In-situ Characterization of Composition Induced Stresses in Thin Film Oxides: Application to Solid Oxide Fuel Cell and Li-ion Battery Electrodes by Jay Sheth Sc.M, Brown University, RI, USA, 2014 B.Tech., Indian Institute of Technology-Banaras Hindu University, 2011 A dissertation submitted in partial fulfillment of the requirements for the Degree of Doctor of Philosophy in School of Engineering at Brown University Providence, Rhode Island May, 2017 i © Copyright 2017 by Jay Sheth ii This dissertation by Jay Sheth is accepted in its present form by the School of Engineering as satisfying the dissertation requirement for the degree of Doctor of Philosophy Date ______________ ______________________________________ (Professor Brian W. Sheldon), Advisor Recommended to the Graduate Council Date ______________ ______________________________________ (Professor Eric Chason), Reader Date ______________ ______________________________________ (Professor Pradeep R. Guduru), Reader Approved by the Graduate Council Date ______________ ______________________________________ (Andrew G. Campbell) Dean of the Graduate School iii Curriculum Vitae Education - Ph.D. in Material Science and Engineering 2017 Brown University, Providence, RI, USA Advisor: Prof. Brian W. Sheldon - Sc.M. in Material Science and Engineering 2014 Brown University, Providence, RI, USA Advisor: Prof. Brian W. Sheldon - B.Tech. in Ceramic Engineering 2011 Indian Institute of Technology- Banaras Hindu University (IIT-BHU), Varanasi, UP, India Publications [1] J. Sheth, N. K. Karan, D. P. Abraham, C. C. Nguyen, B. L. Lucht, B. W. Sheldon and P. R. Guduru, “In-situ stress evolution in Li1+xMn2O4 thin films during electrochemical cycling in Li-ion cells", Journal of The Electrochemical Society, 163 (13) (2016) A2524- A2530. [2] J. Sheth, D. Chen, J. J. Kim, W. J. Bowman, P. A. Crozier, H. L. Tuller, S. T. Misture, S. Zdzieszynski, B. W. Sheldon and S. R. Bishop, “Coupling of strain, stress and oxygen non-stoichiometry in thin film Pr0.1Ce0.9O2-", Nanoscale, 8 (2016) 16499-16510. [3] J. Sheth, D. Chen, H. L. Tuller, S. T. Misture, S. R. Bishop and B. W. Sheldon, “Role of grain size on redox induced compositional stresses in Pr doped ceria thin films", Submitted to PCCP. [4] S. R. Bishop, D. Chen, J. Sheth, S. T. Misture, B. W. Sheldon, J. J. Kim, and H. L. Tuller, “Impact of size scale on electro-chemo-mechanical coupling properties in MIECs: Bulk and thin film (Pr,Ce)O2-", ECS Transactions, 61 (1) (2014) 31-36. iv Acknowledgements Several individuals have directly or indirectly contributed towards the completion of this thesis. I would like to take this opportunity to thank them all for their support and help. First and foremost, I would like to thank Prof. Brian W. Sheldon for guiding my academic and research work that led to the completion of my degree. He has been very patient and extremely supportive of me over the last couple of years. I would also like to thank him for giving me the freedom in terms of attending conferences, setting up collaborations, designing of experiments, etc. I would like to thank my thesis readers, Prof. Pradeep R. Guduru and Prof. Eric Chason for their time and constructive suggestions that have helped improve this thesis. I would also like to express my deepest gratitude to all my teachers both before and at Brown who have constantly inspired and motivated me during different stages of my student life. I owe many thanks to all of my collaborators, namely Di Chen, Jae Jin Kim, William J. Bowman, Prof. Peter A. Crozier, Prof. Harry L. Tuller, Prof. Scott T. Misture, Jessica G. Swallow, Frank McGrogan, Prof. Krystyn Van Vliet and Dr. Daniel P. Abraham for their close collaboration on several different projects. I would like to specially thank Dr. Sean R. Bishop and Dr. Naba K. Karan for their valuable insights as some of their ideas, critical discussion and analysis helped put this thesis together. v I am grateful to the technical and administrative staff within the School of Engineering at Brown for their continuous assistance, especially Brian Corkum, Anthony McCormick, Michael Jibitsky, Paul Waltz, Charles Vickers, Michael Packer, Diane Felber, Peggy Mercurio, and Tara Greenwood. Thanks guys! I must thank the graduate students and post-docs in both Sheldon and Guduru Labs: Ravi Kumar, Leah Nation, Anton Tokranov, Teng Ma, Dawei Liu, Xin Su, Xin Liang, Sugeetha Vasudevan, Sumit Kumar Soni, Amartya Mukhopadhyay, Aaron Kessman, Susan Herringer, Maria Cristina Ramirez, Lei Yang, Mok Yun Jin, Jung Hwi Cho, Insun Yoon, Odysseas Skartsis, Michael Chon, Shaghayegh Rezazadeh, Pinkesh Malhotra, Kai Yan, Ron Dunn, Vijay Sethuraman, and Siva Nadimpalli. They were always there to have lively discussions and to help me out in the lab. Over the last couple of years in Providence, I have made many friends whom I would like to thank as well; namely Jonathan Estrada, Benjamin Johnson, Steven Ahn, Chun Hao Chen, Archita Agarwal, Aruna Sigdel, Cindy Lung, Aakash Sharan, Bhavuk Nagpal, Hasnain Vora, Siddhant Jaitpal, Srinivas Karthik, Karthik Desingh, Valay Shah, Evgenios Kornaropoulos, Srivatsan Hulikal, Krishnanand Murthy, Ashish Garg, Neha Garg, Stylianos Siontas, Lindsay Kuhn, Amanda Krause, Onkar Game, Hector Garces, Michael Monn, Nicholas Mostovych, Ian Harding, Gerardo Pradillo, Reza Azimi, Jessica Claflin, Soheil Hashemi, Dimitra Papagiannopoulou, Amalia Avila, Hokchhay Tann, Ramona Vladea, Vaios Laschos, Andrea Weber, Sebastjan Glinsek, Eirini Kilikian and the aforementioned members of Sheldon and Guduru lab. I feel truly blessed to be surrounded by such an amazing pool of people during my journey at Brown. vi This section would be incomplete without special thanks to my close group of friends who have been by my side through all the thick and thin, who have given me memories to cherish for my lifetime, who have been my partners-in-crime, from hiking and biking to being the guinea pigs of my cooking and baking experiments; this journey was surely impossible without these guys- Maria Stournara, Kapil Dev, Ravi Kumar, Fernanda Lugo Bolanos, Anton Tokranov, Kaushik Vijaykumar, Anshul Jain, Vineeth Venugopal, Daniel Gerbig, Alexandra Papoutsaki, Martha Gialampouki, and Daniel Moreno. I would also like to thank Akshay Dhar and Amey Vijay Baokar. Thanks guys for making this journey fulfilling and for your lifelong friendship. I am confident that no matter where we are going to be in the future, we will always be in touch. Finally, I am extremely grateful to my parents and my brother for their unconditional love. Thank you for believing in me. I certainly would have not made it this far without your hard work, support and encouragement. vii This work is dedicated to my parents Mrs. Mita Sheth & Mr. Hemant Sheth and to my grandparents Mrs. Rekha Sheth & Late Mahasukhlal Sheth viii Table of Contents Signature Page iii Curriculum Vitae iv Acknowledgments v Table of Content ix List of Tables xiii List of Figures xv Abstract xxi 1. INTRODUCTION.................................................................................................1 1.1. General Background.........................................................................................1 1.2. Basics of SOFCs...............................................................................................4 1.3. Basics of LIBs...................................................................................................7 1.4. Motivation.........................................................................................................8 1.5. Thesis Organization........................................................................................10 1.6. References.......................................................................................................12 2. COUPLING OF STRAIN, STRESS AND OXYGEN NON- STOICHIOMETRY IN THIN FILM Pr0.1Ce0.9O2-.........................................14 2.1. Introduction.....................................................................................................14 2.2. Experimental...................................................................................................18 2.3. Results.............................................................................................................22 2.4. Discussion.......................................................................................................40 ix 2.5. Conclusion......................................................................................................45 2.6. References.......................................................................................................47 3. ROLE OF GRAIN SIZE ON REDOX INDUCED COMPOSITIONAL STRESSES IN Pr DOPED CERIA THIN FILMS...........................................50 3.1. Introduction.....................................................................................................50 3.2. Experimental...................................................................................................53 3.3. Results.............................................................................................................55 3.4. Analysis and Discussion.................................................................................65 3.5. Conclusion......................................................................................................81 3.6. References.......................................................................................................83 4. IN-SITU STRESS EVOLUTION IN Li1+xMn2O4 THIN FILMS DURING ELECTROCHEMICAL CYCLING IN Li-ion CELLS.................86 4.1. Introduction.....................................................................................................86 4.2. Experimental...................................................................................................89 4.3. Results.............................................................................................................94 4.4. Discussion.....................................................................................................102 4.5. Conclusions...................................................................................................111 4.6. References.....................................................................................................113 5. EFFECT OF INTERNAL STRESSES ON PHASE TRANSFORMATION IN VANADIUM OXIDE ELECTRODES..................................................................................................117 5.1. Introduction ..................................................................................................117 5.2. Experimental.................................................................................................119 5.3. Results...........................................................................................................123 5.4. Analysis and Discussion...............................................................................136 x 5.5. Conclusions...................................................................................................147 5.6. References.....................................................................................................149 6. CONCLUSIONS AND FUTURE DIRECTIONS...........................................151 6.1. Conclusions...................................................................................................151 6.2. Future Directions..........................................................................................154 APPENDICES: A. ADDITIONAL MEASUREMENTS ON PCO......................................................156 A.1. Determination of CTE of PCO..........................................................................156 A.2. Stress Reversal in PCO at High Temperatures and very Low pO2....................161 A.3. Full Brick Layer Model (3-D)...........................................................................167 A.4. References..........................................................................................................172 B. MEASUREMENTS ON AMORPHOUS ALUMINUM OXIDE FILMS DEPOSITED BY MOCVD.....................................................................................173 B.1. Determination of CTE.......................................................................................173 B.2. References..........................................................................................................184 C. ADDITIONAL MEASUREMENTS ON LMO SAMPLES.................................185 C.1. In-situ AFM on LMO Films During First Delithiation Cycle...........................185 C.2. Surface XPS Measurement of LMO Films at Different Open Circuit Potentials.......................................................................................189 C.3. High Temperature MOSS Measurements on LMO Films.................................201 C.4. Additional Electrochemical and MOSS Measurements on LMO Films............220 xi C.5. Nanoscale Electrochemomechanical (NECS) Technique: Application to LMO Thin Films......................................................225 C.6. References..........................................................................................................233 D. SiC OXIDATION MEASUREMENTS.................................................................234 D.1. High Temperature Oxidation of SiC and the Corresponding Curvature Change Measured by MOSS.............................................................234 D.2. References..........................................................................................................237 E. MODEL: STRESS CONTRIBUTION TO TWO PHASE EQUILIBRIUM.......................................................................................................238 E.1. Complete Formulation........................................................................................238 E.2. References...........................................................................................................248 xii List of Tables Table 2.1 Slopes from Figure 2.8 following equations 2.9 and 2.10. The “(2)” at 750 oC represents the measurements performed on a second film. Values in parenthesis represent selected higher temperature strain and stress data derived using the bulk defect equilibria model.................40 Table 2.2 Chemical expansion coefficient and elastic modulus derived from data in Table 2.1 assuming Poisson’s ratio of 0.33 for indicated substrates. Thin film and bulk defect models used for 650 – 700oC and 750 – 800oC data..........................................................................................45 Table 3.1 Grain size, thickness, and respective deposition conditions for Pr 0.1Ce0.9O2- thin films grown on indicated sapphire substrate geometries.............................................................................56 Table 3.2 Elastic modulus values derived from the slopes in Figure 3.5 assuming = 0.33 at 750oC................................................................................................................................ .......65 Table 3.3  values for PCO, undoped ceria and GDC as calculated using the slopes in Figure.3.10..............................................................................................................................80 Table 5.1 Initial stress measured in the pristine and as deposited films using MOSS..........................126 Table 5.2 Variations in the two phase plateaus observed by different authors throughout the literature and those observed in this study............................................................................................131 Table 5.3 Lattice parameters (as calculated by Rocquefelte et al.) and the volumetric strains corresponding to the values of x in LixV2O5. Note that the stress and strain are calculated with respect to x = 0..............................................................................................................137 Table 5.4 Lattice parameters (as found experimentally from different references) and the volumetric strains corresponding to the values of x in LixV2O5. Note that the stress and strain are calculated with respect to x = 0.............................................................................................137 Table 5.5 Table.5.5. Equilibrium plateau positions for the film on Al and the film on Au and the potential drop calculated using Equation 5.9........................................................................145 Table 5.6 Details about individual phases of lithiated V2O5. Note that, the density of each phase is taken to be the same as V2O5.As such, Vm of each of the phases is calculated using this value......................................................................................................................................146 Table A.1.1 CTE values of PCO film determined using the thermal stress values as measured by the HTMOSS system...................................................................................................................160 Table A.2.1 Details of the gas compositions used during oxidation and reduction and the corresponding equilibrium oxygen partial pressures....................................................................................166 Table B.1.1 Deposition parameters for MOCVD grown amorphous alumina films................................175 Table B.1.2 CTE values of amorphous alumina film deposited on sapphire and YSZ substrates. The values were determined using the thermal stress values as measured by the HTMOSS system....................................................................................................................................183 Table C.2.1 Sample IDs and the corresponding OCVs of the LMO films used for the XPS measurements........................................................................................................................192 xiii Table C.2.2 Change in the manganese oxidation states in the LMO films at different OCVs. These values are obtained by resolving the Mn2p3/2 peak in terms of contributions from the Mn2+, Mn3+ and Mn4+ peaks using the fitting protocol as described in the text.......................................198 Table C.3.1 Experimental conditions at different stages for the experiment in figure C.3.9 (a)..............218 xiv List of Figures Figure 1.1 Ragone plot showing the specific energy density vs. specific power density for various energy storage and conversion devices.....................................................................................2 Figure 1.2 Schematic showing the working of a SOFC.............................................................................5 Figure 1.3 Schematic showing the working of a LIB.................................................................................8 Figure 1.4 Electrochemical cycling induced mechanical degradation of the electrode/solid electrolyte materials used in SOFCs and LIBs...........................................................................................9 Figure 2.1 The X-ray diffraction patterns for the two films with the diffraction vector normal to the film surfaces is shown in (a). Reciprocal space maps of a PCO thin film on (b and c) YSZ and (d) sapphire, with peaks indicated................................................................................................25 Figure 2.2 Cross-section TEM images of PCO thin films after HTXRD measurements. (a-c) Film on YSZ. (a) Vertical threading dislocations visible via strain contrast; highlighted with arrows. (b) Atomic resolution image with highlighted region with visible threading extra half plane. (c) Atomic resolution image of PCO-YSZ interface showing partial epitaxy: continuous (111) planes extended from substrate into film. (d-f) Film on sapphire. (d) Columnar grains and grain boundaries (highlighted) extending through the film. (e) Atomic resolution image of grain boundary at surface of film showing atomically abrupt boundaries. (f) Atomic resolution image of PCO-sapphire interface showing atomic disorder at the base of a grain