Sr 9.137 8.688 9.580 9.553 7.986 8.473 9.401 10.279 9.378 9.051 10.229 8.838 10.075 9.671 10.762 sd 0.398 0.545 1.273 0.692 0.680 0.904 1.202 0.762 0.766 0.615 1.319 0.934 0.799 1.177 1.438 Y 72.233 44.693 24.048 32.314 25.793 30.991 28.565 21.615 28.371 29.657 29.638 38.156 26.482 38.021 37.634 sd 10.539 3.722 1.695 2.275 2.339 1.948 2.799 2.002 1.461 4.900 2.174 4.036 1.312 2.265 6.375 378 Zr 77.067 67.261 37.271 66.218 47.761 68.361 51.390 44.411 59.398 45.068 47.054 66.887 50.673 64.876 43.792 sd 18.959 15.728 11.590 7.521 13.163 12.713 10.748 10.106 11.355 15.968 8.494 10.543 6.535 15.499 12.849 Nb 0.243 0.141 0.168 0.111 0.137 0.158 0.116 0.180 0.173 0.108 0.128 0.129 0.164 0.131 0.130 sd 0.146 0.060 0.066 0.009 0.048 0.071 0.067 0.025 0.027 0.039 0.090 0.070 0.052 Cs 0.062 0.060 0.105 0.045 0.013 0.036 0.039 0.072 0.047 0.034 0.047 sd 0.040 0.019 0.022 0.022 0.022 0.066 0.014 0.040 Ba 1.233 0.793 0.343 0.453 0.580 0.269 0.669 0.439 0.670 0.826 0.378 0.493 0.482 0.486 0.425 sd 0.968 0.517 0.309 0.223 0.440 0.171 0.335 0.274 0.438 0.542 0.209 0.323 0.485 0.351 0.346 La 7.124 4.906 4.588 5.326 4.292 2.188 5.442 2.767 4.382 5.570 5.965 5.128 4.119 4.193 6.218 sd 0.360 0.262 0.600 0.833 0.312 0.347 0.823 0.526 0.357 0.357 0.797 0.778 0.701 0.320 0.849 Ce 34.161 22.859 17.793 22.558 17.918 12.653 22.963 12.972 18.494 23.127 21.686 23.768 17.652 18.533 26.260 sd 2.209 1.096 1.851 2.127 1.096 1.510 3.086 1.285 1.170 2.030 1.593 3.497 1.613 1.380 3.778 Pr 6.330 4.284 2.832 3.940 2.910 2.562 3.653 2.240 3.030 3.635 3.406 4.160 2.965 3.383 4.537 sd 0.535 0.259 0.327 0.347 0.188 0.208 0.364 0.177 0.238 0.420 0.267 0.577 0.186 0.281 0.757 Nd 33.512 21.211 13.404 19.262 14.165 14.329 16.980 11.122 14.508 17.141 16.621 20.083 14.243 17.287 22.129 sd 3.108 1.446 1.540 1.461 1.094 1.246 1.570 1.010 1.149 2.397 1.419 2.485 0.882 1.372 3.994 Sm 10.049 6.208 3.602 5.168 3.995 4.331 4.623 3.113 3.977 4.601 4.556 5.682 4.062 5.119 6.103 sd 1.337 0.470 0.405 0.484 0.365 0.352 0.455 0.377 0.296 0.737 0.312 0.588 0.205 0.326 1.216 Eu 0.631 0.549 0.577 0.674 0.511 0.477 0.643 0.519 0.545 0.590 0.682 0.596 0.598 0.537 0.648 sd 0.031 0.034 0.027 0.064 0.053 0.058 0.046 0.040 0.062 0.052 0.075 0.103 0.039 0.068 0.049 Gd 11.978 7.173 4.081 5.594 4.462 5.439 5.056 3.670 4.588 5.105 5.361 6.501 4.626 6.080 6.892 sd 1.796 0.724 0.296 0.454 0.487 0.408 0.395 0.414 0.357 0.963 0.465 0.774 0.256 0.400 1.387 Tb 1.862 1.194 0.677 0.915 0.747 0.909 0.815 0.615 0.718 0.871 0.866 1.062 0.750 1.037 1.141 sd 0.249 0.131 0.047 0.061 0.065 0.068 0.082 0.071 0.066 0.171 0.062 0.125 0.043 0.076 0.221 Dy 13.115 8.109 4.706 6.130 4.687 5.937 5.452 3.923 4.739 5.655 5.574 6.922 5.099 6.855 7.500 sd 1.969 0.821 0.352 0.452 0.405 0.373 0.445 0.452 0.435 1.103 0.354 0.791 0.251 0.500 1.340 Ho 2.573 1.693 0.937 1.269 0.985 1.145 1.144 0.827 0.987 1.106 1.096 1.362 1.018 1.424 1.494 379 sd 0.377 0.183 0.072 0.098 0.109 0.077 0.093 0.103 0.082 0.180 0.083 0.164 0.049 0.104 0.243 Er 7.849 4.954 2.721 3.655 2.860 3.313 3.310 2.301 2.865 3.295 3.308 3.994 3.115 4.112 4.172 sd 1.027 0.474 0.209 0.327 0.261 0.195 0.295 0.235 0.258 0.524 0.285 0.466 0.180 0.298 0.662 Tm 0.941 0.673 0.387 0.519 0.409 0.414 0.443 0.338 0.380 0.424 0.440 0.557 0.400 0.544 0.540 sd 0.112 0.062 0.034 0.063 0.032 0.026 0.045 0.034 0.045 0.057 0.032 0.079 0.020 0.052 0.076 Yb 6.855 4.556 2.463 2.942 2.547 2.586 2.816 2.048 2.407 2.760 2.770 3.456 2.554 3.487 3.289 sd 0.777 0.419 0.229 0.214 0.292 0.255 0.241 0.175 0.288 0.294 0.208 0.500 0.168 0.335 0.376 Lu 0.912 0.646 0.366 0.451 0.349 0.370 0.405 0.306 0.340 0.416 0.411 0.504 0.389 0.497 0.495 sd 0.109 0.045 0.027 0.054 0.035 0.023 0.034 0.034 0.037 0.047 0.034 0.060 0.021 0.038 0.060 Hf 2.204 1.752 1.430 2.584 1.664 2.357 2.012 1.596 1.802 1.291 1.837 2.198 1.745 1.997 1.701 sd 0.803 0.652 0.547 0.286 0.641 0.568 0.508 0.451 0.361 0.675 0.404 0.571 0.335 0.498 0.727 Ta 0.020 0.014 0.017 0.018 0.013 0.016 0.021 0.021 0.018 0.018 0.016 0.012 0.020 0.011 0.019 sd 0.011 0.004 0.005 0.006 0.004 0.008 0.005 0.005 0.008 0.003 0.005 0.005 0.005 0.003 0.004 Pb 0.403 0.243 0.279 0.432 0.361 0.286 0.295 0.273 0.364 sd 0.068 0.064 0.140 0.115 0.071 0.063 0.100 0.118 0.106 Th 0.577 0.510 0.430 0.457 0.385 0.196 0.555 0.334 0.317 0.430 0.470 0.340 0.464 0.318 0.451 sd 0.171 0.155 0.124 0.238 0.181 0.080 0.220 0.182 0.182 0.145 0.252 0.139 0.301 0.094 0.286 U 0.123 0.164 0.145 0.220 0.086 0.014 0.188 0.099 0.152 0.101 0.141 0.077 0.180 0.094 0.147 sd 0.046 0.125 0.060 0.206 0.025 0.016 0.114 0.079 0.177 0.044 0.131 0.035 0.164 0.066 0.126 Plagioclase P (ppm) 123.240 90.389 75.933 72.675 47.657 47.567 74.466 sd 4.397 12.880 6.833 Li 2.172 2.804 2.964 3.383 2.712 2.047 2.044 2.091 1.515 1.864 2.398 2.227 sd 0.574 0.166 0.540 1.688 0.634 0.317 0.443 0.516 0.577 0.741 0.824 Sc 4.134 4.324 3.904 3.880 3.291 4.224 3.670 3.482 sd 0.555 0.696 0.061 0.265 0.607 0.253 380 Ti 136.879 145.424 162.134 179.202 143.925 182.215 172.414 177.494 200.795 189.094 219.218 137.175 198.867 180.439 187.434 sd 52.096 15.112 85.528 44.017 49.721 36.816 41.081 25.176 45.365 80.267 55.260 39.499 40.655 35.320 68.883 V 3.848 3.007 3.332 2.661 2.321 3.033 2.806 2.657 3.226 3.207 2.402 2.642 3.664 3.714 3.079 sd 0.434 0.670 1.204 0.308 0.427 0.369 0.856 0.754 0.827 0.545 0.443 0.564 1.431 1.145 0.586 Cr sd Co 0.948 1.142 2.037 0.846 sd Ni 2.108 6.960 9.458 7.115 2.998 2.706 sd Rb 3.764 0.933 0.318 0.720 0.450 0.435 0.324 0.294 0.325 0.374 0.395 sd 0.419 0.076 0.877 0.049 0.079 0.046 0.070 0.164 0.143 Sr 320.678 306.260 304.711 356.293 308.829 328.090 331.245 374.536 361.882 334.117 352.128 296.686 380.092 359.890 343.644 sd 21.038 9.050 21.340 23.493 16.134 11.298 24.322 13.701 22.037 24.995 19.108 15.412 18.361 16.492 15.966 Y 0.523 0.433 0.295 0.324 0.245 0.312 0.292 0.253 0.322 0.377 0.299 0.346 0.323 0.386 0.397 sd 0.144 0.115 0.034 0.062 0.048 0.039 0.031 0.033 0.053 0.069 0.038 0.036 0.054 0.049 0.046 Zr 0.531 0.065 0.086 0.609 0.065 0.200 sd 0.037 0.003 0.039 0.076 Nb 0.279 