boundary..................................................................................................................................26 Figure 2.3 Absorption coefficient (A) for PCO thin films deposited on either sapphire or YSZ substrates measured in-situ......................................................................................................................28 Figure 2.4 Oxygen non-stoichiometry derived from optical transmission measurements in Figure 2.3 using a reference point based on the thin film (a) and bulk (b) defect equilibria models. Dashed and solid lines show non-stoichiometry derived from the thin film and bulk defect equilibria models, respectively................................................................................................30 Figure 2.5 Isotherms of out-of-plane lattice parameter for PCO films on sapphire and YSZ substrates measured in-situ. Bulk, isotropic data points are also shown, indicated for each temperature by color. Uncertainties are smaller than the data points.........................................................32 Figure 2.6 MOSS results for PCO film on YSZ cycled at 750 oC in indicated reducing and oxidizing atmospheres.............................................................................................................................35 Figure 2.7 MOSS results for PCO film on sapphire. The reference stress for each data set is defined as the stress at 0.1 atm. O2, at the temperature of interest (i.e., ∆𝜎 = 0 under these conditions). (a) Stress during cycling at 750oC in the indicated reducing and oxidizing atmospheres. (b) Increase of in-plane compressive stress of a PCO film with decreasing pO2 for the two measured temperatures............................................................................................................37 Figure 2.8 Out-of-plane strain plotted against the oxygen content of the PCO film derived from the thin film defect model. Solid, dashed, and dotted lines represent linear fits to films supported on an Al2O3 substrate, a second Al2O3 substrate, and a YSZ substrate, respectively. Half-filled symbols are for the second film on an Al2O3 substrate...........................................................38 xv Figure 2.9 Change of in-plane stress plotted against the oxygen content of the PCO film supported on Al2O3 derived from the thin film defect model.......................................................................38 Figure 3.1 Representative X-ray diffraction pattern for the PCO thin films of avg. grain size of 72, 50 and 27 nm on 1 cm x 1 cm sapphire substrates.......................................................................55 Figure 3.2 (a) Out of plane lattice parameter for PCO films measured in-situ at 750oC and the lattice parameter, ao, of the bulk. (b) Out-of-plane expansion for PCO films measured in-situ at room temperature with 0% strain at 0.13 atm. of O2...............................................................57 Figure 3.3 MOSS results for the PCO27w film cycled at 750oC in indicated reducing and oxidizing atmospheres, demonstrating reversible redox behavior..........................................................60 Figure 3.4 (a) Change in stress for the PCO films with changing pO2 showing greater change in stress with decreasing grain size. Each data set is defined with zero change in stress at 0.13 atm. of O2. The symbols represent the measured values and the solid lines represent the corresponding polynomial fits. (b) Change in stress for PCO72w thin film with changing pO2 relative to that in 100 Torr O2 determined experimentally. The solid, dashed and short dashed line shows the predicted stress obtained from the defect equilibria model using E = 174 GPa, = 0.33 and c = 0.064 (for solid line); E = 200 GPa, = 0.33 and c = 0.064 (for dashed line); and E = 174 GPa, = 0.33 and c = 0.084 (for short dashed line), respectively..............................................................................................................................61 Figure 3.5 Change in in-plane stress plotted against change out-of-plane strain plots for PCO films of avg. grain size of (a) 27 nm and (b) 72 nm. Thec and z values were obtained by interpolating the HTMOSS and HTXRD data at respective pO 2’s. The filled symbols represent the interpolated data and the solid lines represent linear fits (fixing the intercept at 0) to the plotted symbols.........................................................................................................64 Figure 3.6 a) Schematic of the grain structure considered for the brick layer model. For simplicity, the grains are considered as cubes of length L, b) Grain intersection showing the grain boundary (GB) region of length b and grains of size L, c) An individual grain of length L showing the three orthogonal orientations of the grain boundaries namely b1 (lying along the YZ plane), b2 (lying along the XZ plane and b3 (lying along the XY plane)...........................................66 Figure 3.7 (a) fgb/ fbulk vs. the inverse of the grain size (1/L) plots at pO2 =10-3 atm. (b) fgb/ fbulk vs. the log(pO2) for the three PCO films and (c) fgb/ fbulk vs. fbulk for the three PCO films and that for undoped ceria. The plots were generated by applying the analytical solution to the brick layer model (discussed in the Appendix A3) to the MOSS data collected at 750oC............................................................................................................................ ...........69 Figure 3.8 Schematic of the grain structure considered for the simplified 1-D model. The model assumes the grains to have a columnar structure of height, hf (thickness of the film) and width, L (grain size)................................................................................................................74 Figure 3.9 Comparison of fgb/fbulk values for PCO72 obtained using the simplified 1-D model (as discussed above) and that obtained using the 3-D brick layer model at 750oC and at different pO2s. The values are obtained for b =1 nm.............................................................................76 Figure 3.10 Change in stress as a function of average grain sizes for (a) undoped ceria (at 515 oC, pO2 = 4.27×10-30 atm. and  = 0.0095) and PCO (at 750oC, pO2 = 10-5 atm. and  = 0.018) and (b) the undoped ceria and 25% Gd doped ceria films (at 515 oC, and pO2= 4.27×10-30 atm.). Each data set is defined with zero change in stress at 0.13 atm. of O 2...................................79 xvi Figure 4.1 Schematics of the Multi-beam Optical Stress Sensor (MOSS) set-up and the electrochemical cell (cross section). Note that the reflecting surface (i.e. substrate) is completely submerged into the electrolyte i.e. the beaker cell is filled with liquid electrolyte. Beaker cell assembly and MOSS measurements were performed in an Ar filled glove box. Also note that the refraction of the laser beams (for both incident/reflected), occurring before and after passing the optical window, is also shown in the schematic................................................................91 Figure 4.2 A representative SEM image of the surface of a pristine LMO film......................................95 Figure 4.3 Representative (a) XRD pattern (also showing the background from the annealed platinum coated quartz wafer) and (b) Raman spectra of a pristine LMO film on Pt/Ti/quartz substrate...................................................................................................................................96 Figure 4.4 (a) Charge-discharge profiles and (b) accompanying stress evolution of a ~150 nm thick LMO film cycled in the 3.5-4.3 V (vs. Li/Li+) range with a constant current density of 2.5 µA/cm2. For clarity an expanded view of the first cycle is shown in panel (c). dQ/dV vs. potential plots for the first three cycles derived from the galvanostatic charge discharge profiles in panel (a) are shown as an inset in panel (c)...........................................................99 Figure 4.5 Charge/discharge profiles and accompanying stress evolution (a) for a pristine LMO film and (b) for a reannealed LMO film. Both tests were performed in the 3.5-4.3 V (vs. Li/Li+) range with a constant current density of 2.5 µA/cm2. See text for details............................101 Figure 4.6 SEM image of cycled LMO film (a) OCV= 3.5 V (after 10 cycles in 3.5- 4.3 V range at 2.5 A/cm2) and (b) OCV= 4.5 V (after 10 cycles in 3.5- 4.3 V range and then charged to 4.5 V at 2.5 A/cm2). In contrast to the study by Malav et al., no apparent fracture/micro-cracks are visible for the cycled LMO films in this work................................................................105 Figure 4.7 Mn 2p XPS spectra of LMO films at different charge state (a) pristine (Sample A), (b) discharged at the end of two cycles i.e. run 1 (Sample B) and (c) reannealed sample B......110 Figure 5.1 Schematic showing the details of the film fabrication processes..........................................120 Figure 5.2 Representative XRD measurement (also showing the background from the annealed Al coated quartz substrate) of the V2O5 film on Au and Al.......................................................124 Figure 5.3 A representative SEM image of the surface of the pristine V 2O5 films on (a) Al and (b) Au..........................................................................................................................................125 Figure 5.4 Lattice fringe image confirming the crystallinity of the pristine V 2O5 films........................125 Figure 5.5 Charge-discharge profile and accompanying stress evolution for as-deposited amorphous VOx films (no annealing). Note that the plot shows the 31 st and 32nd cycle.........................127 Figure 5.6 In-situ voltage and stress measurements for crystalline a) V2O5 film on Al (cycled galvanostatically against Li metal in 4-1.5 V range) and b) V2O5 film on Au current collectors (cycled galvanostatically against Li metal in the 4-2V range)............................130 Figure 5.7 A typical current response of a V2O5 film on Al at constant voltage holds at 4, 3 and 2 V against Li metal.....................................................................................................................132 Figure 5.8 Post cycling XRD measurements of a) V2O5 film on Al and b) V2O5 film on Au cycled potentiostatically with voltage holds at 4, 3 and 2 V............................................................134 xvii Figure 5.9 Voltage-capacity curves for a) V2O5 film on Al and b) V2O5 film on Au cycled galvanostatically between 4-2 V...........................................................................................135 Figure 5.10 SEM images comparing the top surfaces of the V2O5 films on (a) Al and (b) Au after 3 potentiostatic charge-discharge cycles..................................................................................136 Figure 5.11 Schematic showing (a) the representative phase transformation (from phase p  phase q) upon lithiation of a material, and (b) graphical representation of the free energy curves of two phases, p and q with (solid lines) and without (dashed lines) strain energy contributions..........................................................................................................................139 Figure 5.12 A graphical representation of the free energy curves of V 2O5 film on Al (solid line) and Au (long dash dot line) for two phases, p and q with and without (dashed lines) strain energy contributions..........................................................................................................................145 Figure A.1.1 MOSS measurement of a PCO film (avg. grain size of 72 nm) heated from room temperature (25oC) to (a) 750oC and (b) 800oC. Note that the room temperature stress is taken as the reference stress state and so the change in stress at room temperature in the plots shown in (a) and (b) has a value of zero MPa......................................................................................159 Figure A.2.1 In-situ stress measurements for the PCO film on sapphire substrate cycled at 800 oC in indicated reducing and oxidizing atmospheres. At low pO 2, the film shows a stress reversal during reduction....................................................................................................................163 Figure A.2.2 pO2 dependence of the onset of the stress reversal during reduction cycle for a PCO film on sapphire substrate at (a) 750oC, (b) 775oC and (c) 800oC.....................................................166 Figure B.1.1 MOSS measurement of an amorphous alumina film on sapphire substrate heated from room temperature (25oC) to (a) 420oC, (b) 480oC and (c) 600oC. Note that the stress change during cooling (cooling) is used to calculate CTE values of the films at any given temperature............................................................................................................................178 Figure B.1.2 MOSS measurement of an amorphous alumina film on YSZ substrate heated from room temperature (25oC) to (a) 420oC, (b) 480oC (c) measurement repeated at 480oC, (d) 600oC and (e) measurement repeated at 600oC. Note that the stress change during cooling (cooling) is used to calculate CTE values of the films at any given temperature. Also, the stress relaxations during the initial dwell cycles are absent when the measurements are repeated at a particular temperature ((c) and (e))....................................................................................180 Figure B.1.3 CTE values plotted against the annealing temperatures for amorphous alumina films deposited on (a) sapphire and (b) YSZ..................................................................................182 Figure C.1.1 (a) Charge-discharge profile of a 120 nm thick LMO film cycled between 3.5-4.3 V (vs. Li/Li+). (b) First delithiation cycle and the corresponding AFM scan numbers for the LMO film shown in panel (a). Note that the shaded region corresponds to the scan numbers shown in Figure C.1.2.......................................................................................................................187 Figure C.1.2 AFM topographs of a LMO film during the first delithiation cycle at (a) Scan No. 0, (b) Scan No. 5, (c) Scan No. 10 and (d) Scan No. 15. The scan numbers are in accordance to the ones shown in Figure C.1.1(b). Note that scan numbers 5, 10 and 15 are the voltage regions where the anomalous drop is observed............................................................................................188 xviii Figure C.2.1 Sample IDs for the XPS measurements superimposed to the corresponding charged state on a typical charge/discharge profile of the LMO film. Note that, the XPS measurements were conducted on separate LMO samples that were separately charged or discharged to different OCVs.....................................................................................................................................192 Figure C.2.2 Mn2p XPS spectra of LMO films at different charge state (a) pristine (Sample A), (b) charged to 3.9 V (sample B), (c) charged to 4.16 V (sample C), (d) charged to 4.3 V (sample D), (e) discharged to 3.6 V at the end of two cycles (sample E) and (f) re-annealed sample E (Sample F). The vertical line in the plot is shown to provide a visual guide in order to observe the relative change in the Mn2p3/2 peak shape and position for various LMO samples..................................................................................................................................193 Figure C.2.3 Fitted Mn2p3/2 XPS spectra of LMO films at different charge state (a) pristine (Sample A), (b) charged to 3.9 V (sample B), (c) charged to 4.16 V (sample C), (d) charged to 4.3 V (sample D), (e) discharged to 3.6 V at the end of two cycles (sample E) and (f) re-annealed sample E (Sample F). The peak fits are obtained using the fitting protocols as described in the text...................................................................................................................................201 Figure C.3.1 LMO sample placed in a quartz container. It was then loaded into the HTMOSS system for the re-annealing measurements.............................................................................................202 Figure C.3.2 (a) Stress evolution in a pristine LMO sample measured at 750oC and at 0.13 atm. of O2. (b) and (c) shows the corresponding XRD and Raman measurements respectively of the sample in (a)......................................................................................................................................204 Figure C.3.3 (a) Stress evolution and (b) the corresponding charge/discharge for a LMO film cycled using the experimental scheme as shown in figure 4.5. For clarity, the stress evolution during the re-annealing step of the LMO film in (a) is shown in (c). The inset shows an expanded view of the stress evolution during the heating and dwelling cycles.............................................206 Figure C.3.4 Stress evolution and the corresponding charge/discharge for LMO films cycled using the experimental scheme as shown in figure 4.5 and re-annealed at 750oC and at (a) in air, (b) pO2= 10-2 atm., (c) pO2= 10-3 atm., (d) pO2= 10-4 atm., (e) pO2~ 10-6 atm. (in pure Argon gas)........................................................................................................................................211 Figure C.3.5 XRD measurements performed on the LMO films (a) pristine and those that were re- annealed at 750oC and at (b) in air, (c) pO2= 10-2 atm., (d) pO2= 10-3 atm., (e) pO2= 10-4 atm., (f) pO2~ 10-6 atm. (in pure Argon gas). Note that the substrates used for sample d and the other samples were from different batches and hence XRD plots corresponding to annealed platinized substrates from two different batches (new and old) are also shown in the plot............................................................................................................................. ............213 Figure C.3.6 LMO samples re-annealed at 750oC and (a) in air and (b) in pure Ar (pO 2~ 10-6 atm.). These images were taken after re-annealing (before run 2). The samples that were re-annealed at pO2 < 10-2 atm. all showed similar color changes which indicate towards possible irreversible phase transformations taking place in LMO during the re-annealing step...........................214 Figure C.3.7 Open circuit potentials (vs. Li/Li+) as measured before run 2 of the LMO films re-annealed at different pO2s. The samples re-annealed at a pO2 of 10-3, 10-4 and 10-6 atm., undergo phase transformation and therefore have lower OCV values before run 2.....................................215 Figure C.3.8 heating and cooling values measured for the cycled samples re-annealed at different pO2s. The dashed line shows the measured thermal stress values for LMO-quartz system at 750oC (1.23 GPa).............................................................................................................................217 xix Figure C.3.9 (a) Stress evolution during the control experiment as described in the text and (b) the XRD measurement carried out on the sample after the control experiment. Stages I-X in figure (a) corresponds to the experimental conditions tabulated in Table C3.1...................................219 Figure C.4.1 (a) Stress evolution and (b) the corresponding charge-discharge profiles of a ~100 nm thick LMO film cycled in the 4.3-2 V (vs. Li/Li+) range with a constant current density of 25 µA/cm2. The XRD measurement of the LMO sample before and after the electrochemical cycling in (a) is shown in (c).................................................................................................222 Figure C.4.2 (a) Stress evolution and (b) the corresponding charge-discharge profiles for sample I cycled as per the experimental protocol described above and with a constant current density of 2.5 µA/cm2..................................................................................................................................224 