sd Cs 0.308 sd Ba 95.916 90.310 101.556 103.080 87.136 91.817 112.307 102.503 111.711 123.227 130.175 96.450 127.970 100.984 119.013 sd 18.221 14.234 23.004 25.817 17.391 8.206 24.900 11.671 13.040 22.984 29.548 12.842 13.508 13.208 11.411 La 4.435 4.433 3.370 6.355 3.964 3.513 4.753 3.687 4.429 4.703 6.771 3.832 4.296 3.523 3.665 sd 2.592 1.146 2.006 1.643 2.238 0.965 1.960 0.830 1.607 1.622 2.218 1.883 1.336 1.654 1.718 Ce 7.855 7.552 5.083 9.505 5.830 5.864 7.471 5.903 6.695 7.766 9.311 6.498 6.906 5.540 6.397 381 sd 4.110 1.479 2.465 1.741 2.918 1.566 2.641 1.153 1.979 1.906 2.338 2.832 1.677 2.148 2.669 Pr 0.781 0.738 0.455 0.830 0.484 0.557 0.631 0.527 0.576 0.707 0.779 0.604 0.612 0.534 0.648 sd 0.376 0.128 0.170 0.102 0.241 0.144 0.152 0.085 0.154 0.128 0.156 0.226 0.107 0.169 0.230 Nd 2.637 2.376 1.486 2.408 1.562 1.855 1.943 1.620 1.742 2.158 2.166 1.877 1.855 1.769 2.090 sd 1.161 0.383 0.418 0.225 0.478 0.408 0.424 0.207 0.361 0.302 0.283 0.612 0.264 0.425 0.690 Sm 0.409 0.340 0.257 0.305 0.246 0.272 0.241 0.221 0.277 0.306 0.280 0.292 0.266 0.286 0.307 sd 0.120 0.067 0.132 0.045 0.053 0.060 0.030 0.040 0.046 0.052 0.112 0.039 0.047 0.077 Eu 0.609 0.524 0.532 0.624 0.487 0.493 0.606 0.529 0.544 0.619 0.613 0.498 0.610 0.590 0.580 sd 0.057 0.035 0.052 0.048 0.053 0.040 0.069 0.041 0.086 0.057 0.050 0.056 0.041 0.081 0.027 Gd 0.287 0.202 0.122 0.171 0.135 0.171 0.149 0.140 0.150 0.185 0.152 0.140 0.136 0.160 0.203 sd 0.079 0.043 0.027 0.046 0.020 0.046 0.027 0.025 0.030 0.041 0.033 0.024 0.029 0.034 0.044 Tb 0.037 0.027 0.027 0.024 0.031 0.021 0.019 0.027 0.028 0.021 0.021 0.022 0.023 0.030 sd 0.011 0.001 0.004 0.005 0.006 0.003 0.001 0.004 0.005 0.003 Dy 0.173 0.112 0.086 0.094 0.066 0.079 0.097 0.081 0.094 0.095 0.076 0.085 0.079 0.110 0.119 sd 0.047 0.021 0.022 0.061 0.023 0.023 0.025 0.016 0.019 0.020 0.031 0.031 0.021 0.020 0.030 Ho 0.029 0.022 0.016 0.018 0.013 0.015 0.018 0.017 0.017 0.017 0.011 0.014 0.019 0.020 0.026 sd 0.009 0.006 0.008 0.007 0.004 0.006 0.005 0.005 0.004 0.004 0.006 0.005 0.005 0.006 0.005 Er 0.077 0.057 0.036 0.032 0.030 0.037 0.053 0.039 0.037 0.037 0.026 0.048 0.045 0.051 0.067 sd 0.023 0.024 0.017 0.022 0.021 0.013 0.019 0.011 0.008 0.014 0.011 0.022 0.012 0.018 0.013 Tm 0.011 0.007 0.008 0.013 0.004 0.007 0.011 0.009 0.010 0.007 0.004 0.008 0.008 0.012 0.011 sd 0.004 0.003 0.005 0.011 0.003 0.003 0.003 0.003 0.005 0.003 0.002 0.003 0.002 0.003 0.004 Yb 0.055 0.037 0.058 0.036 0.032 0.040 0.025 0.071 sd 0.016 0.029 0.031 0.013 0.007 0.014 Lu 0.014 0.018 0.008 0.004 0.011 0.010 0.009 0.012 0.010 0.009 sd 0.000 0.001 0.009 0.004 0.000 0.005 0.002 Hf 0.048 0.020 0.016 0.031 0.015 0.017 0.023 0.030 0.014 0.013 0.013 0.013 0.019 0.019 0.033 sd 0.018 0.010 0.012 0.017 0.008 0.011 0.008 0.012 0.012 0.012 0.008 0.008 0.009 0.011 0.009 382 Ta 0.012 0.006 0.011 0.006 0.004 0.007 0.009 0.007 0.005 0.005 0.005 0.005 0.007 0.008 0.012 sd 0.005 0.004 0.017 0.005 0.002 0.005 0.003 0.002 0.003 0.003 0.003 0.004 0.003 0.004 0.004 