Figure C.4.3 (a) Stress evolution and (b) the corresponding charge-discharge profiles for sample II cycled as per the experimental protocol described above and with a constant current density of 2.5 µA/cm2..................................................................................................................................225 Figure C.5.1 (a) Schematic of the LMO films used for the measurements. (b) A typical sinusoidal voltage input and the corresponding stress response of the LMO film in the voltage range of 4.2-3.6 V and at a frequency of 10-3 Hz............................................................................................227 Figure C.5.2 LMO films electrochemically cycled in the voltage range of 4.1-3.5 V vs. Li/Li+ at a frequency of (a) 10-1, (b) 5×10-2, (c) 10-2, (d) 5×10-3, (e) 10-3, (f) 5×10-4 and (g) 10-4 Hz. The sample was cycled at each frequency for more than 10 cycles.............................................229 Figure C.5.3 LMO films electrochemically cycled in the voltage range of 4.2-3.6 V vs. Li/Li+ at a frequency of (a) 10-2, (b) 5×10-3, (c) 10-3, (d) 5×10-4 and (e) 10-4 Hz. The sample was cycled at each frequency for more than 10 cycles. At frequencies < 10 -2 Hz, the MOSS data was very noisy and so, is not shown here.....................................................................................230 Figure C.5.4 LMO films electrochemically cycled in the voltage range of 4.3-3.7 V vs. Li/Li+ at a frequency of (a) 10-1, (b) 5×10-2, (c) 10-2, (d) 5×10-3, (e) 10-3, (f) 5×10-4 and (g) 10-4 Hz. The sample was cycled at each frequency for more than 10 cycles.............................................232 Figure D.1.1 Schematic of the SiC/SiO2 sample used for the HTMOSS measurement. The laser spots during the MOSS measurement were reflected from the polished (un-oxidized) side.........235 Figure D.1.2 Curvature of the SiC/SiO2 sample as measured by MOSS technique during the high temperature oxidation. A flat mirror was used as reference for the measurement. The laser spots during the MOSS measurement were reflected from the polished (un-oxidized) side........................................................................................................................................236 Figure E.1.1 (a) Free energy curves for the two phases p =  and q = as calculated using the formulation 𝑝 described in the text, for the case when 𝜀𝑜 = 0.008, = 800000 and 𝑉𝑚𝐿𝑖 = 3.5 mL/mole. For clarity, an expanded view of the free energy curve for phase q showing the shift in the 𝑞 ∆𝐺𝑡𝑜𝑡𝑎𝑙 due to stress contributions is shown in (b)...............................................................246 Figure E.1.2 equilibrium voltage plateau position plotted against the initial stress state in the film calculated using the formulation for the case when = 800000 and 𝑉𝑚𝐿𝑖 = 3.5mL/mole......247 xx Abstract Abstract of “In-situ Characterization of Composition Induced Stresses in Thin Film Oxides: Application to Solid Oxide Fuel Cell and Li-ion Battery Electrodes” by Jay Sheth, Ph.D., Brown University, May 2017. Energy storage and conversion systems rely heavily on the exchange of ions, be it Li-ion batteries (LIBs), which rely on Li+ ions or solid oxide fuel cells (SOFCs) that rely on O2- ions. Exchange of these ions often results in large volumetric changes of the host material, and in constrained geometries, such strains lead to stress build up in the material commonly referred to as compositional stresses. Additionally, heat treatments employed during the growth and fabrication of these systems could also contribute to the stress build up in the material. Given the brittle nature of the oxide ceramic electrodes commonly used in SOFCs and LIBs, such stress build up can lead to mechanical instabilities like fracture or micro-cracks which results in the performance degradation of the device over time, and in extreme cases it could ultimately cause failure of the device. In this dissertation, we will discuss in-situ evolution of the compositional stresses, obtained by wafer curvature measurements, of three material systems; namely 10% Praseodymium doped ceria (PCO, a typical cathode used in intermediate temperature SOFC), spinel Li1+xMn2O4 (LMO) and V2O5 (both LMO and V2O5 are typical cathodes used in LIB), in thin film configuration. xxi The first half of the dissertation discusses in-situ wafer curvature along with high temperature x-ray diffraction (HTXRD) measurements that were employed to measure stresses and strains, respectively on the PCO films during oxidation-reduction cycling and over the pO2 range of 10-1-10-5 atm. at 750oC. This preliminary study is then followed by a discussion on the dependence of these stress and strain on the average grain size of the PCO films. The latter half of the dissertation discusses the in-situ stress evolution in thin films of LMO during electrochemical cycling in a specially designed beaker cell in the 3.5–4.3 V (vs. Li/Li+) voltage range. This is followed by a study that employs thin V2O5 films as model cathode material for LIB, to systematically investigate relationships between stress (intrinsic and extrinsic), phase transformations, and degradation of the cathode. xxii CHAPTER 1 INTRODUCTION 1.1 General Background Over the past decades, a significant majority of the world’s energy consumption is derived from the combustion of fossil fuels.1 As a result, series of factors including an increase in the demand for oil, the depletion of non-renewable resources, the dependency on politically unstable oil producing countries and ever-increasing CO2 emissions leading to climate change has put the present energy economy based on fossil fuels at serious risk. As such, a lot of interest now lies in developing and moving towards a cleaner, sustainable and environmental friendly form of energy. It is now a general consensus that the issue of CO2 emissions and the consequent air pollution could be solved by employing clean energy conversion devices such as, fuel cells, batteries, etc. Many countries and corporations have taken several initiatives in this direction. For example, president Barack Obama announced the Clean Power Plan in 2015 to reduce greenhouse gas emissions from electric power generation, while Chinese president Xi Jinping announced economic incentives to reduce emissions.2, 3 Germany’s federal council has passed a resolution calling for a ban on combustion engine cars by 2030, thereby promoting battery and/or fuel cell powered cars.4 The U.S. Navy is evaluating the use of solid oxide fuel cell (SOFC) power for propulsion and ship power of unmanned 1 submarine applications. SOFCs virtual lack of emissions, high efficiency, and quiet operating nature are well suited for stealthy operations.5 DARPA is evaluating SOFC based systems for unmanned airborne applications.6 With significant technological advances, there is a great need for electrical energy storage, not only for portable electronic devices, but also for transportation and generation of stationary power and for the effective commercialization of renewable resources such as solar and wind power. Figure 1.1 shows a Ragone plot which compares the energy and power densities of different energy storage and conversion devices. This plot suggests that fuel cells and batteries can be considered to be high-energy systems, with batteries also having moderate power densities. Indeed, batteries with thin film electrodes exhibit power densities similar to those of supercapacitors. As such, batteries and fuel cell research has received much attention in recent years. Figure.1.1. Ragone plot showing the specific energy density vs. specific power density for various energy storage and conversion devices.7 2 Both fuel cells and batteries are classified into several types based on their operating conditions and applications. For the purpose of this dissertation, we will only talk about the solid oxide fuel cell (SOFC) and lithium-ion battery (LIB) technologies. SOFCs and LIBs work on similar principles. Both systems employ two electrodes, namely an anode and a cathode where the electrical energy is generated by conversion of chemical energy via reduction-oxidation reactions. As reactions at the anode usually take place at lower electrode potentials than at the cathode, the terms negative and positive electrode are used. The more negative electrode is designated the anode, whereas the cathode is the more positive one. The difference between batteries and fuel cells is related to the locations of energy storage and conversion and is discussed in section 1.2 and 1.3. Typical SOFCs operate in the temperature range of 800–1000°C, typified by developers such as Siemens Westinghouse and Rolls-Royce.8 High operating temperatures are advantageous as they enhance the electrochemical reaction kinetics. This reduces the losses due to irreversible side reactions and ohmic resistances. Furthermore, the high operating temperature facilitates their use in combined heat and power applications or efficiently coupled with gas turbines.9 Therefore, high temperature SOFCs generally provide the highest conversion efficiency among the various types of fuel cells, while reducing the catalytic activity requirements of the electrode materials. 10 In addition, at high temperatures, it is easier to break C-C bonds and thus some hydrocarbons can be directly utilized at the anode providing flexibility of fuel choices; from hydrogen to hydrocarbons (especially natural gas).11 3 Over the years, batteries have evolved from lead-acid through nickel–cadmium and nickel–metal hydride (NiMH) to lithium-ion. NiMH batteries were the initial workhorse for electronic devices such as computers and cell phones, but they have almost been completely displaced from that market by lithium-ion because of the latter’s higher energy storage capability; a typical Li-ion battery can store approximately 200 Wh of energy in 1 kg of battery, which is almost seven times more energy compared to the automotive lead-acid battery (30 Wh kg−1).12 This thesis is organized in such a way that the introductory sections of each chapter will provide the reader with sufficient background information and references to the literature for the material system discussed in the respective chapters. Therefore, in order to avoid redundancy, additional introductory remarks for each specific material system have been omitted here. 1.2 Basics of SOFCs A fuel cell using a solid metal oxide electrolyte that is conductive to oxygen ions was first reported by Baur and Preis in 1937.13 This is now called a solid oxide fuel cell (SOFC). In a SOFC, the energy storage and conversion are locally separated i.e., the anode and cathode serves only as the charge-transfer media and the active masses undergoing the redox reaction are delivered from outside the cell, either from the environment, for example, oxygen from air, or from a tank, for example, fuels such as 4 hydrogen and hydrocarbons. The electrolyte serves as a barrier to gas diffusion, but allows the ions to migrate across it. Figure 1.2 shows the fundamental building block of a SOFC. It consists of an anode and a cathode that is separated by an electrolyte. Redox reactions occur at the anode and cathode producing ions that traverse through the electrolyte, while electrons travel through the external load, thereby generating electricity. Reduction of oxygen into oxygen ions occurs at the cathode. These ions then diffuse through the solid oxide electrolyte to the anode where they oxidize the fuel. In this reaction, a water byproduct is generated along with two electrons. These electrons then flow through an external circuit where they can do work. The cycle then repeats as those electrons enter the cathode material again. Figure.1.2. Schematic showing the working of a SOFC.14 The most common material used as an anode is a cermet made up of nickel mixed with the ceramic material that is used for the electrolyte in that particular cell, typically yttria stabilized zirconia (YSZ) nanomaterial-based catalysts. The electrolyte is a dense 5 layer of ceramic with poor electronic conductivity (to prevent leakage currents) but has a superior ionic conductivity so that it conducts oxygen ions. The high operating temperatures of SOFCs allow the kinetics of oxygen ion transport to be sufficient for good performance. Popular electrolyte materials include YSZ, scandia stabilized zirconia (ScSZ) and gadolinium doped ceria (GDC). At present, the commercial SOFC cathode choice is lanthanum strontium manganite (LSM) because of its compatibility with doped zirconia electrolytes. Unfortunately, LSM is a poor ionic conductor, which limits the redox reaction sites to the triple phase boundary (TPB) where the electrolyte, air and electrode meet. Also, its performance degrades as the operating temperature is lowered below 800°C. This limitation of availability of the electrochemical active reaction site could be resolved by using cathode materials that conduct both electrons and ions. As such, mixed ionic and electronic conducting (MIEC) ceramics, such as lanthanum strontium cobalt ferrite (LSCF; perovskite structure) and praseodymium doped ceria (PCO; fluorite structure) are being researched for use in intermediate temperature SOFCs. MIEC ceramics are more active and can make up for the increase in the activation energy of the reaction at low temperatures. Based on the fuel type, the half cell reactions are as follows: At Anode: 𝐻2 + 𝑂2− ↔ 𝐻2 𝑂 + 2𝑒 − (1.1) 𝐶𝑂 + 𝑂2− ↔ 𝐶𝑂2 + 2𝑒 − (1.2) 𝐶𝐻4 + 4𝑂2− ↔ 2𝐻2 𝑂 + 𝐶𝑂2 + 8𝑒 − (1.3) At Cathode: 𝑂2 + 4𝑒 − ↔ 2𝑂2− (1.4) 6 1.3 Basics of LIBs Unlike SOFCs, batteries are closed systems i.e., the anode and cathode not only serve as the charge-transfer medium but also takes an active part in the reduction- oxidation reaction. In other words, energy storage and conversion occur in the same compartment. Figure 1.3 shows the fundamental building block of a Li-ion battery. During charging, the positive electrode gives up some of its lithium ions. These ions move through the electrolyte to the negative electrode. In the case of a graphitic carbon anode, these ions sit between the layered graphene sheets; if the anode is made of Si or Sn, the intercalated Li ions form solid solution alloys with the active material. The battery takes in and stores energy during this process. When the battery is discharging, the lithium ions move back across the electrolyte to the positive electrode, producing the energy that powers the external device connected to the battery. In both cases, electrons flow through the outer circuit. The movement of ions (through the electrolyte) and electrons (around the external circuit, in the opposite direction) are interconnected processes, and if one stops so does the other. If ions stop moving through the electrolyte because the battery completely discharges, electrons can't move through the outer circuit either and vice versa. Conventional Li-ion batteries use graphite as the negative electrode and a transition metal oxide as the positive electrode in the form of LiMO2, where M= Mn, Co, Ni. The half reaction for charge and discharge process in this case can be given as follows: 7 At Anode: 𝑥𝐿𝑖 + + 𝑥𝑒 − + 𝐶6 ↔ 𝐿𝑖𝑥 𝐶6 (1.5) At Cathode: 𝐿𝑖𝑀𝑂2 ↔ 𝐿𝑖(1−𝑥) 𝑀𝑂2 + 𝑥𝑒 − + 𝑥𝐿𝑖 + (1.6) Figure.1.3. Schematic showing the working of a LIB.15 1.4 Motivation Of the several issues that SOFC and LIB technologies have, one key problem is mechanical instability. As discussed above, both these technologies rely heavily on the intake and release of large quantities of ions; Li-ion batteries rely on Li+ ions and SOFCs rely on O2- ions. Exchange of these ions results in significant volume changes, and in constrained geometries (which these systems usually are in), these strains lead to stress build up in the systems, termed as “compositional stresses” in the literature. Moreover, heat treatments employed during the growth and fabrication of the electrodes/solid electrolytes could also lead to a significant stress build up in the material. Given the brittle nature of the oxide ceramics used, these stresses can lead to mechanical instabilities in the form of micro-cracks or fracture, which can lead to loss of contact with the conducting medium in the electrode resulting in poor performance of the device over 8 time. In extreme cases, such mechanical instabilities could lead to complete failure of the device. Figure 1.4 shows some examples of cycling induced mechanical degradation of the electrode/solid electrolyte materials used in SOFC and LIB. Figure.1.4. Electrochemical cycling induced mechanical degradation of the electrode/solid electrolyte materials used in SOFCs and LIBs.16-21 Strained/stressed material systems are not necessarily unfavorable. It has been shown both experimentally and computationally that strains in the oxide thin films can be tuned to affect properties like ionic conductivities, reaction rate kinetics, diffusivities of the point defects, etc.22, 23 Therefore, it is essential to understand the sources and extent of the stresses that are generated in these oxide materials both before and during the operation of a battery or a fuel cell. To date, volume change effects and their impact on 9 film stress have received limited attention, due to the dual difficulties associated with characterizing composition changes in thin films and monitoring the corresponding electrical-chemical-mechanical changes in the film, in-situ, under typical operating conditions. This thesis primarily discusses the in-situ evolution of the compositional stresses, obtained by wafer curvature measurements, of three material systems; 10% Praseodymium doped ceria (PCO, a cathode used in intermediate temperature SOFCs), spinel Li1+xMn2O4 (LMO), and V2O5 (LMO and V2O5 are cathodes used in LIBs), in thin film configuration. Thin film configuration facilitates easy data interpretation. It allows for the sample to have high surface area with a controlled morphology, which is ideal for studying stress and strain evolution. Also, studying these materials in thin film form eliminates the need to add binders, or conductive medium such as carbon; usually added in the bulk electrodes to hold the particles together and to collect electrons from the reaction sites, respectively. As such, the analysis of stress and strain measurements become much simpler since the contributions from the impurities and side reactions are negligible. 1.5 Thesis Organization The work presented in this thesis is divided into six chapters. Chapter 2 discusses the in-situ stress and strain induced by large deviations from oxygen stoichiometry in thin films of Pr0.1Ce0.9O2- (PCO), supported on yttria stabilized zirconia (YSZ) and sapphire 10 substrates. Chapter 3 discusses the dependence of the stress and strain on the average grain size of PCO thin films. We also employ an analytical model here, calculations from which support our experimental findings. Chapter 4 discusses the in-situ stress evolution in spinel LMO thin films during electrochemical cycling. This material shows a rather unique stress reversal (anomalous drop) during the first delithiation cycle. By means of various experimental techniques, this chapter explores the possible cause for such an anomalous drop. In Chapter 5, thin V2O5 films are employed as a model cathode material, to systematically investigate relationships between stress, phase transformations, and electrode degradation. To directly probe the impact of stress, processing conditions were controlled to vary the initial stress state over a wide range (while maintaining similar grain structures). In this chapter, we also compare our experimental data to a thermodynamic model that takes into account the impact of initial and lithiation induced stresses. Chapter 6 draws the main conclusions from various thin films studies as discussed in Chapters 2-5 and also highlights possible future work. Several additional/preliminary studies have been included in the appendices to this thesis. 11 1.6 References 1. BP, Statistical Review of World Energy 2010. 2. United States Environmental Protection Agency, FACT SHEET: Overview of the Clean Power Plan, Link: http://www2.epa.gov/cleanpowerplan/fact-sheet-overview-clean- power-plan. 3. A. Powell, Political climate, changed, Harvard Gazette, (2015). Link: http://news.harvard.edu/gazette/story/2015/09/political-climate-changed/ 4. S. Khan, Germany pushes to ban petrol-fueled cars within next 20 years, independent.co.uk, (2016). Link: http://www.independent.co.uk/news/world/europe/germany-petrol-car-ban-no- combustion-diesel-vehicles-2030-a7354281.html 5. GM and U.S. Navy collaborating on fuel cell-powered underwater unmanned vehicles, GM corporate newsroom, (2016). Link:http://media.gm.com/media/us/en/gm/home.detail.html/content/Pages/news/us/en/2 016/jun/0623-gm-us-navy.html 6. Versa Power Wins Boeing/DARPA Contract to Supply Continuous Energy Storage and Generation Technology for Ultra-Long Endurance Aircraft, Business Wire (2010). Link: http://www.businesswire.com/news/home/20101130005564/en/Versa-Power-Wins- BoeingDARPA-Contract-Supply-Continuous 7. M. S. Whittingham, MRS Bulletin, 33, 411 (2008). 8. D. J. L. Brett, A. Atkinson, N. P. Brandon and S. J. Skinner, Chemical Society Reviews, 37, 1568 (2008). 9. J. Richter, P. Holtappels, T. Graule, T. Nakamura and L. J. Gauckler, Monatshefte Fur Chemie, 140, 985 (2009). 10. N. Q. Minh, Journal of the American Ceramic Society, 76, 563 (1993). 11. M. Mogensen and K. Kammer, Annual Review of Materials Research, 33, 321 (2003). 12. X. Xu, C. Wang, G. Liao, C. P. Yeh and W. Stark, in 41st North American Power Symposium, p. 1 (2009). 13. E. Baur and H. Preis, Zeitschrift für Elektrochemie und angewandte physikalische Chemie, 43, 727 (1937). 14. Getting electricity from solid oxide fuel cell, in, Electrical engineering portal, (2012). Link: http://electrical-engineering-portal.com/getting-electricity-from-solid-oxide-fuel- cell 12 15. P. G. Bruce, B. Scrosati and J. M. Tarascon, Angewandte Chemie-International Edition, 47, 2930 (2008). 16. L. Y. Beaulieu, K. W. Eberman, R. L. Turner, L. J. Krause and J. R. Dahn, Electrochemical and Solid State Letters, 4, A137 (2001). 17. D. Y. Wang, X. D. Wu, Z. X. Wang and L. Q. Chen, Journal of Power Sources, 140, 125 (2005). 18. H. F. Wang, Y. I. Jang, B. Y. Huang, D. R. Sadoway and Y. T. Chiang, Journal of the Electrochemical Society, 146, 473 (1999). 19. T. Hashida, K. Sato, Y. Takeyama, T. Kawada and J. Mizusaki, ECS Transactions, 25 (2), 1565 (2009). 20. S. Patel, Journal of Fuel Science and Technology, 9 (2012). 21. J. Malzbender and R. W. Steinbrech, Journal of Power Sources, 173, 60 (2007). 22. A. Kushima and B. Yildiz, ECS Transactions, 25 (2), 1599 (2009). 23. N. Schichtel, C. Korte, D. Hesse and J. Janek, Physical Chemistry Chemical Physics, 11, 3043 (2009). 13 CHAPTER 2 COUPLING OF STRAIN, STRESS, AND OXYGEN NON-STOICHIOMETRY IN THIN FILM Pr0.1Ce0.9O2-δ 2.1 Introduction The growth and optimization of thin films have long been essential hallmarks of the microelectronics revolution, with film properties ranging from insulating/dielectric and semiconducting to metallic. In recent decades, the functionality and complexity of electronic devices have continued to grow at a rapid pace and have extended into the realms of micro-electromechanical (MEMS) devices, micro-batteries, micro-fuel cells, chemical and biological sensors, etc., thereby requiring the addition of thin film materials with new and distinctive properties, sometimes operating at temperatures considerably above ambient. This, in particular, has resulted in the inclusion of metal oxides with varied properties including ferroelectric,1 piezoelectric,2 high K dielectric,3 electro-optic,4 semiconducting,5 metallic6 and ionic conducting properties7. Metal oxides, particularly those with transition metal or rare earth ions that can exist in multiple oxidation states, exhibit considerable ranges of cation or oxygen nonstoichiometry δ (e.g. SrTi 1-xFexO3-δ8– 10 or Cu1-δO11) that can have a major impact on their electrical, optical and magnetic properties.8,12–14 Much less appreciated are the corresponding changes in lattice parameter 14 that accompany these excursions in δ, typically leading to dilation upon reduction and shrinkage upon oxidation.15 Such, so called chemical expansion in materials is quantified by a chemical coefficient of expansion (αc) which relates the chemically induced strain (εc) with the non-stoichiometry change (Δδ) by Equation 2.1. εc = αc Δδ (2.1) This definition utilizes similar terminology as the much better known thermal coefficient of expansion, relating the strain induced in a material to the change in temperature. Isothermal stoichiometry changes are routine in the operation of electrochemical devices such as thin film batteries, fuel cells, and chemical sensors, and can be expected to exhibit constrained expansion due to substrate clamping, with potential for cracking and delamination.16,17 As briefly discussed in Chapter 1, strain induced in films does not necessarily lead to degradation of properties, but can be used to tune and optimize certain properties, such as electron mobility in strained films or superlattices.18 As a consequence, it is essential to understand the sources and extent of expansion to be expected in a given material under defined operating conditions. To complicate the matter, transitioning from micro- to nano-scale morphology can not only lead to dramatic changes in film electrical and optical properties, but also mechanical properties, such as film stress and strain. This can come about, for example, from space charge effects associated with the creation of a significantly greater fraction of interfaces/grain boundaries, with associated accumulation or depletion of charged defects.19,20 In metal oxide thin films, in contrast to the more traditional covalent semiconductors such as Si or GaAs, such space charge regions will exhibit the 15 accumulation or depletion of ionic defects, such as vacancies or interstitials, in addition to electronic carriers, thus leading to potential spatial variations in strain across the film.20 To date, chemical expansion effects and their impact on film strain have received only very limited attention, due to the dual difficulties associated with characterizing nonstoichiometry in thin films and monitoring changes in the film, in-situ, under typical operating conditions. In the past couple of years, Prof. Harry L. Tuller’s research group at MIT has made important strides in developing and applying electrochemical and optical means for detecting changes in stoichiometry in oxide thin films, with a particular focus on the model fluorite-structured non-stoichiometric solid solution oxide (Pr,Ce)O2-δ (PCO)21,22 that readily forms vacancies under relatively oxidizing conditions (e.g., air) upon heating, due to the ease of reduction of the Pr ion.23–25 Furthermore, they have developed defect models for these PCO films, the energetics parameters of which differ from bulk defect equilibria, that enable us to correlate measured chemical expansion, upon the generation of Pr3+ ions and oxygen vacancies, during reduction.22 Specifically, the oxygen vacancy defect formation reaction for (Pr,Ce)O2-δ is described in terms of Kröger-Vink notation as in Equation 2.2: × 2PrCe + OO× ↔ 2PrCe ′ + VO∙∙ + 1/2O2 (𝑔) (2.2) in which lattice oxygen (O× O ) leaves the material to form doubly positively charged oxygen vacancies (VO∙∙ ) and reduced Pr ions sitting substitutionally on Ce sites (PrCe ′ ). The concentrations of the species in Equation 2.2 can be related to the enthalpy of reaction (Hr), temperature (T), Boltzmann constant (k), and a pre-exponential factor (Ko) 16 accounting for vibrational entropy, by Equation 2.3, where concentration is indicated by brackets. ' 2 1/2 PrCe VO∙∙ 𝑝O2 𝐻 × 2 = 𝐾0 exp − 𝑘𝑇𝑟 (2.3) PrCe O× O It is apparent from this equation that oxygen vacancy concentrations will depend on both temperature and the oxygen partial pressure of the environment. The oxygen non-stoichiometry described with equations 2.1-2.3 is typically evaluated in bulk materials. For example, values for the enthalpy of reaction, Hr, and the pre-exponential factor Ko can be found for the bulk in references [23] and [24]. In the new work reported here, we are primarily interested in evaluating how this non- stoichiometry leads to strain and stress in thin films (e.g., per equation 2.1, etc). Full consideration of thin film materials includes a wide range of microstructural complexity, with monocrystalline, polycrystalline, and amorphous structures along with a variety of possible substrate effects. Our work initially focused on polycrystalline films on sapphire where there is no clear crystallographic relationship with the substrate. This removes issues associated with epitaxy, such that the primary impact of the substrate is to constrain volume changes, which leads to in-plane stress in the film. Polycrystalline films grown on YSZ were also investigated, where local epitaxy between the film and substrate leads to important differences in the structure and stress-strain responses. In-situ wafer curvature and high temperature X-ray diffraction measurements are employed to measure stresses and strains in (Pr0.1Ce0.9)O2-δ thin films during oxidation-reduction cycling and over the pO2 range of 10-1-10-5 atm. at 750oC. In-situ optical transmission 17 measurements were also performed to explore thin film oxygen content of PCO films on insulating sapphire substrates (used for wafer curvature) as compared to previous chemical capacitance measurements of non-stoichiometry on ionically conducting yttria- stabilized zirconia (YSZ) substrates.22,26 Finally transmission electron microscopy studies were used to identify the structural relationships between the substrate and thin films. Combining these different measurements made it possible to relate the structure of these films to their mechanical response during redox cycling. 2.2 Experimental Film growth and thickness measurement Films were deposited using pulsed laser deposition (PLD). Films for optical transmission measurements and HTXRD were deposited on 1 x 1 square cm (0001) oriented sapphire (Al2O3) substrates. A film for wafer curvature measurement was deposited on a 2.5 cm diameter sapphire substrate. A film for optical transmission measurements was also deposited on a 1 x 1 square cm (001) oriented yttria-stabilized- zirconia (YSZ) substrate. Film growth has been described previously, a short description will be given here.27 A target of Pr0.1Ce0.9O2-δ was prepared by sintering pressed powders prepared by wet chemical reaction, followed by calcination. Deposition was carried out using a 248 nm KrF excimer laser (400 mJ/pulse at 8 Hz) in oxygen with 10 mTorr total pressure and an 854oC substrate heater temperature (approx. 725oC sample temperature). 18 Following deposition and prior to cooling, the oxygen pressure in the chamber was increased to approximately 6–7 Torr to facilitate more complete oxidation of the films. High temperature X-ray diffraction (HTXRD) In-situ diffraction was undertaken using a Bruker D8 Discover instrument with an Anton Paar HTK1100 thin film furnace. The diffractometer was equipped with a Lynxeye linear position-sensitive detector to allow collection scattered X-rays over an angular range of 2.5° 2θ, which enabled rapid measurements of the reciprocal space maps (RSMs) and single scans to measure the film lattice constants. The X-ray patterns were analyzed using Leptos from Bruker-AXS. Extensive testing was undertaken to evaluate sample position displacement during heating and cooling, by measuring RSMs and single scans through at least one substrate and film peak. The X-ray furnace was modified to reduce the dead space within the gas lines and the oxygen pressure was set using automated mass flow controllers mixing ultra-high purity N2 with pure oxygen. Furthermore, an automated gas flow-by system was built to allow equilibration of the gas mixture in the gas lines before entering the furnace sample chamber, thus facilitating rapid changes in the oxygen partial pressure. A zirconia oxygen sensor was mounted downstream of the diffraction furnace, and the pO2 was measured and recorded in intervals of two seconds. Measurements were all performed by heating the sample under the lowest pO2, and increasing the pO2 during the in-situ experiment. 19 Transmission electron microscopy (TEM) TEM analysis was performed on films grown on sapphire and YSZ following in- situ HTXRD. Specimens were prepared by standard lift-out techniques28 using an FEI Nova NanoLab200 SEM equipped with Ga+ focused ion beam. Film cross-sections were imaged using a JEOL 2010F TEM operating at 200 kV. Image data were analyzed using Gatan Digital Micrograph. High spatial resolution electron energy-loss spectroscopy was also performed using the same instrument operating in scanning TEM mode. The STEM focused probe size was less than 0.5 nm. Oxygen non-stoichiometry measured using optical transmission In-situ optical transmission measurements were performed on PCO thin films deposited both on sapphire and YSZ substrates to examine substrate dependence on defect concentration, if any. Measurements were performed following the experimental techniques outlined in our previous work, a short description is given here.21 A beam of 532 nm light was transmitted through the thin film and substrate, supported inside an atmosphere controlled quartz tube in a furnace. The transmitted intensity was measured using a photodetector and changes in source intensity were monitored and corrected for in the final data. The absorption coefficient for the thin film was calculated following the Beer-Lambert law for absorbing centers, in this case Pr4+ ,29 and related to oxygen content through defect chemical relationships and supported by complimentary electrochemical thin film characterization techniques.21,22 20 In-situ stress measurements The apparatus used to measure the real-time compositional stresses during redox cycling is described in detail in previous publications.30,31 A brief description is provided here. A multi-beam optical stress sensor (MOSS) provided in-situ measurements of the substrate curvature, . The average stress in the film, 〈〉, was then obtained with a modified form of the Stoney equation,30–32 as follows. M s hs2 h Mh    h    ( z )dz  [1  4 ] (2.4) 0 6 M s hs where, z is the dimension normal to the film surface, and h and M are the thickness and biaxial modulus of the substrate (subscript s) and the film (no subscript), respectively. To study compositional stresses, the films were subjected to cyclic annealing experiments in reducing and oxidizing atmospheres. The gas atmospheres used in the current work were obtained by a calibrated mixture of argon and oxygen. Pure oxygen was chosen as the oxidizing media, with the furnace chamber maintained at 100 Torr maximum pressure and continuously flowing gas. The switch from oxidizing to reducing media, or vice versa, was done by shutting off the gas supply, evacuating the furnace chamber to 0.03 Torr, and then opening the valves for the next gas to fill the chamber to 10 - 100 Torr. The time between switching from one media to another was less than one minute and was performed while monitoring changes in curvature. Each sample was subjected to at least one cycle consisting of oxidation, reduction, then oxidation to ensure reproducibility of compositional stresses. The magnitude of these reversible compositional stresses is then given by the difference in the steady state stress from a 21 reference stress, the latter defined as the stress measured at each temperature in the most oxidizing conditions, as shown by equation 2.5. ∆𝜎 = 𝜎 − 𝜎𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 (2.5) 2.3 Results Film structure and morphology For comparison with wafer curvature measurements, X-ray diffraction (XRD) was performed on PCO films deposited on the same substrate composition under the same conditions. Films on both sapphire and YSZ 1 cm2 substrates exhibited the cubic fluorite structure with a (001) texture (but also significant evidence for (111) orientation in the case of deposition on sapphire), as shown by Figure 2.1(a). Films on the larger sapphire substrates exhibited largely (111) orientation. X-ray reciprocal space mapping (RSM) provides information about the film microstructures and film relaxation. Two films on YSZ were interrogated via reciprocal space mapping (Figure 2.1 (b) and c) using the (113), (224), and (115) reflections, and the extent of film relaxation was 87 ± 2% (i.e. 87% of the difference in lattice parameter between YSZ (~5.139 Å) and PCO (~5.411 Å) is relieved). This indicates that the substrate does not clamp the film to match its lattice constant, instead the film relaxes to a large extent so that the lattice constant is closer to bulk PCO. The presence of a large density of misfit dislocations is necessary to achieve this extensive film relaxation. It is worth noting that both PCO and YSZ exhibit the fluorite structure, and as such the high degree of orientation with the substrate that is 22 found here is expected. The RSMs for the films on YSZ show broadening of the symmetric and asymmetric reciprocal lattice points that are characteristic of mosaic spread and/or misfit dislocations. For films on sapphire, Figure 2.1(d), the RSM also shows evidence of only some misfit dislocations, with broadening normal to the diffraction vector. TEM imaging supports the XRD finding, and clearly showed that the films deposited on YSZ had extensive defects in the form of threading dislocations propagating from the substrate to the film surface (see Figure 2.2(a)-(c)). Diffraction contrast imaging shows strain features, also indicating the existence of threading dislocations. Atomic-resolution imaging shows the dislocation core between the dashed lines in Figure 2.2(b). An extra half plane discontinuity is visible via careful comparison of the lattice fringes above and below the dislocation core, confirming the presence of a dislocation. Nanoscale elemental analysis of the threading features was performed via spatially-resolved STEM EELS following the method described in reference [33] for grain boundary composition analysis. Analysis of the Ce and Pr M45 core-loss EELS signals, whose relative intensity and fine structure were previously characterized for Pr0.1Ce0.9O2-δ under various oxygen non-stoichiometry conditions,34 confirmed that no compositional variation was present in the vicinity of the threading features. Analysis of atomic resolution images of the YSZ/PCO interface (e.g. Figure 2.2(c)) indicated that the interface was not atomically sharp, exhibiting 1-2 nm interfacial roughness. Regions of epitaxial registry between the substrate and film were also observed, but these were typically separated by relatively disordered interfacial regions. It is believed that poor epitaxy between the PCO and YSZ contributes to the presence of threading dislocations in the film. 23 Imaging of films on sapphire (see Figure 2.2(d)-(f)) show films with crystalline columnar grains 50–80 nm in diameter (Figure 2.2(d)). Atomically abrupt grain boundaries free of an intergranular phase were readily observed throughout the film via atomic resolution imaging (e.g. Figure 2.2(e)). Unlike the PCO/YSZ interface, however, no obvious epitaxial relationship could be observed in atomic resolution images of the PCO/sapphire interface (e.g. Figure 2.2(f)). Rather, an amorphous region approximately 1 nm thick was observed between PCO and sapphire. Indeed it was possible to grow (001) and (111) PCO films on sapphire, as well as films with mixed orientation, as mentioned above. The absence of any registry with the substrate is not unexpected, given the very different crystalline structures of sapphire and PCO. The thickness of the PCO films deposited on sapphire and studied for XRD were 160 nm as measured by profilometry, in very good agreement with the TEM study (see Figure 2.2(d)). One PCO film, deposited on a larger sapphire substrate, as discussed in the experimental section, was used for wafer curvature measurements and had a thickness of approximately 200 nm as determined by profilometry. 