Pb 4.090 2.263 2.574 3.755 4.740 2.640 2.859 2.400 3.419 sd 0.503 0.125 0.537 0.479 0.623 0.266 0.218 0.549 0.304 Th 0.019 0.025 0.011 0.008 0.007 0.008 0.015 0.010 0.008 0.006 0.007 0.015 0.008 0.011 0.014 sd 0.010 0.040 0.010 0.005 0.004 0.005 0.019 0.004 0.007 0.004 0.006 0.030 0.003 0.007 0.008 U 0.011 0.012 0.009 0.007 0.005 0.004 0.006 0.007 0.005 0.006 0.005 0.009 0.005 0.006 0.007 sd 0.005 0.015 0.008 0.008 0.003 0.003 0.002 0.003 0.002 0.004 0.004 0.012 0.002 0.005 0.005 383 APPENDIX A A Parameterized Lattice Strain Model for Ti, Hf, and Zr Partitioning between Clinopyroxene and Basaltic Melt 384 Titanium, Hf, and Zr are high field strength elements (HFSEs) characterized by their high charge (tetravalent) and small ionic radii (0.605 – 0.72 Å in VI-fold co-ordination; Shannon, 1976). Due to their small ionic radii, Ti, Hf and Zr preferentially enter the M1 site in pyroxene. Experimental studies have shown that their partition coefficients between clinopyroxene and melt are strongly correlated with tetrahedrally coordinated Al (AlT) in clinopyroxene (Lundstrom et al., 1998; Hill et al., 2000; see also Fig. 10 in Lo Cascio et al. 2008 for a recent compilation). In the Onuma diagram (partition coefficients vs. ionic radii; Onuma et al., 1968), Ti, Hf and Zr partition coefficients between clinopyroxene and melt from a given partitioning experiment vary systematically with their ionic radii, and can be quantitatively described by the lattice strain model (Brice, 1975; Blundy and Wood, 1994; see Eq. 1 in Chapter 1). In general, the lattice strain parameters (D0, r0, and E) are functions of pressure, temperature and composition and may be quantified using (empirical) parameterized models. Hill et al. (2011) developed the first lattice strain model for Ti, Hf, and Zr partitioning between clinopyroxene and melt. They eliminated D0 in the lattice strain model (Eq. 1 in Chapter 1) by using Ti as a “proxy” for Hf and Zr. Based on 264 experimentally determined Ti partitioning data, they first parameterized clinopyroxene-melt Ti partition coefficients as a function of temperature, pressure and clinopyroxene composition in a thermodynamic framework. They then used partitioning data from 41 experiments published in the literature and in their own study, and parameterized E and r0 as functions of temperature, pressure and the Al content in clinopyroxene. Fig. A1a compares the predicted partition coefficients for Ti, Hf, and Zr by Hill et al.’s model with the experimentally measured values from our compiled dataset (a total of 123 data from 41 experiments) including those used in Chapter 1 and those from a recent experimental study by Dygert et al. (2014). Note that Hill et al.’s model underestimates a significant amount of partitioning data by up to one order of magnitude. To better understand Ti, Hf and Zr partitioning in clinopyroxene, here we develop a new model for Ti, Hf and Zr partitioning between clinopyroxene and basaltic melt based on our recently compiled