24 Figure.2.1. The X-ray diffraction patterns for the two films with the diffraction vector normal to the film surfaces is shown in (a). Reciprocal space maps of a PCO thin film on (b and c) YSZ and (d) sapphire, with peaks indicated. 25 Figure.2.2. Cross-section TEM images of PCO thin films after HTXRD measurements. (a-c) Film on YSZ. (a) Vertical threading dislocations visible via strain contrast; highlighted with arrows. (b) Atomic resolution image with highlighted region with visible threading extra half plane. (c) Atomic resolution image of PCO-YSZ interface showing partial epitaxy: continuous (111) planes extended from substrate into film. (d-f) Film on sapphire. (d) Columnar grains and grain boundaries (highlighted) extending through the film. (e) Atomic resolution image of grain boundary at surface of film showing atomically abrupt boundaries. (f) Atomic resolution image of PCO-sapphire interface showing atomic disorder at the base of a grain boundary. 26 Film non-stoichiometry As mentioned in the introduction and experimental sections, our group has shown that the oxygen content of thin films can be extracted using in-situ optical transmission measurements. These studies found a linear relationship between non-stoichiometry, measured by chemical capacitance, with the change in optical absorption measured at the same time on the same film, consistent with the Beer-Lambert law for absorbing centers. In this work we compare the change in optical absorption with a change in oxygen partial pressure for PCO films supported on sapphire (as used in the mechanical analysis here) to those supported on YSZ (as used in the prior non-stoichiometry study). Figure 2.3 shows that the optical absorption coefficient of the film decreases with decreasing pO2 and/or increasing temperature, consistent with a decrease in the Pr4+ absorbing center concentration, and thus a corresponding increase in oxygen vacancy content, as previously demonstrated.21 At 600oC, both the PCO film on sapphire and YSZ exhibit approximately the same absorption coefficient, indicating similar oxygen non- stoichiometries, though it is worth noting that the magnitude of absorption coefficient can depend significantly on film thickness and thickness fringes. 27 4.0 Log(A [cm-1]) 3.5 900 oC 3.0 800 oC Open: YSZ sub. 700 oC Closed: Al2O3 sub. 600 oC 2.5 -5 -4 -3 -2 -1 0 Log(pO2 [atm]) Figure.2.3. Absorption coefficient (A) for PCO thin films deposited on either sapphire or YSZ substrates measured in-situ. Figure 2.4 shows the non-stoichiometry derived from the change in absorption coefficient. As described in literature,17 given that absorptivity of the PCO thin film is × × linearly dependent on Pr4+ color center concentration ( PrCe ), changes in PrCe can be calculated from the measured absorption coefficient (𝐴) directly by using a reference × state of absorption coefficient (𝐴𝑟𝑒𝑓 ) with known PrCe , as in the following relationship. × 𝐴 × PrCe =𝐴 PrCe 𝑟𝑒𝑓 (2.6) 𝑟𝑒𝑓 From the charge neutrality and mass/site conservation equations listed below, and equation 2.6, the oxygen non-stoichiometry is derived. ′ PrCe = 2 VO∙∙ (2.7) ′ × PrCe + PrCe = PrCe total = 0.1 Pr0.1 Ce0.9 O2 (2.8) where Pr0.1 Ce0.9 O2 represents the concentration of PCO in #cm-3. When dealing with site fractions, the term can be omitted. 28 The oxygen non-stoichiometry derived using the above relationships and data × from Figure 2.3 are shown in Figure 2.4. PrCe 𝑟𝑒𝑓 was calculated, from a reference point chosen at the highest pO2, using non-stoichiometry from either the thin film defect model (Figure 2.4(a)) or the bulk defect model (Figure 2.4(b)) described in references.22,23 As observed in the figure, at temperatures less than 700oC, the thin film model fits the data better, while at temperature greater than 800oC, the bulk model fits the data better. At approximately the temperature where the change in best model lies (750oC), the magnitude of stress, relative to lower temperatures, approaches its lowest value, indicating a potential impact of stress on the film defect formation energy at lower temperatures, as described later. In the following work, strain and stress measurements are made in between, or in either of these temperature ranges. Therefore, one or both models will be considered, where appropriate. 29 -1.2 -1.2 (a) (b) -1.4 -1.4 -1.6 -1.6 Log() Log() -1.8 -1.8 900 oC 900 oC -2.0 800 oC -2.0 800 oC 700 oC 700 oC -2.2 -2.2 600 oC 600 oC -2.4 Open: YSZ sub. -2.4 Open: YSZ sub. Closed: Al2O3 sub. Thin Film Ref. Closed: Al2O3 sub. Bulk Ref. -2.6 -2.6 -5 -4 -3 -2 -1 0 1 -5 -4 -3 -2 -1 0 1 Log(pO2 [atm]) Log(pO2 [atm]) Figure.2.4. Oxygen non-stoichiometry derived from optical transmission measurements in Figure 2.3 using a reference point based on the thin film (a) and bulk (b) defect equilibria models. Dashed and solid lines show non-stoichiometry derived from the thin film and bulk defect equilibria models, respectively. HTXRD measurements Initial evaluation of the film durability during temperature and pO2 cycling was performed by measuring a (001) oriented film on a YSZ substrate at 750°C cycled 5 times between pO2 = 0.20 and 10-5 atm. The film was cycled between room temperature and 750°C twice during the course of the 5 pO2 cycles. The in-plane and out-of-plane components of the strain in the PCO film were determined by measuring the (004) and (224) reflections. For the in-plane lattice constant, the values before and after cycling expectedly remained unchanged over the first 3 cycles, but the last two cycles reached strain values of -0.013% with respect to the initial conditions. In the out-of-plane direction, the film expansion was reproducible in the first two cycles, but the strain irreversibly increased to 0.03% in the third through fifth cycles. As described earlier, the films on YSZ are highly defective, with regions of poorly-ordered substrate-film interface, which likely contribute to some additional strain developing in the in-plane 30 direction. As shown later, the maximum out-of-plane chemical expansion strain from oxidizing to reducing conditions reaches values in excess of 0.25%, giving confidence that the films are robust enough to allow accurate in-situ XRD analysis over the course of one or two cycles to the extremes of pO2. For the studies of PCO films supported on sapphire, no irreversible strains were observed over the course of the three pO2 cycles studied, giving confidence in measurement reliability if the number of pO2 cycles at temperature is limited to 3 or fewer. The strains measured in-situ behave as expected, with increasing temperature and decreasing pO2, increasing the out-of-plane lattice parameter (a), as shown in Figure 2.5 for both sapphire and YSZ substrates. With increasing temperature, films on sapphire show a consistently larger change in lattice parameter than films on YSZ, though isothermal changes in lattice parameter with pO2 are approximately similar. The larger (~20%) difference in thermal expansion mismatch between PCO and sapphire as compared to PCO and YSZ accounts for at least part of the difference. It is worth noting that there was no evidence of cracking or delamination of the films discussed here before or after the measurements (based on optical microscopy). Turning to a comparison of the film with bulk powder, it is clear that the increase in lattice parameter with increasing temperature from 650 – 800oC is much greater for the film (~Δa = 0.026 Å on sapphire) as compared to the bulk (Δa = 0.012 Å). As discussed in more detail later, part of the difference arises from the approximate factor of two conversion from isotropic (bulk) expansion to out-of-plane film expansion (where the in- plane expansion is constrained by the substrate). The film out-of-plane lattice parameter 31 is smaller than that for the bulk case for 750oC and lower, indicating a tensile stress in- plane for the film. At 800oC, out-of-plane film strain exceeds the isotropic bulk value, representing a flip from tensile to compressive in-plane stress. It is worth noting that the transition temperature is higher than the estimated growth temperature of 725oC, indicating that at growth, the films are slightly tensile, though close to being free of stress and strain. 5.50 out-of-plane lattice parameter [Å] Open: YSZ sub Filled: Al2O3 sub. 5.49 5.48 5.47 650 oC 700 oC 750 oC 5.46 800 oC (+) Bulk 5.45 -6 -4 -2 0 Log(pO2 [atm]) Figure.2.5. Isotherms of out-of-plane lattice parameter for PCO films on sapphire and YSZ substrates measured in-situ. Bulk, isotropic data points are also shown, indicated for each temperature by color (derived from interpolation of XRD data in reference [26]). Uncertainties are smaller than the data points. MOSS measurements The initial curvature of the substrate without a film was recorded prior to deposition and was found to be negligible compared to a flat mirror. The measured curvature after deposition thus provides a measure of the stresses produced during film growth and during cooling to room temperature. These post-deposition stresses at room 32 temperature were ~1-3 GPa tensile for the studied films (with one anomalous case in compression). This is evident in the initial stress in Figure 2.6 for a PCO film supported on YSZ, where heating to 750oC in oxidizing conditions (0.13 atm. O2) then leads to a stress decrease of about 1.4 GPa due to the larger thermo-chemical expansion coefficient of the film compared to the substrate. Using elastic constants from the literature35 for ceria coupled with our thin film defect equilibria model described elsewhere,22,24 and using chemical expansion coefficient values derived in this chapter later, the predicted stress resulting from thermo-chemical mismatch between the growth condition to room temperature is ~1.5 GPa in tension (for films supported on sapphire, the stress is predicted to be ~1.2 GPa, a lower value due to orientation anisotropy described later in this chapter). Subtracting the thermo-chemical mismatch stress from the measured stress at room temperature indicates that the stress created by the growth process was, for the YSZ supported film case above, ~1.3 GPa tensile, and for other films, typically 1 GPa or less in tension (with one case in compression). This range indicates significant variation in the initial growth stress, even for films grown on the same type of substrate under the same deposition conditions. After stabilization in oxidizing conditions, two reduction-reoxidation cycles were performed on the PCO film supported on YSZ shown in Figure 2.6. Following the first cycle (to 10-3 atm. O2), it is clear that the film did not fully recover its initial stress when it was reoxidized. During the second reduction step (10-5 atm. O2), the film stress approaches zero, but then returns to almost the previous stress value during reoxidation. At the end of this experiment, the change in stress during cooling from 750 oC to room temperature is approximately 1.4 GPa, similar in magnitude to the stress change observed 33 during initial heating to 750oC. However, there is now a slight decrease in stress of the sample at room temperature. The similarity between change in stress upon cooling and heating indicates that the overall shift in stress at room temperature following the experiment is due to processes that occur at elevated temperature during reduction/oxidation cycles. During reduction-oxidation cycling at elevated temperature, the creation and removal of oxygen vacancies in the bulk structure via equation 2.2 is expected to be a reversible process. In contrast to this, an “irreversible” net reduction in tensile stress occurs at elevated temperature (primarily during the first reduction-oxidation cycles). This irreversible stress relaxation is qualitatively consistent with strain relaxations that were observed during cycling in the HTXRD measurements of films grown on YSZ. Although the stresses in this film are always tensile, through thickness cracks were not observed for this sample. Also, since the thermal mismatch stress during heating is in the compressive direction, the magnitude of the tensile stress during cycling was always less than the initial state and thus through-thickness cracks are less likely to form at high temperature. Thus the net stress relaxation observed during redox cycling here is likely associated with kinetically limited changes in the film structure described in the Discussion. 34 Figure.2.6. MOSS results for PCO film on YSZ cycled at 750oC in indicated reducing and oxidizing atmospheres. For films grown on sapphire, the in-situ MOSS measurements during redox cycling were fully reversible. An isothermal measurement performed at 750oC is shown in Figure 2.7(a). As expected, upon reduction, the constrained film becomes more compressed in-plane over several hours as the film undergoes chemical expansion. After exposure to the same initial oxidizing conditions, the film nearly fully returns to its original stress. This reversibility demonstrates that these stresses are caused by compositional changes. Other changes in the film structure such as grain growth, densification, or interface reactions will generally lead to irreversible stresses. The slow kinetics may be an indication of large levels of impurities blocking oxygen surface exchange as previously demonstrated by our group.36,37 Due to the slow kinetics, measurements were performed at a temperature high enough to accelerate kinetics but where large expansions still occurred (i.e., the Pr was not fully reduced by an excessively high temperature in oxidizing conditions). It is worth noting that the change of in-plane stress for the film supported on sapphire (~0.3 GPa) following reduction (to 10-4 atm. O2) 35 is smaller than the change in stress for the film supported on YSZ (~0.4 GPa) during the first reoxidation step from a less reducing condition (10-3 atm. O2), and much less than the next reoxidation step from a more reducing condition (~1 GPa, 10-5 atm. O2). While the aforementioned relaxation may be occurring in the YSZ case, leading to unexpected stress behavior, the larger stress changes observed in YSZ can be related to the role of film orientation, as described in more detail in the discussion section. The change in stress (∆𝜎) derived from in-situ time dependent MOSS data (e.g. data in Figure 2.7(a)) using equation 2.5 is shown in Figure 2.7(b). As expected, the stress increases compressively as pO2 is decreased. The non-linear behavior observed in this stress response is consistent with the non-stoichiometry () of the PCO film that is induced by similar variations in the pO2 (Figure 2.4(a)). Here as the pO2 is reduced, the rate of increase in  decreases, eventually leading to a plateau at ~ 0.05. This indicates that there is little to no additional change in  when pO2 is decreased further (i.e. because further oxygen loss does not occur once all the Pr4+ ions are reduced to Pr3+). The plateau in the log( vs log(pO2) plot (Figure 2.4(a)) reflects this behavior, and leads to the corresponding non-linear behavior in Figure 2.7(b), where the stress change flattens out as the pO2 approaches the regime where the non-stoichiometry plateau occurs in Figure 2.4(a). At pO2 levels below those in Figure 2.7(b), the same plateau in the stress response should occur (the instrumentation employed for the stress measurements did allow us to accurately control the pO2 in this regime). 36 Figure.2.7. MOSS results for PCO film on sapphire. The reference stress for each data set is defined as the stress at 0.1 atm. O2, at the temperature of interest (i.e., ∆𝜎 = 0 under these conditions). (a) Stress during cycling at 750oC in the indicated reducing and oxidizing atmospheres. (b) Increase of in-plane compressive stress of a PCO film with decreasing pO2 for the two measured temperatures. Relationship of stress and strain to oxygen content (δ) The film expansion and compressive stress were shown above to increase with decreasing pO2, corresponding to an expected decrease in oxygen content of the film. Using oxygen non-stoichiometry (δ) derived from the thin film model, Figure 2.8 shows the approximately linear relationship of strain with δ, expected from equation 2.1. An approximate linear relationship is also found for in-plane stress with respect to δ, shown in Figure 2.9. 37 0.5 650 oC Open: YSZ sub Closed: Al2O3 sub. 700 oC Out-of-plane strain [%] 0.4 750 oC 800 oC 0.3 0.2 0.1 0.0 0.01 0.02 0.03 0.04 0.05 in Pr0.1Ce0.9O2- Figure.2.8. Out-of-plane strain plotted against the oxygen content of the PCO film derived from the thin film defect model. Solid, dashed, and dotted lines represent linear fits to films supported on an Al2O3 substrate, a second Al2O3 substrate, and a YSZ substrate, respectively. Half-filled symbols are for the second film on an Al2O3 substrate. 0 (in-plane stress) [MPa] -100 -200 -300 750 oC -400 800 oC -500 0.03 0.04 0.05 in Pr0.1Ce0.9O2- Figure.2.9. Change of in-plane stress plotted against the oxygen content of the PCO film supported on Al2O3 derived from the thin film defect model. 38 For a constrained film of an isotropic material, the strain in the out-of-plane direction (εz) and the in-plane change in stress (Δζxy) can be modeled by the following two equations. 1+𝜐 𝜀𝑧 = 𝛼𝐶 𝛥𝛿 (2.9) 1−𝜐 𝐸 𝛥𝜎𝑥𝑥 = 𝛥𝜎𝑦𝑦 = − 𝛼𝐶 𝛥𝛿 (2.10) 1−𝜐 where ν, αc, and E are the Poisson’s ratio, chemical expansion coefficient, and elastic modulus. Since αc relates strain to δ (see equation 2.1), both unitless, it is also unitless. It is worth mentioning that though αc is typically reported this way for simplicity, basing it on number of vacancies per volume, rather than formula unit, is necessary for comparison across materials with different crystal structures.38 The quantities preceding Δδ in equations 2.9 and 2.10 are equivalent to the slopes of the linear fits in Figure 2.8, and are reported in Table 2.1, for δ derived from the thin film model (as shown in Figure 2.8 and Figure 2.9) and bulk model (not shown). For strain, the slope does not appear to show a significant dependence on temperature. The slope related to stress, however, shows a much larger, 70% increase for a relatively narrow temperature range. These results, converted to chemical expansion coefficients and elastic moduli, are discussed in more detail in the next section. 39 Strain (%) Stress (GPa) o Temp. ( C) 650 700 750 750 (2) 800 750 800 Slope 13.526 14.441 13.819 20.09 34.76 14.128 12.764 (Al2O3 sub.) (12.568) (13.317) (11.601) (16.47) (26.47) Slope - 12.655 11.137 - 13.182 - - (YSZ sub.) Table.2.1. Slopes from Figure 2.8 following equations 2.9 and 2.10. The “(2)” at 750oC represents the measurements performed on a second film. Values in parenthesis represent selected higher temperature strain and stress data derived using the bulk defect equilibria model. 2.4 Discussion As observed from the TEM and the XRD measurements, the PCO films grown on YSZ are highly oriented with respect to the substrate, with misfit dislocations partially relieving the lattice mismatch stress. On the other hand, the PCO films grown on sapphire are polycrystalline, with presence of a disordered region at the interface between PCO and sapphire while often exhibiting mixed orientations. The crystal structures of the YSZ and sapphire substrates are very different from each other [i.e., the YSZ substrate has a fluorite type structure (similar to PCO) and its lattice parameter (5.139 Å) is comparable to that of PCO (5.411 Å), whereas sapphire has a corundum structure]. In this context, it appears that the choice of substrate plays an important role, at least in part, in determining the morphology of the PCO films that are deposited on them. The highly oriented, but heavily dislocated structure of the film on YSZ is typical of heteroepitaxial films where the crystallographic structure matches the substrate. In contrast, the 40 disordered region for PCO on sapphire is often observed when there is a poor match with the structure of the substrate. Oxygen non-stoichiometry was found to be similar for PCO films grown on both YSZ and sapphire, indicating that microstructural differences in the films supported on either substrate are not significant enough to influence stoichiometry. Based on the comparison between bulk and thin films models, the enthalpy of reduction (see equation 2.3) is less in the lower temperature range (650 – 700oC) as compared to the higher temperature range (750 – 800oC). Simultaneously, stress is found to become tensile below 750oC, while at or near this temperature, it is at a minimum, and at higher temperature it becomes compressive (as noted by the comparison of bulk with thin film lattice parameter in Figure 2.5, where a smaller-than-bulk out-of-plane lattice parameter indicates an in-plane tensile stress due to the biaxial stress case described by equations 2.9 and 2.10). It has been suggested and experimentally observed that tensile stresses may reduce the defect formation energy due in part to a driving force for the film to expand via chemical expansion and relieve the stress.39 For a drop in temperature of the film from 775oC (bulk defect equilibria regime) to 675oC (thin film defect equilibria regime), the in-plane tensile stress rises by ~140 MPa for PCO films supported on sapphire. The difference in enthalpy of reduction between the two models is 0.1 eV, and taking the ratio of change in enthalpy to stress yields 0.7 meV/MPa. Since similar defect equilibria behavior were observed for PCO films supported on YSZ, a similar reduction enthalpy dependence is expected. Further work is needed to validate this stress-reduction enthalpy hypothesis. 41 Larger stress changes for a similar change in oxygen partial pressure were observed for films supported on YSZ substrates as compared to sapphire (compare Figure 2.6 and Figure 2.7(a)). While relaxations of the film on YSZ may explain part of the behavior, the role of film orientation is also expected to play a significant role. As reported in reference [40], the elastic modulus of a (111) oriented cubic structured material differs from the (001) orientation by an anisotropic factor, which for many materials is far from unity. Using the compliance values for c11, c12, and c14 summarized from both experimental and computational results for CeO2 in reference [35], an anisotropic factor of ~0.46 is obtained, leading to an approximate 40% decrease in the biaxial modulus for the (111) orientation vs. (001). The fact that mixed (111) and (001) orientations were observed for films on sapphire, while only (001) was observed for films on YSZ, provides an explanation for the larger stress change observed in the latter case. Besides the above anisotropic consideration, a key distinction between the different substrates are the irreversible changes in stress and strain that were only observed with the films on YSZ. In general, the stress magnitude at elevated temperature was somewhat higher with YSZ (the large RT tensile stresses were comparable in all cases, but the thermal expansion mismatch is larger with sapphire). TEM images for PCO on YSZ show threading dislocations that propagate from the substrate into the film. It is well established that threading dislocations will lead to stress relaxation in epitaxial films.41,42 Misfit dislocations at the interface of PCO on YSZ may relieve the expected compressive stress in the film due to epitaxial mismatch, but this is not consistent with the growth stress estimated from Figure 2.6. Here, most of the initial strains created during film growth are tensile, an effect which is often attributed to grain boundary 42 formation.43,44 For example, tensile growth stresses up to several GPa have been reported in other epitaxial films where there is a large lattice mismatch, relatively low atomic mobility, and grain boundary structures due to misorientations between epitaxial domains.45,46 It appears that the expected compressive misfit strains are largely relaxed during growth, based on the XRD results and the threading dislocations observed by TEM. This dislocation mitigated relaxation requires cation mobility at the growth temperatures, at least in the vicinity of the dislocation cores. The relaxation of tensile stress during redox cycling observed in Figure 2.6 appears to require a different, additional type of mechanism. It is difficult to evaluate the cause of this relaxation, but as noted above the conventional motion of threading dislocations to relax misfit stresses is not applicable. Under the premise that the tensile stress is associated with grain boundary formation, one possible explanation is that annealing leads to surface diffusion followed by adatom incorporation into grain boundaries.47 Given the complex structure of these films, further investigation of this and other possible mechanisms is clearly needed. Regardless of this uncertainty, the observation that high temperature stress relaxation occurs with films on YSZ is intriguing. The absence of this phenomena in the films on sapphire reflects either the smaller driving force (i.e., lower initial stress at elevated temperature), or that the defect structures that occur in the films on YSZ enable the operative relaxation mechanism. Turning now to the slopes reported in Table 2.1, the chemical expansion coefficient and elastic modulus can be derived assuming a Poisson’s ratio of 0.33 (commonly used for isotropic solids and previously found experimentally for bulk ceria based oxides48). The results are reported in Table 2.2 with the thin film defect model used 43 for 650 – 700oC and the bulk defect model used for 750 – 800oC datasets. A decreasing trend in αC now emerges, after factoring in the relevant defect models. A temperature dependence for αc has been observed for other materials,49,50 although in bulk ceria based oxides it is usually minimal in this temperature range.26,51 The average αC and the standard deviation for all the temperatures is also reported in the table. This average is very similar between the sapphire and YSZ supported films, indicating, similar to δ, an insignificant impact from the different substrates on αC. The average is ~25% less than the bulk value (0.084,26), indicating that there is an impact on expansion coefficient from the thin film morphology. The elastic modulus measured at 750oC (derived using the αC reported for films supported on sapphire in Table 2.2) is nearly identical to the value reported under similar conditions for Gd0.1Ce0.9O1.95-δ (~170 GPa,48). At higher temperature the modulus is much greater than would be expected, and may be attributed to a change in microstructure upon heating significantly above the growth temperature. Interestingly, such a large change is not observed for αC; the difference may be related to the time required for measurements with HTXRD vs. wafer curvature (in general longer hold times were used during the wafer curvature measurements, up to several days in some cases). It is worth noting that the average of these measurements is similar to values reported for high temperature nanoindentation on Pr0.2Ce0.8O2-δ thin films (150 - 250 GPa).52 44 Temp. (oC) αC (Al2O3) αC (YSZ) E (Al2O3) [GPa] 650 0.071 - - 700 0.064 0.064 - 750 0.063 0.063 174 800 0.058 0.057 304 Average 0.064 ± 0.005 0.062 ± 0.004 239 Table.2.2. Chemical expansion coefficient and elastic modulus derived from data in Table 2.1 assuming Poisson’s ratio of 0.33 for indicated substrates. Thin film and bulk defect models used for 650 – 700oC and 750 – 800oC data. 2.5 Conclusions Films supported on sapphire were found to exhibit similar oxygen content to films supported on YSZ. Comparison of oxygen content with prior film and bulk defect modeling uncovered a trend of shifting defect formation energy from lower values (consistent with the thin film model [22,26]) at 700 and 750oC to higher values 24 (consistent with the bulk model ) at 800 and 850oC. Thin film chemical expansion coefficients are found to decrease with increasing temperature, and are about 18% less than in the bulk solid. Stress measurements of PCO on sapphire substrates at 750 oC revealed an elastic modulus about 16% greater than in the bulk case for a similar ceria based compound measured in-situ,48 though similar to prior nanoindentation studies52. At 800oC, the modulus was significantly larger, and may be related to microstructural changes induced at the higher temperature, above the growth temperature of ~725 oC. Wafer curvature measurements performed on PCO films supported on YSZ substrates were not reversible. On the one hand, mechanical instabilities for PCO films supported 45 on YSZ substrates were found using HTXRD after multiple cycles, though initial cycles yielded meaningful data. On the other hand, films supported on sapphire substrates exhibited reproducible behavior. Stress relaxation observed on YSZ may be associated with differences in the grain boundary structures (as observed by TEM). However, it is difficult to interpret these observations without more detailed investigations of the operative mechanisms. Finally, the role of film orientation by way of the anisotropic factor on the biaxial modulus was used to explain, in part, the larger observed stresses of films supported on YSZ as compared to sapphire substrates. 46 2.6 References 1. J.F. Scott, L. Kammerdiner, M. Parris, S. Traynor, V. Ottenbacher, A. Shawabkeh, et al., J. Appl. Phys., 64, 787 (1988). 2. S. Trolier-McKinstry, P. Muralt, J. Electroceramics, 12, 7–17 (2004). 3. Y. Choi, I.D. Kim, H.L. Tuller, A.I. Akinwande, IEEE Trans. Electron Devices, 52, 2819– 2824 (2005). 4. J. Hiltunen, D. Seneviratne, R. Sun, M. Stolfi, H.L. Tuller, J. Lappalainen, et al., Appl. Phys. Lett., 89, 242904 (2006). 5. E. Fortunato, P. Barquinha, R. Martins, Adv. Mater., 24, 2945–86 (2012). 6. S. Vunnam, K. Ankireddy, J. Kellar, W. Cross, Nanotechnology, 25, 195301 (2014). 7. H.L. Tuller, Ionic Conduction and Applications, in: P. Capper, S. Kasap (Eds.), Handb. Electron. Photonic Mater., Springer, 2006: pp. 213–228. 8. A. Rothschild, W. Menesklou, H.L. Tuller, E. Ivers-Tiffee, Chem. Mater., 18, 3651–3659 (2006). 9. N.H. Perry, D. Pergolesi, S.R. Bishop, H.L. Tuller, Solid State Ionics, 273, 18–24 (2015). 10. M. Kuhn, J.J. Kim, S.R. Bishop, H.L. Tuller, Chem. Mater., 25, 2970–2975 (2013). 11. J. Xue, R. Dieckmann, J. Phys. Chem. Solids, 51, 1263–1275 (1990). 12. D.P. Volanti, A.A. Felix, M.O. Orlandi, G. Whitfield, D.-J. Yang, E. Longo, et al., Adv. Funct. Mater., 23, 1759–1766 (2013). 13. B.K. Meyer, A. Polity, D. Reppin, M. Becker, P. Hering, P.J. Klar, et al., Phys. Status Solidi, 249, 1487–1509 (2012). 14. P. Jiang, L. Bi, X. Sun, D.H. Kim, D. Jiang, G. Wu, et al., Inorg. Chem., 51, 13245– 13253 (2012). 15. S.R. Bishop, D. Marrocchelli, C. Chatzichristodoulou, N.H. Perry, M.B. Mogensen, H.L. Tuller, et al., Annu. Rev. Mater. Res., 44, 205-239 (2014). 16. T. Kushi, K. Sato, A. Unemoto, K. Amezawa, T. Kawada, S. Singhal, et al., ECS Trans., 35, 1145–1149 (2011). 17. C. Chatzichristodoulou, M. So̸gaard, J. Glasscock, A. Kaiser, S.P.V. Foghmoes, P.V. Hendriksen, J. Electrochem. Soc., 158, F73 (2011). 18. M.L. Lee, E.A. Fitzgerald, M.T. Bulsara, M.T. Currie, A. Lochtefeld, J. Appl. Phys., 97, 47 011101 (2005). 19. A. Tschope, R. Birringer, J. Electroceramics, 7, 169–177 (2001). 20. B.W. Sheldon, V.B. Shenoy, Phys. Rev. Lett., 106, 216104 (2011). 21. J.J. Kim, S.R. Bishop, N.J. Thompson, D. Chen, H.L. Tuller, Chem. Mater., 26, 1374– 1379 (2014). 22. D. Chen, S.R. Bishop, H.L. Tuller, Adv. Funct. Mater., 23, 2168–2174 (2013). 23. S.R. Bishop, T.S. Stefanik, H.L. Tuller, J. Mater. Res., 27, 2009–2016 (2012). 24. S.R. Bishop, T. Stefanik, H.L. Tuller, Phys. Chem. Chem. Phys., 13, 10165–10173 (2011). 25. C. Chatzichristodoulou, P. V Hendriksen, J. Electrochem. Soc., 157, B481–B489 (2010). 26. S.R. Bishop, H.L. Tuller, Y. Kuru, B. Yildiz, J. Eur. Ceram. Soc., 31, 2351–2356 (2011). 27. D. Chen, S.R. Bishop, H.L. Tuller, J. Electroceramics, 28, 62–69 (2012). 28. L.A. Giannuzzi, F.A. Stevie, Introduction of Focused Ion Beam: Instrumentation, Theory, Techniques and Practice, Springer, 2005. 29. J.J. Kim, S.R. Bishop, N. Thompson, Y. Kuru, H.L. Tuller, Solid State Ionics, 10–12 (2012). 30. S. Bhatia, B.W. Sheldon, J. Am. Ceram. Soc., 91, 3986–3993 (2008). 31. E. Chason, B.W. Sheldon, Surf. Eng., 19, 387–391 (2003). 32. L.B. Freund, J. Mech. Phys. Solids, 48, 1159–1174 (2000). 33. W.J. Bowman, J. Zhu, R. Sharma, P.A. Crozier, Solid State Ionics, 272, 9–17 (2015). 34. W.J. Bowman, K. March, C.A. Hernandez, P.A. Crozier, Ultramicroscopy, 167, 5–10 (2016). 35. V. Kanchana, G. Vaitheeswaran, A. Svane, A. Delin, J. Phys. Condens. Matter, 18, 9615 (2006). 36. S.R. Bishop, J. Druce, J.J. Kim, J.A. Kilner, H.L. Tuller, ECS Trans., 50, 35–38 (2013). 37. L. Zhao, N.H. Perry, T. Daio, K. Sasaki, S.R. Bishop, Chem. Mater., 27, 3065–3070 (2015). 38. D. Marrocchelli, C. Chatzichristodoulou, S.R. Bishop, Phys. Chem. Chem. Phys., 16, 9229–9232 (2014). 48 39. T. Kawada, T. Masumitsu, Y. Kimura, S. Watanabe, S. Hashimoto, K. Yashiro, et al., J. Electroceramics, 32, 78–85 (2014). 40. L.B. Freund, S. Suresh, Thin Film Materials: Stress, Defect Formation and Surface Evolution, Cambridge University Press, 2009. 41. J.W. Matthews, A.E. Blakeslee, J. Cryst. Growth, 27, 118–125 (1974). 42. E.A. Fitzgerald, Annu. Rev. Mater. Sci., 25, 417–454 (1995). 43. R. Abermann, R. Koch, Thin Solid Films, 142, 65–76 (1986). 44. B.W. Sheldon, K.H.A. Lau, A. Rajamani, J. Appl. Phys., 90, 5097 (2001). 45. B.W. Sheldon, A. Rajamani, A. Bhandari, E. Chason, S.K. Hong, R. Beresford, J. Appl. Phys., 98, 043509 (2005). 46. B. W. Sheldon, A. Bhandari, A. Bower, S. Raghavan, X. Weng, J. Redwing, Acta Mater., 55, 4973–4982 (2007). 47. E. Chason, B.W. Sheldon, L.B. Freund, J.A. Floro, S.J. Hearne, Phys. Rev. Lett., 88, 156103 (2002). 48. K. Amezawa, T. Kushi, K. Sato, A. Unemoto, S. Hashimoto, T. Kawada, Solid State Ionics, 198, 32–38 (2011). 49. N.H. Perry, J.J. Kim, S.R. Bishop, H.L. Tuller, J. Mater. Chem. A, 3, 3602–3611 (2015). 50. X.Y. Chen, J.S. Yu, S.B. Adler, Chem. Mater., 17, 4537–4546 (2005). 51. S.R. Bishop, K.L. Duncan, E.D. Wachsman, Acta Mater., 57, 3596–3605 (2009). 52. J.G. Swallow, J.J. Kim, M. Kabir, J.F. Smith, H.L. Tuller, S.R. Bishop, et al., Acta Mater., 105, 16–24 (2016). 49 CHAPTER 3 ROLE OF GRAIN SIZE ON REDOX INDUCED COMPOSITIONAL STRESSES IN Pr DOPED CERIA THIN FILMS 3.1 Introduction As discussed in Chapter 2, the physical and chemical properties of the non- stoichiometric oxides are highly sensitive to and directly related to changes in their defect chemistry. In particular, SOFC electrodes and electrolytes for example, Pr0.1Ce0.9O2- (PCO) and La0.6Sr0.4Co0.2Fe0.8O3- often undergo significant changes in oxygen stoichiometry when operating in extreme temperatures (~ 600-1000oC) and varying oxygen partial pressure conditions.1, 2 These changes in oxygen non-stoichiometry, , are known to be accompanied by lattice strains (commonly referred to as “chemical expansion” in the literature). As noted in the previous chapters, such lattice strains lead to significant mechanical stresses in constrained cell geometries. Experimental data have indicated that mechanical properties such as elastic modulus and fracture toughness are strongly dependent on the generation of defects resulting from deviations from stoichiometry.3-8 Moreover, when transitioning from micro-scale (bulk geometries) to nano-scale (thin film geometries), grain boundaries can play a crucial role in determining 50 the defect chemistry and corresponding mass transport properties. For example, the specific grain boundary conductivities of doped and undoped CeO 2 systems are frequently several orders of magnitude lower than the bulk conductivity; thus, grain boundaries are believed to block charge carrier transport.9-16 As noted in Chapter 2, in PCO, many experimental measurements have confirmed the existence of chemical expansion.1, 17-20 It arises during oxygen vacancy defect formation/annihilation which can be described by the following reaction in terms of Kröger-Vink notation: × 2Pr× ′ ∙∙ Ce + OO ↔ 2PrCe + VO + 1/2O2 (𝑔) (3.1) in which, lattice oxygen (O× O ) leaves the material to form doubly positive charged oxygen vacancies (V∙∙O ) and reduced Pr ions on Ce sites (Pr′Ce ). At relatively high pO2’s (0.13-10-6 atm.), a decrease in pO2 causes oxygen vacancies to form which is accompanied by the reduction of Pr4+ to Pr3+(as given by Equation 3.1). In the intermediate pO2 range (10-6 and 10-18 atm.), the oxygen non-stoichiometry is largely fixed and for charge neutrality reasons 𝑃𝑟𝑐𝑒′ = 2 𝑉𝑂∙∙ . At pO2’s < 10-18 atm., additional oxygen vacancies are created accompanied by the reduction of Ce4+ to Ce3+.17 It is important to note that reduction of Ce at low pO2’s takes place in both undoped and doped ceria systems. In the case of an aliovalent dopant like Pr, cation reduction occurs at the relatively high pO2 range (0.13- 10-5 atm.). The focus of this chapter is therefore on this high pO2 range (i.e., where Pr reduction takes place). In this pO2 range, chemical expansion is believed to be due to two competing effects: i) expansion from the increased diameter of the reduced cations (Pr′Ce ), and ii) contraction around the oxygen vacancies due to relaxation of the cations around it. 51 The overall result is significant lattice dilation during exposure to reducing conditions (oxygen removal) and lattice shrinkage when exposed to oxidizing conditions (oxygen incorporation). For ceria based systems, it is believed that space charge effects cause substantial variations in ionic and electrical conductivity. Numerous theoretical as well as experimental studies have shown the existence of a space charge region near grain boundaries and surfaces enriched in dopant concentration (for example, Gd, Pr, Sm, etc.) and deficient in oxygen vacancy concentration with respect to the bulk.21-24 Such point defect redistribution is known to have a strong impact on the electrical conductivity and is also known to contribute to localized stresses and strains near the grain boundaries. For example Kim and Maier investigated the conductivity of nanocrystalline ceria and concluded that the space charge effect leads to high grain boundary ionic resistivity.25 Tschope et al., investigated the electrical transport properties of nanocrystalline and microcrystalline ceria as a function of temperature and oxygen partial pressure and concluded that the electronic conductivity of nanocrystalline ceria increases with decreasing grain size.21, 26 These opposite effects are explained by positive trapped charge at the boundary contributing to depletion of positively charged oxygen vacancies and the accumulation of negatively charged electrons within the space charge regions. Space charge considerations are also used to predict that chemical expansion results in higher stresses at grain boundaries/interfaces as a result of accumulation/depletion of point defects (such as vacancies, or interstitials).27 This becomes all the more important given that undoped and doped nanocrystalline ceria thin films have reduced enthalpies of reduction and correspondingly higher point defect concentrations compared to coarse 52 grain material.28-30 Therefore, it becomes essential to characterize and understand the sources and extent of expansion in a given material under defined operating conditions and with varying size scale (i.e., bulk to nano-structured geometries). To date, such studies have received limited attention, partly because of the difficulty in characterizing stresses and strains in-situ, under typical operating conditions. In the work reported here, we investigate the grain size dependence of compositional stresses in PCO thin films. To do so, Pr0.1Ce0.9O2- thin films of varying grain size were prepared on sapphire substrates by pulsed laser deposition. In-situ high- temperature X-Ray diffraction and in-situ wafer curvature measurements were employed to measure the strains and stresses in these films during oxidation-reduction cycling and over a wide pO2 range (10-1 to 10-5 atm.) at 750oC. 3.2 Experimental Film growth and thickness measurement Polycrystalline films of PCO were deposited using pulsed laser deposition (PLD). Films for HTXRD were deposited on 1 x 1 square cm (0001) oriented sapphire (Al2O3) substrates. Films for wafer curvature were deposited on a 2.5 cm diameter sapphire substrate. Briefly, a target of Pr0.1Ce0.9O2-δ was prepared by sintering pressed powders prepared by wet chemical reaction, followed by calcination. To obtain films with different grain sizes, deposition conditions (deposition pressure, heater temperature) were varied. The deposition conditions are tabulated in Table 3.1. More detailed descriptions of the 53 deposition process is provided in our previous publication.19 For convenience, the PCO films used for HTXRD are named as PCOyx where y is the average grain size measured by SEM and PCO films used for wafer curvature technique are labeled as PCOyw where y is the same as before. Microstructure characterizations of thin films were done using LEO 1530 VP Scanning electron microscope (SEM). The images were taken at multiple locations to take into account the range of grain sizes in the film surface and then the final value was measured by averaging over these locations. High temperature X-ray diffraction (HTXRD) The in-situ HTXRD setup and experimental conditions for the strain measurements are described in Section 2.2 of this thesis. In-situ stress measurements The in-situ stress measurement setup (MOSS) and the corresponding experimental conditions are described in Section 2.2 of this thesis. 