high quality 385 data in Chapter 1 and those from Dygert et al. (2014) and the lattice strain model (Eq. 1 in Chapter 1). Following the procedures described in Chapters 1-3, we parameterized the lattice strain parameters (D0, r0 and E) as functions of temperature, pressure and compositions of clinopyroxene and melt through parameter swiping and simultaneous or global nonlinear least squares inversion of all the filtered partitioning data. We found that D0 is negatively correlated with temperature and the Fe content in the M1 site of clinopyroxene (FeM1), positively correlated with AlT and the Ca content in the M2 site of clinopyroxene (CaM2); r0 also shows a positive correlation with CaM2 but a negative correlation with FeM1; E and r0 are positively correlated. The global fit to the 123 clinopyroxene-melt Ti, Hf and Zr partition coefficients generates the following expressions for the lattice strain parameters: 5.21( ±1.30 ) × 104 ln D0 = −6.27 ( ±0.98) + + 7.20 ( ±0.75) AlT RT (A1) ( + 2.71( ±0.96 ) Ca ) ( − 3.60 ( ±0.93) Ca ) 2 M2 M2 × Fe M1 ( ) r0 Å = 0.638 ( ±0.011) + 0.027 ( ±0.013) Ca M2 − 0.015 ( ±0.009 ) FeVI (A2) E ( GPa ) = ⎡⎣1.48 ( ±0.92 ) r0 − 0.95( ±0.60 ) ⎤⎦ × 105 (A3) where T is the temperature in K; and numbers in parentheses are 2σ uncertainties estimated directly from the simultaneous inversion. The large 2σ errors in Eqs. (A1-A3) are due to a combination of analytical uncertainties, the limited number of trace elements (three) from each experiment used in the model calibration, and trade-offs among lattice strain parameters. Six-fold coordinated ionic radii were used to calibrated Eqs. (A1-A3). Combining with Eq. (1) in Chapter 1, Eqs. (A1-A3) provide a simple model for Ti, Hf and Zr partitioning between clinopyroxene and basaltic melt. Fig. A1b shows that the predicted partition coefficients by this model are in excellent agreement with the experimentally measured values. To compare the goodness of the fit between models from this study and Hill et al. (2011), we calculated the Pearson’s Chi-square ( 386 χ P2 ) defined in Eq. (7) in Chapter 1. The χ P2 value produced by our model ( χ P2 = 5.8 ) is much smaller than that calculated using Hill et al.’s model (2011; χ P = 82.2 ). This indicates that our 2 new model shows a significant improvement over Hill et al.’s model. In Chapter 2, we developed a parameterized lattice strain model for Ti, Hf and Zr partitioning between low-Ca pyroxene and basaltic melt. Because both our models indicate that temperature and pyroxene composition dominate Ti, Hf and Zr partitioning between pyroxene and basaltic melt, we can combine these two models to obtain a predictive model for orthopyroxene-clinopyroxene Ti, Hf and Zr partitioning, viz., D opx-melt D opx-cpx j = j (A4) D cpx-melt j opx-cpx where D j is the partition coefficient of element j between orthopyroxene and clinopyroxene. We can then independently test the internal consistency of the clinopyroxene-melt and low-Ca pyroxene-melt partitioning models