54 3.3 Results Film structure and morphology The PLD deposition conditions employed here resulted in dense nano-crystalline films as evidenced by SEM images (not shown here). The grain sizes for the PCO films were estimated by applying the linear intercept method (ImageJ software) for the SEM images of the film surfaces. These images indicate the films to be polycrystalline with an average grain size decreasing from 72 to 27 nm with decreasing heater temperature during deposition. The grain size, thickness, and corresponding deposition conditions are reported in Table 3.1. X-ray diffraction (XRD) measurements performed on different PCO samples (Figure 3.1) confirms that the films exhibited a cubic fluorite structure with a highly textured (111) orientation for PCO27x and PCO50x. The PCO72x film on the other hand had a mixed (111) and (200) orientation. sapphire PCO(111) PCO(200) Intensity (a.u) PCO72x PCO50x PCO27x 25 30 35 40 45 2 (deg) Figure.3.1. Representative X-ray diffraction pattern for the PCO thin films of avg. grain size of 72, 50 and 27 nm on 1 cm x 1 cm sapphire substrates. 55 Sample Deposition Substrate Film Initial Pressure Heater Thickness grain size (torr) Temp (nm) (nm) (oC) PCO72x 1x10-2 854 160 72 PCO50x 6.7x10-5 854 210.3 50 PCO27x 7x10-5 600 164 27 PCO72w 1x10-2 854 200 72 PCO50w 6.7x10-5 854 200 50 PCO27w 7x10-5 600 200 27 Table.3.1. Grain size, thickness, and respective deposition conditions for Pr0.1Ce0.9O2- thin films grown on indicated sapphire substrate geometries. HTXRD measurements Figure 3.2(a) shows the out of plane lattice parameter as a function of log(pO2) for PCO72x and PCO27x thin films and that for bulk PCO. As evident from the figure, the out-of-plane lattice parameter for the PCO films increases with decreasing the pO2. Moreover, the lattice parameter of the PCO27x film is always greater than that of the PCO72x film in the measured pO2 range. Figure 3.2(b) compares the out-of-plane expansion (i.e., the change in out-of-plane lattice parameter with respect to that at pO2 = 0.13 atm. for the PCO72x and PCO27x films with average grain sizes of 72 and 27 nm, respectively. With a decrease in pO2, the smaller grain size film shows a larger expansion compared to the larger grain size film. 56 (a) ( Å) o 5.496 At 750 C out-of-plane lattice parameter 5.490 5.484 5.478 PCO27x 5.472 PCO72x Bulk 5.466 -6 -5 -4 -3 -2 -1 0 Log10 (pO2[atm]) (b) 0.4 o At 750 C out of plane expansion (%) 0.3 0.2 0.1 PCO27x 0.0 PCO72x -6 -5 -4 -3 -2 -1 Log10 (pO2[atm]) Figure.3.2. (a) Out of plane lattice parameter for PCO films measured in-situ at 750oC and the lattice parameter, ao, of the bulk (derived from the interpolation of XRD data in reference [31] at 750oC). (b) Out-of-plane expansion for PCO films measured in-situ at room temperature with 0 % strain at 0.13 atm. of O2. MOSS measurements The initial in-plane compositional stresses in the PCO films were measured using MOSS. The initial curvature of the substrate without the film is measured as a baseline. 57 This is subtracted from the post-deposition curvature to determine the residual stresses produced during the film growth and cooling to room temperature. These post-deposition stresses at room temperature were 1-2.5 GPa. Differences in the growth stresses can arise because of different intrinsic mechanisms during film formation, and also because of the different deposition conditions used to obtain different grain sizes. The complete experimental protocol for the wafer-curvature measurement is as follows. The film-substrate system was heated from room temperature to 750oC in an oxidizing atmosphere (0.13 atm. O2), followed by the step change in pO2 to the desired reducing atmosphere (usually between 0.13 to 10-5 atm. O2). The atmosphere was then returned to oxidizing conditions (as shown in Figure 3.3), which was followed by cooling the sample back to room temperature. The step changes in oxygen partial pressure were performed isothermally at 750oC, after the stress equilibrated in the previous reducing/oxidizing atmospheres. A typical time dependent in-situ MOSS measurement performed isothermally at 750oC for a step change from oxidizing (0.13 atm. O2) to reducing (10-4 atm. O2) and back to oxidizing conditions is shown in Figure 3.3 for a PCO27w film. Note that the temperature change during heating and cooling also changes the curvature of the film-substrate system, due to the larger thermal-chemical expansion coefficient of the film compared to the substrate. This corresponds to a stress change of ~1.29 GPa in the film (per Equation 2.4), i.e., the stress decreases from 1.62 GPa (the stress state of the pristine sample at room temperature) to ~300 MPa when the film was heated from room temperature to 750oC and in 0.13 atm. oxygen (as shown at t=0 in 58 Figure 3.3) and increases by the same amount during the cooling cycle. Although the stress change during the heating and cooling cycles is not shown in Figure 3.3, it is important to note that upon cooling from 750oC to room temperature, the film regains its initial stress of ~1.62 GPa. This indicates that the whole process is therefore reversible (including the stresses generated due to thermal and compositional effects). Other changes in the film structure such as grain growth, densification, or interface reactions will generally lead to irreversible stresses. As seen in Figure 3.3, the measured composition induced stress response is qualitatively consistent with the expected behavior of the PCO films under redox cycling i.e., the PCO films expand under reducing conditions and contract under oxidizing conditions.18 Given that the films are constrained by an underlying thick substrate, compressive stresses develop during reduction and tensile stresses develop during oxidation. This behavior is consistent with the HTXRD measurements that indicate an increase in the lattice parameter upon decrease in the pO2 (Figure 3.2(a)). After exposure to the initial oxidizing conditions, the film nearly fully returns to its original stress state (i.e., the stress state at 750oC during the first oxidation step). This demonstrates that the stresses generated due to compositional changes (during the reduction/oxidation step) are fully reversible. The slow reaction kinetics might be caused by a large level of surface impurities which block the exchange of oxygen at the surface.32 As a result, measurements were performed at a temperature high enough to accelerate kinetics but where large expansions still occurred (i.e. the Pr was not fully reduced). 59 500 Oxidation Reduction Oxidation 400 (0.13 atm O2) -4 (10 atm O2) (0.13 atm O2) 300 Stress (MPa) 200 100  0 -100 -200 0 5 10 15 20 Time (hrs) Figure.3.3. MOSS results for the PCO27w film cycled at 750oC in indicated reducing and oxidizing atmospheres, demonstrating reversible redox behavior. The change in stress () derived from in-situ time dependent MOSS data (for example, data in Figure 3.3) using Equation 2.5 for PCO films with different grain sizes is shown in Figure 3.4(a). For all samples studied here, the measured stress becomes more compressive with a decrease in pO2. Additionally, the increase in stress is larger for films with smaller grain sizes. Such dependence of the compositional stresses indicates a dominant role played by grain boundaries. This is explored further in the analysis and discussion section. As mentioned earlier, for temperatures lower than 750oC the reduction-oxidation kinetics for the PCO films were slow. Moreover, at temperatures ~775-800oC, grain growth was observed for the small grain size film. As such, the HTXRD and MOSS measurements on different grain size PCO films were carried out at 750oC for the purpose of this study. 60 o At 750 C 100 (a) PCO72w 0 PCO50w PCO27w -100 -200  (MPa) -300 -400 -500 decreasing grain size -600 -5 -4 -3 -2 -1 Log10(pO2 [atm]) o At 750 C (b) 100 PCO72w Thin film defect model c=0.064; E= 174 GPa, n=0.33 0 Thin film defect model c=0.064; E= 200 GPa, n=0.33 -100 Thin film defect model  (MPa) c=0.084; E= 174 GPa, n=0.33 -200 -300 -400 -6 -5 -4 -3 -2 -1 0 Log10(pO2[atm]) Figure.3.4. (a) Change in stress for the PCO films with changing pO2 showing greater change in stress with decreasing grain size. Each data set is defined with zero change in stress at 0.13 atm. of O2. The symbols represent the measured values and the solid lines represent the corresponding polynomial fits. (b) Change in stress for PCO72w thin film with changing pO2 relative to that in 100 Torr O2 determined experimentally. The solid, dashed and short dashed line shows the predicted stress obtained from the defect equilibria model using E = 174 GPa, = 0.33 and c = 0.064 (for solid line); E = 200 GPa, = 0.33 and c = 0.064 (for dashed line); and E = 174 GPa, = 0.33 and c = 0.084 (for short dashed line), respectively. 61 Comparison to thin film defect model In Figure 3.4(b), the compositional stress for PCO72w measured at 750oC is compared to the stress values predicted using a thin film defect equilibria model developed by the authors.33 In summary, the isothermal chemical expansion (c) can be predicted by the following equation: f bulk   c   c  (3.2) where, c is the coefficient of chemical expansion for PCO,  is the change in oxygen non-stoichiometry relative to the value at 0.13 atm. O2 (taken as the reference point in our experiments) and fbulk or c is the linear strain in the bulk of the film due to oxygen non-stoichiometry. Given that the thin film under study is constrained by a thick elastic substrate and assuming an isotropic behavior, the predicted chemical expansion can then be converted to an in plane change in compositional stress (c) and out of plane strain (z) using the following equations: E  c    c (3.3) (1   ) (1   )  z   c (3.4) (1   ) where, E is the Young’s Modulus and  is the poisson’s ratio of the film. In a recent publication,18 with the help of MOSS and HTXRD measurement, the authors calculated the average elastic modulus (E) and the coefficient of chemical expansion (c) for PCO thin films at 750oC to be 174 GPa and 0.064 respectively. Using these values in Equation 62 3.2 and 3.3 we get a good fit to the experimental data for the PCO72 w film. The small deviation observed for the predicted values (using the aforementioned model) and the measured values (using wafer-curvature method) in Figure 3.4(b), could be accounted for by considering the role played by the grain boundaries (discussed later in this chapter). The thin film defect equilibrium model does not take into account the additional stress contributions from the grain boundary regions and so the c and the c in Equations 3.2 and 3.3 can be defined as the change in the stress and strain in the bulk of the film due to the change in the oxygen non-stoichiometry. It is worth noting that the out of plane strain and the compositional stress values plotted for PCO films with different grain sizes in Figures 3.2 and 3.3 respectively, are consistent with each other, i.e., both the out-of-plane strain and the compositional stress in the PCO films increase with decreasing grain sizes. Change in stress, c (obtained from HTMOSS measurements) is plotted against the change in out-of-plane film expansion, z (obtained from the HTXRD measurements) in Figure 3.5 for two different PCO films with an average grain size of 27 and 72 nm. Assuming an approximate linear relation between c and z (based on Equations 3.3 and 3.4), the slope of the linear fits in the figure then yields the quantity E/(1+). The E values for the two films derived from the slopes in Figure 3.5 (assuming = 0.33) are tabulated in Table 3.2. A comparison of the slopes of the linear fits for the two PCO films indicates that the mechanical constant of the two films are similar (well under the error range) yielding an average value of E ~ 174 GPa for = 0.33. This suggests that the higher compositional stress values (Figure 3.4(a)) measured for the film with the smaller grain size are largely 63 driven by the higher strain values (Figure 3.2) and not by the change in the elastic constants of the two films. (a) 0 sl op -100 e = 13 9. 5 c (MPa) -200  14 G Pa -300 -400 -500 -600 0.000 0.001 0.002 0.003 0.004 z (b) 0 sl -100 op e = 12 c (MPa) 2  -200 15 G Pa -300 -400 0.000 0.001 0.002 0.003 z Figure.3.5. Change in in-plane stress plotted against change out-of-plane strain plots for PCO films of avg. grain size of (a) 27 nm and (b) 72 nm. The c and z values were obtained by interpolating the HTMOSS and HTXRD data at respective pO2’s. The filled symbols represent the interpolated data and the solid lines represent linear fits (fixing the intercept at 0) to the plotted symbols. 64 PCO film average Slope (GPa) assumed) Calculated E grain size (nm) (GPa) 72 122 0.33 162.25 27 139.5 0.33 185.53 Average 130.75 0.33 173.9 Table.3.2. Elastic modulus values derived from the slopes in Figure 3.5 assuming = 0.33 at 750oC. 3.4 Analysis and Discussion Brick layer model To evaluate the impact of grain boundaries on the measured compositional stress, we employ a brick layer model.34, 35 The basis for this is shown schematically in Figure 3.6. An analytical solution to the model is provided in reference [34] and is also described in the Appendix A3 (the full brick layer model). The subscripts bulk and gb represent the grain and the grain boundary regions respectively. For simplicity, the grain boundary region includes both the space charge layer and the grain boundary core. Given the size scale of the grain boundary core, deconvolution of the individual stress and strain contributions from the space charge region and the grain boundary core requires further atomistic considerations which are outside the scope of this chapter. 65 Figure.3.6. a) Schematic of the grain structure considered for the brick layer model. For simplicity, the grains are considered as cubes of length L, b) Grain intersection showing the grain boundary (GB) region of length b and grains of size L, c) An individual grain of length L showing the three orthogonal orientations of the grain boundaries namely b1 (lying along the YZ plane), b2 (lying along the XZ plane and b3 (lying along the XY plane). The analytical treatment in the Appendix A3 is applied to the experimental results (MOSS measurements) to obtain the non-stoichiometry induced average strain in the grain boundary region, <fgb>. With Ebulk, Egb, bulk, gb, b (width of the grain boundary region), fbulk and  values as inputs to the model, we can solve for fgb at any given temperature and oxygen partial pressure. The calculations were further simplified by equating the elastic constants in the bulk and the grain boundary regions i.e., Ebulk = Egb and bulk = gb. Figure 3.7(a) shows the ratio of fgb/ fbulk against the inverse of the grain 66 size of the various PCO films for the data collected at 750oC and pO2 = 10-3 atm. The plot shows that for all the PCO films investigated, the grain boundary regions experience higher strains compared to the bulk of the film. Values of Ebulk = 174 GPa (as computed in Table 3.2), bulk ranging from 0.25 to 0.33, c = 0.064 1, 18 and b = 1 and 3 nm (similar grain boundary width was observed in references [22] and [36] for GDC and GPDC) were used to generate the plots shown in Figure 3.7(a). Note that to account for the uncertainties in the values of the elastic modulus, Poisson’s ratio and the coefficient of chemical expansion for thin films, the model was also evaluated for Ebulk ranging from 150-239 GPa and c from 0.064-0.087 (not shown here). Independent of the values selected, the ratio of fgb/fbulk was found to be greater than 1 for most of the cases (exceptions being a combination of higher values of Ebulk and c). To further take into account the morphology of the film, the model was also solved considering the grains to be columnar. This modification to the model was done by neglecting the contribution from the b3 boundaries. Columnar grain analysis of the brick layer model resulted in even higher values of fgb / fbulk. 67 30 (a) Ebulk=Egb=174 GPa; bulk=gb=0.33; -3 25 b=1 nm; c=0.064; pO2=10 atm Ebulk=Egb=174 GPa; bulk=gb=0.25; 20 -3 b=3 nm; c=0.064; pO2=10 atm fgb/ fbulk 15 Ebulk=Egb=170 GPa; bulk=gb=0.25; -3 b=1 nm; c=0.073; pO2=10 atm 10 5 0 0.01 0.02 0.03 0.04 -1 1/L (nm ) 30 (b) PCO72; b= 1 nm; Ebulk=Egb=174 GPa, bulk=gb= 0.33 25 PCO50; b= 1 nm; Ebulk=Egb=174 GPa, bulk=gb= 0.33 PCO27; b= 1 nm; Ebulk=Egb=174 GPa, bulk=gb= 0.33 20 fgb/fbulk 15 10 5 0 -5.0 -4.5 -4.0 -3.5 -3.0 -2.5 -2.0 Log10(pO2 [atm]) 68 30 (c) Undoped Ceria PCO72; b=1 nm; E=174 GPa; =0.33 25 PCO50; b=1 nm; E=174 GPa; =0.33 PCO27; b=1 nm; E=174 GPa; =0.33 20 fgb/fbulk 15 10 5 0 0.0002 0.0004 0.0006 0.0008 0.0010 0.0012 0.0014 fbulk Figure.3.7. (a) fgb/ fbulk vs. the inverse of the grain size (1/L) plots at pO2 =10-3 atm. (b) fgb/ fbulk vs. the log(pO2) for the three PCO films and (c) fgb/ fbulk vs. fbulk for the three PCO films and that for undoped ceria (from reference [42]). The plots were generated by applying the analytical solution to the brick layer model (discussed in the Appendix A3) to the MOSS data collected at 750oC. Grain boundary properties As mentioned in the Results section, with a decrease in pO2, the smaller grain size PCO films undergo a larger change in stress and lattice parameter than the large grain size film. The brick layer model provides a basis for interpreting this effect. Specifically, it points to two general effects that need to be factored into our interpretation: variations in the elastic constants of the PCO films, and localized strains at the grain boundaries (for the latter, space charge effects are believed to be relevant).22, 27 As shown in Figure 3.5, the modulus for PCO27 and PCO72 films were similar. This suggests that the increase in the stress for the small grain size film is not a direct 69 manifestation of different modulus values for the two films. This supports our assumption that the PCO films with different grain sizes (used in this chapter) have similar elastic constants. Since the change in grain size does not significantly alter the elastic constants, it appears that grain boundary structures lead to higher strains. In ionic solids, the defect formation energies in the bulk of a material differ from those at the boundary. As a consequence, a space charge potential, o, can develop between the surface or grain boundary, and the bulk. In response to this electrochemical potential, the point defects redistribute to maintain thermodynamic equilibrium. In undoped ceria, o is known to be positive,30 the oxygen vacancies are depleted, and excess electrons accumulate in these space charge layers (the thickness of this layer is defined by the screening length, ). For acceptor doped (e.g. Pr, Gd) ceria, this positive space charge potential results in a space charge layer that is enriched with electrons and reduced cations (PrCe` or GdCe`).37- 40 It is widely believed that such space charge effect at the grain boundaries have a significant impact on ionic and electronic conductivity. For example, Tschope et al.,21, 26 observed that in undoped ceria and Gd doped ceria, nanocrystalline specimens exhibit electronic conductivity under conditions at which the microcrystalline samples showed impurity controlled ionic conductivities. Moreover, they observed that the electronic/ionic conductivity increased/decreased with decreasing grain sizes. They explained such grain size dependence of the electronic/ionic conductivity by taking into consideration the effect of space charge layers (i.e., the accumulation/depletion of point defects within the layer) and grain size on the partial conductivities. 