by comparing the predicted orthopyroxene-clinopyroxene partition coefficients by Eq. (A4) with the measured data from well-equilibrated mantle xenoliths. Witt-Eickschen and O'Neill (2005), Witt-Eickschen et al. (2009) and Bedini and Bodinier (1999) reported major element and trace element (including Ti, Hf and Zr) compositions of orthopyroxene and clinopyroxene from well-equilibrated spinel-peridotite xenoliths. Using their major element compositions and Eq. (A4), we calculated Ti, Hf and Zr partition coefficients between orthopyroxene and clinopyroxene for their samples. The two-pyroxene thermometer of Brey and Köhler (1990) was used to calculate equilibrium temperatures (903–1245 °C) for these samples by assuming a pressure of 1.5 GPa. Fig. A2 demonstrates that the predicted and measured orthopyroxene-clinopyroxene partition coefficients for Ti, Hf and Zr are in excellent agreement. Note that both our models for Ti, Hf and Zr partitioning were calibrated independently at magmatic conditions. The excellent agreement not only indicates the internal consistency of our two models, but also demonstrates that the calibrated lattice strain parameters 387 in these models can be extrapolated to peridotites at subsolidus conditions. With these internally consistent partitioning models for Ti, Hf, and Zr, it may also be possible to develop thermometers based on Ti, Hf and Zr partitioning between orthopyroxene and clinopyroxene. It is interesting that our new model shows that water in the melt does not play an important (or direct) role in determining Ti, Hf and Zr partitioning in clinopyroxene, though 15 of the 41 experiments in our compiled dataset were conducted under hydrous conditions (See Table 1 in Chapter 1 for details). By contrast, our model for rare earth element (REE) partitioning in clinopyroxene shows that water in the melt can significant decrease clinopyroxene-melt REE partition coefficients (Chapter 1). Thus, under hydrous conditions, HFSEs and REEs may be significantly fractionated during mantle melting or during clinopyroxene fractional crystallization. References Bedini, R. M., & Bodinier, J. L. (1999). Distribution of incompatible trace elements between the constituents of spinel peridotite xenoliths: ICP-MS data from the East African Rift. Geochimica et Cosmochimica Acta, 63(22), 3883-3900. Blundy, J. D., & Wood, B. J. (1994). Prediction of crystal-melt partition coefficients from elastic moduli. Nature, 372, 452-454. Brey, G. P., & Köhler, T. (1990). Geothermobarometry in four-phase lherzolites II. New thermobarometers, and practical assessment of existing thermobarometers. Journal of Petrology, 31(6), 1353-1378. Brice, J. C. (1975). Some thermodynamic aspects of the growth of strained crystals. Journal of Crystal Growth, 28(2), 249-253. Dygert, N., Liang, Y., Sun, C., & Hess, P. (2014). An experimental study of trace element partitioning between augite and Fe-rich basalts. Geochimica et Cosmochimica Acta, 132, 170-186. 388 Hill, E., Wood, B. J., & Blundy, J. D. (2000). The effect of Ca-Tschermaks component on trace element partitioning between clinopyroxene and silicate melt. Lithos, 53(3), 203-215. Hill, E., Blundy, J. D., & Wood, B. J. (2011). Clinopyroxene–melt trace element partitioning and the development of a predictive model for HFSE and Sc. Contributions to mineralogy and petrology, 161(3), 423-438. Lo Cascio, M., Liang, Y., Shimizu, N., & Hess, P. C. (2008). An experimental study of the grain- scale processes of peridotite melting: implications for major and trace element distribution during equilibrium and disequilibrium melting. Contributions to Mineralogy and Petrology, 156(1), 87-102. Lundstrom, C. C., Shaw, H. F., Ryerson, F. J., Williams, Q., & Gill, J. (1998). Crystal chemical control of clinopyroxene-melt partitioning in the Di-Ab-An system: implications for elemental fractionations in the depleted mantle. Geochimica et Cosmochimica Acta, 62(16), 2849-2862. Onuma, N., Higuchi, H., Wakita, H., & Nagasawa, H. (1968). Trace element partition between two pyroxenes and the host lava. Earth and Planetary Science Letters, 5, 47-51. Shannon, R. D. (1976). Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides. Acta Crystallographica Section A: Crystal Physics, Diffraction, Theoretical and General Crystallography, 32(5), 751-767. Witt-Eickschen, G., & O'Neill, H. S. C. (2005). The effect of temperature on the equilibrium distribution of trace elements between clinopyroxene, orthopyroxene, olivine and spinel in upper mantle peridotite. Chemical Geology, 221(1), 65-101. Witt-Eickschen, G., Palme, H., O’Neill, H. S. C., & Allen, C. M. (2009). The geochemistry of the volatile trace elements As, Cd, Ga, In and Sn in the Earth’s mantle: new evidence from in situ analyses of mantle xenoliths. Geochimica et Cosmochimica Acta, 73(6), 1755-1778. 389 1 1 10 10 0 10 0 10 10 10 10 10 2 = 82.2 2 = 5.8 p p 0 1 10 0 1 10 10 10 10 10 10 10 10 Figure A1. Comparisons between model-predicted clinopyroxene-melt Ti, Hf and Zr partition coefficients and experimentally determined values. (a) shows the predicted partition coefficients calculated using Hill et al.’s model (2011), and (b) shows the predicted partition coefficients calculated using Eq. (1) in Chapter 1 and Eqs. (A1-A3). Error bars for measured partition coefficients are reported standard errors, while those for predicted values in (b) are 2σ errors estimated directly by the model. See text for data sources. 0 10 Predicted opx-cpx D 10 = 0.41 p 10 0 10 10 10 Observed opx-cpx D Figure A2. Comparisons of predicted and measured Ti, Hf and Zr partition coefficients between orthopyroxene and clinopyroxene from well-equilibrated spinel-peridotite xenoliths. The peridotite samples are well-equilibrated spinel-peridotite xenoliths from cratonic lithospheric mantle (Witt-Eickschen and O'Neill, 2005; Witt-Eickschen et al., 2009) and from East African Rift (Bedini and Bodinier, 1999). The predicted partition coefficients were calculated using Eq. (A4). 390