70 Sheldon et al.,27, 34 pointed out that the standard space charge analysis ignores the volume changes that are associated with the variation in point defect concentrations. They suggested that the bulk grain imposes constraints on the point defect induced volume changes near the surfaces (space charge layers). This leads to composition induced stress in the space charge region. By taking into account the volume changes associated with the near-surface variations in the point defect concentrations, they showed that significant stress could build up in the boundary region and alter the thermodynamic equilibrium. By employing TEM, energy dispersive x-ray spectroscopy (EDX) and electron energy loss spectra (EELS) measurements, Bowman et al.,22 recently showed that the dopant concentrations at the grain boundaries were significantly higher than in the grains in Gd0.2Ce0.8O2- (GDC) and Gd0.11Pr0.04Ce0.85O2- (GPDC). Moreover, they also observed a significant reduction in the oxygen vacancy migration activation energy at the boundaries. This experimental observation is consistent with the space charge effect mentioned above. Ye et al.,24 also observed similar dopant redistribution near the surfaces in 10-30% Gd doped ceria. They attributed the domain formation in Gd doped ceria to the segregation of dopant cations and oxygen vacancies. The data in Figures 3.2 and 3.4 can also be analyzed in the context of space charge contributions. Doping CeO2 with Pr, increases its intrinsic oxygen vacancy concentration. Upon exposing the PCO film to a pO2 step change in the range of 0.13 to 10-5 atm. O2 (i.e. oxidizing to reducing conditions) as done in our experiments (Figure 3.3), the oxygen vacancy concentration increases (governed by the oxygen partial pressure in the reducing conditions). Simultaneous reduction of the Pr4+ to Pr3+ ions also 71  ] + [PrCex ] ) takes place as per Equation 3.1 (note that the total Pr concentration (i.e. [PrCe remains constant throughout. This means that the Pr3+ ions are generated at the expense of the existing Pr4+ ions). To maintain the charge neutrality, the relation between [VO  ]  ] can be given as: and [PrCe  ]  2[VO ] [PrCe (3.5) The lower the oxygen partial pressure during the reducing condition, the higher would be  concentrations in the PCO film. As mentioned earlier, the oxygen vacancy and PrCe similar reduction mechanism takes place at much lower pO2’s (below 10-18 atm.), where oxygen vacancy creation leads to reduction of Ce4+ to Ce3+. The experimental observation that the compositional stress increases with decreasing grain size is consistent with the space charge effects discussed above. In response to the positive space charge potential in ceria systems,  the space charge layer is deficient of VO  , whereas the PrCe concentration is increased (while the total concentration of Pr3+ + Pr4+ ions within the 22 whole grain is fixed) (consistent with Bowman et al. ). As per Sheldon et al., this deviation in the concentrations of charged species in the space charge layers is likely to cause volume changes that differ from the bulk, which then induce significant stress in the boundary regions.27, 34 This is qualitatively consistent with the higher calculated values of fgb in Figure 3.7(a), for PCO films with varying grain sizes. It is unclear whether the space charge potential varies with the oxygen partial pressure or temperature; this would in turn alter the point defect distributions profiles and thus the total point defect concentrations within the space charge layer. 72 Thus, the fgb/fbulk > 1 results in Figure 3.7(a) support the idea that the grain boundary regions undergo larger strain compared to the bulk of the grain. This follows directly from the fact that a smaller grain size PCO film has a higher grain boundary density. The increased non-stoichiometry induced strains in the grain boundary regions, fgb (as predicted by the model employed in Figure 3.7), will then substantially influence the composition induced stresses in smaller grain size films. This is exactly what is seen in the strain and stress measurements reported in Figure 3.2 and 3.4(a) i.e., the composition induced strain and stress values increase with decreasing grain size for a given oxygen partial pressure (at a given bulk oxygen non-stoichiometry value). It is important to note that the model employed in Figure 3.7 does not directly assume that the stress enhancements observed for smaller grain size films are due to space charge effects. Nonetheless, the computed values of fgb/fbulk >1 for the different grain size films (Figure 3.7(a)) are consistent with the space charge induced stress enhancement described above and in references [27] and [34]. 1-D model and comparisons with other ceria films Using the 3-D brick layer model to analyze the grain size dependence of stress and strain is rather laborious, as it requires knowledge of the elastic constants (E, , c) of the films under study. The approach that we employed above requires a detailed set of in-situ stress and strain experiments to first determine the mechanical constants of the film at a given temperature and oxygen non-stoichiometry. These were then employed as input parameters to the brick model, and used to compare individual strain contributions 73 from the bulk and grain boundary regions. Further complications in performing a detailed fit can arise because the elastic constants can vary with the oxygen non-stoichiometry, reaction temperature, etc.4, 18, 41 For example, we have shown that 10% Pr doped ceria films exhibit a chemical expansion coefficient that decreases with increasing temperature, and is approximately 18% lower than in the bulk solid.18 While this kind of detailed analysis is valuable, it is also challenging and time consuming. In spite of this complexity, the basic stress results reported here and in our previous work are roughly linear as a function of grain boundary density (e.g., the  versus 1/L results in Figure 3.10). This suggests that it should be possible to make basic comparisons between different data sets by examining this type of linear fit (i.e., without full analysis and fit that was presented in the previous sections). Figure.3.8. Schematic of the grain structure considered for the simplified 1-D model. The model assumes the grains to have a columnar structure of height, hf (thickness of the film) and width, L (grain size). Our simplified method for evaluating the grain size dependent compositional stress is based on the film structure in Figure 3.8. The columnar structure here has grain dimensions of height, hf (film thickness) and width, L (grain size). The width of the grain 74 boundary region is denoted as b. Based on this, the biaxial in-plane stress in the thin film, <>, is obtained from the sum of stress contributions due to the bulk and the grain boundary regions, such that: (𝐿−𝑏) 𝑏 <𝜎 >= < 𝜎𝑏𝑢𝑙𝑘 > + < 𝜎𝑔𝑏 > (3.6) 𝐿 𝐿 Re-arranging the above equation gives: 𝛽 < 𝜎 > = < 𝜎𝑏𝑢𝑙𝑘 > 1 + 𝐿 (3.7) ∆𝑓 𝑔𝑏 where, 𝛽=𝑏 −1 (3.8) ∆𝑓 𝑏𝑢𝑙𝑘 and fgb, fbulk, L and b were defined in the brick model. This simplified model does not require the use of elastic constants of the film as long as the stress values at different grain sizes are known. As such, this form is designed to directly fit a series of MOSS (or other stress) measurements. As per Equation 3.7, a linear fit to the thin film stress (in- plane) vs. 1/L plot provides a value of the slope (<bulk). The quantity  essentially characterizes the relative stress enhancement due to the grain boundaries. Following the general procedure that was used when fitting data to the brick layer model,  can be used directly to estimate the ratio, fgb/fbulk for any given value of the grain boundary width, b. In order to assess the accuracy of the 1-D model, we compare the fgb/fbulk values for the PCO72 film that were obtained from the 3-D brick-layer model (assuming columnar grains; neglecting contribution from b3 boundaries) and that from the simplified 1-D model. As seen in Figure 3.9, the fgb/fbulk values for PCO at 750oC 75 calculated with the 1-D model are similar to those calculated using the 3-D model (differs by ~ ±15%). This supports the idea that the 1-D model can provide a useful approximation of the grain size dependent compositional stress. At the same time this comparison also illustrates that the other contributions included in the brick layer model can have a noticeable impact on the resulting fit, and that, this type of more detailed analysis of the PCO results provides a more accurate assessment. 30 o PCO at 750 C 25 20 fgb/fbulk 15 10 5 1-D model 3-D model 0 -5.0 -4.5 -4.0 -3.5 -3.0 -2.5 -2.0 Log10(pO2[atm]) Figure.3.9. Comparison of fgb/fbulk values for PCO72 obtained using the simplified 1-D model (as discussed above) and that obtained using the 3-D brick layer model at 750oC and at different pO2s. The values are obtained for b =1 nm. Although it is less accurate, there are clearly cases where the 1D model is likely to be useful. For example, if a value of < 𝜎𝑏𝑢𝑙𝑘 > is known from other measurements, then the slope can be used to obtain  directly. It should also be noted that the intercept at 1/L = 0 also gives an estimate of < 𝜎𝑏𝑢𝑙𝑘 > that can be used here. In this way, the slope of <> vs. 1/L provides a convenient basis for comparing grain boundary contributions from different data sets. Several examples of this are shown in Figure 3.10. 76 The simplified model developed here also provides a convenient basis for comparing the PCO results to previous work with other types of ceria films that we have previously investigated with HTMOSS. The results in Figure 3.10(a) compare measurements for undoped ceria films, where the bulk non-stoichiometry (at 515oC and pO2 = 4.27×10-30 atm. and  = 0.0095) is close to that of the PCO films in the current study (at 750oC and pO2 = 10-5 atm. and  = 0.018). Details about sample fabrication and the experimental conditions for the undoped ceria films are reported elsewhere.34, 42 The grain boundary contributions for the undoped films are somewhat higher than those observed in the PCO films, which may indicate a more pronounced space charge effect in the undoped materials. Another interesting comparison with previously reported data is shown in Figure 3.10(b). Here, the undoped films in Figure 3.10(a) are compared with 25% Gd doped ceria films (GDC), at the same temperature and pO2. The bulk stress in the Gd doped material is significantly lower than the undoped material, which is consistent with other work on these materials at low temperature and pO2s.43 Although, the measured slope for the Gd doped material is also lower here, it appears that the  values for the GDC films are substantially higher than those for the PCO and undoped films. For the GDC, accurate values for < 𝜎𝑏𝑢𝑙𝑘 > are not available. Upper bound values of -10 MPa were used in Table 3.3 because this is the approximate accuracy of our measurements (i.e., the measured values for the largest grain size GDC films were below this value42). This leads to the lower bound values for  that are shown in the last column, all of which are significantly larger than the corresponding values obtained for undoped films. 77 For GDC it should also be noted that the value of < 𝜎𝑏𝑢𝑙𝑘 > should increase with temperature. Thus, the increase in  with increasing temperature shown here is not expected to be accurate (i.e., because all  values were based on the same upper bound for < 𝜎𝑏𝑢𝑙𝑘 >). The corresponding temperature results for undoped ceria do not suffer from this limitation, and here the decrease  with increasing temperature is an accurate reflection of the experimental results. It is thus possible that the GDC exhibits a similar trend with temperature, but that this is masked by the aforementioned artifact associated with the upper bound < 𝜎𝑏𝑢𝑙𝑘 > values. The overall comparisons in Table 3.3 and Figure 3.10 indicate that enhanced grain boundary contributions are evident in all of these materials. An aliovalent dopant like Pr will generally lead to space charge effects that are similar to those in undoped material. 44 Here, the rough similarity between the magnitude of  for the PCO and undoped films tested at very different temperatures is potentially consistent with the idea that temperature does not have a large effect on the magnitude of the space charge potential. However, the strong impact of temperature on the value of  for the undoped films is unclear at this time. The large values of  for the GDC films are also surprising, since space charge effects in GDC are normally believed to be less substantial than those in undoped ceria and PCO. Further consideration of the dopant and temperature effects seen here is clearly warranted. 78 0 (a) Undoped Ceria o at 515 C and = 0.0095) -100 PCO at 750oC and = 0.018) -200  (MPa) -300 -400 -500 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 -1 1/L (nm ) (b) GDC GDC bulk ~0 0 Undoped Ceria -100  (MPa) -200 -300 o Temp= 515 C -30 -400 pO2= 4.27*10 atm 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 -1 1/L (nm ) Figure 3.10: Change in stress as a function of average grain sizes for (a) undoped ceria (at 515oC, pO2= 4.27×10-30 atm. and  = 0.0095) and PCO (at 750oC, pO2 = 10-5 atm. and  = 0.018) and (b) the undoped ceria and 25% Gd doped ceria films (at 515oC, and pO2= 4.27×10-30 atm.). Each data set is defined with zero change in stress at 0.13 atm. of O2. The experimental details for GDC and undoped ceria could be found in reference [42]. The bulk values for undoped ceria, and GDC are obtained from reference [42]. 79 Sample Log10(pO2) Temperature  Slope bulk (nm) (oC) (bulk) (MPa) PCO -2 750 0.008 -2149 ± 64 -133 16 ± 4 -3 750 0.0133 -3059 ± 378 -222 14 ± 25 -4 750 0.0165 -5337 ± 322 -274 19 ± 16 -5 750 0.0182 -5966 ± 316 -303 19 ± 16 CeO2 -29.369 470 0.0036 -4355 ± 223 -57 76 ± 3 -29.369 485 0.0051 -4445 ± 255 -75 59 ± 4 -29.369 500 0.007 -4785 ± 225 -97 49 ± 5 -29.369 515 0.0095 -4265 ± 337 -118 36 ± 9 25%GDC -29.369 470 -983 ± 148 < -10 > 98 ± 1 -29.369 485 -1163 ± 120 < -10 > 116 ± 1 -29.369 500 -1533 ± 132 < -10 > 115 ± 0.8 -29.369 515 -1695 ± 134 < -10 > 169 ± 0.8 15%GDC -29.369 470 -1456 ± 784 < -10 > 145 ± 5 -29.369 485 -1915± 695 < -10 > 191 ± 4 -29.369 500 -2253 ± 410 < -10 > 225 ± 2 -29.369 515 -2741 ± 69 < -10 > 274 ± 2 Table.3.3.  values for PCO, undoped ceria and GDC as calculated using the slopes in Figure.3.10. The bulk stress values for PCO and undoped ceria were obtained from reference [42]. For bulk GDC (under the experimental condition), these values were measured to be very small (well under the instrumental error) and so, the bulk stress is assumed to be ~ 10 MPa (compressive). 80 3.5 Conclusions PCO thin films of varying grain sizes were prepared on elastic sapphire substrates by PLD. The in-situ strain evolution in these films was measured by monitoring the changes in the out-of plane lattice parameter using a high temperature XRD system whereas, in-situ stress evolution in these films was measured by monitoring the changes in the curvature of an elastic substrate while exposing the samples to desired temperatures and varying oxygen partial pressures. Comparison of the stress and strain measurement with varying oxygen partial pressure at 750oC reveals that the compositional stress and the lattice parameter increases with decreasing grain sizes for the PCO films. Extracting the elastic modulus values from the in-plane stress vs. out-of-plane strain plots reveals that the average elastic constants are similar for the PCO films with different grain sizes. Assuming a brick-layer topology for the polycrystalline PCO films and a separate grain boundary (consisting of the space charge and the boundary core regions) and bulk regions within a grain, an existing analytical model was used to calculate the strains in the grain boundary region as compared to that in the bulk of the grain for different PCO films with varying grain sizes. The calculations indicate that the grain boundary region undergoes higher strains compared to the bulk of the grain. This is consistent with the existing space charge effects in the acceptor doped ceria systems, where, a positive space charge potential results in the redistribution of the point defects (the space charge layer has excess Pr3+ ions and is deficient in oxygen vacancies). Such variations in the point defect concentrations cause a higher expansion (fgb, as used in the 81 model here) in the grain boundary regions compared to the bulk counterpart. For a smaller grain size film with a higher grain boundary density, such an enhancement in strains in the grain boundary regions would have a significant effect on the corresponding composition induced stress experienced by the film. This then explains the observed experimental results. 82 3.6 References 1. S. R. Bishop, H. L. Tuller, Y. Kuru and B. Yildiz, Journal of the European Ceramic Society, 31, 2351 (2011). 2. S. R. Bishop, K. L. Duncan and E. D. Wachsman, Journal of the American Ceramic Society, 93, 4115 (2010). 3. S. P. S. Badwal, F. T. Ciacchi and J. Drennan, Solid State Ionics, 121, 253 (1999). 4. K. L. Duncan, Y. Wang, S. R. Bishop, F. Ebrahimi and E. D. Wachsman, Journal of the American Ceramic Society, 89, 3162 (2006). 5. M. Greenberg, E. Wachtel, I. Lubomirsky, J. Fleig and J. Maier, Advanced Functional Materials, 16, 48 (2006). 6. S. Wang, H. Inaba, H. Tagawa and T. Hashimoto, Journal of the Electrochemical Society, 144, 4076 (1997). 7. S. R. Wang, H. Inaba, H. Tagawa, M. Dokiya and T. Hashimoto, Solid State Ionics, 107, 73 (1998). 8. J. G. Swallow, J. J. Kim, M. Kabir, J. F. Smith, H. L. Tuller, S. R. Bishop and K. J. Van Vliet, Acta Materialia, 105, 16 (2016). 9. S. J. Hong, K. Mehta and A. V. Virkar, Journal of the Electrochemical Society, 145, 638 (1998). 10. K. Eladham and A. Hammou, Solid State Ionics, 9-10, 905 (1983). 11. Y. M. Chiang, E. B. Lavik and D. A. Blom, Nanostructured Materials, 9, 633 (1997). 12. D. Y. Wang and A. S. Nowick, Journal of Solid State Chemistry, 35, 325 (1980). 13. R. Gerhardt and A. S. Nowick, Journal of the American Ceramic Society, 69, 641 (1986). 14. R. Gerhardt, A. S. Nowick, M. E. Mochel and I. Dumler, Journal of the American Ceramic Society, 69, 647 (1986). 15. J. Tanaka, J. F. Baumard and P. Abelard, Journal of the American Ceramic Society, 70, 637 (1987). 16. G. M. Christie and F. P. F. vanBerkel, Solid State Ionics, 83, 17 (1996). 17. S. R. Bishop, T. S. Stefanik and H. L. Tuller, Physical Chemistry Chemical Physics, 13, 10165 (2011). 83 18. J. Sheth, D. Chen, J. J. Kim, W. J. Bowman, P. A. Crozier, H. L. Tuller, S. T. Misture, S. Zdzieszynski, B. W. Sheldon and S. R. Bishop, Nanoscale, 8, 16499 (2016). 19. D. Chen, S. R. Bishop and H. L. Tuller, Journal of Electroceramics, 28, 62 (2012). 20. S. R. Bishop, T. S. Stefanik and H. L. Tuller, Journal of Materials Research, 27, 2009 (2012). 21. A. Tschope, Solid State Ionics, 139, 267 (2001). 22. W. J. Bowman, J. T. Zhu, R. Sharma and P. A. Crozier, Solid State Ionics, 272, 9 (2015). 23. T. Mori, R. Buchanan, D. R. Ou, F. Ye, T. Kobayashi, J. D. Kim, J. Zou and J. Drennan, Journal of Solid State Electrochemistry, 12, 841 (2008). 24. F. Ye, T. Mori, D. R. Ou, J. Zou, G. Auchterlonie and J. Drennan, Solid State Ionics, 179, 827 (2008). 25. S. Kim and J. Maier, Journal of the Electrochemical Society, 149, J73 (2002). 26. A. Tschope, E. Sommer and R. Birringer, Solid State Ionics, 139, 255 (2001). 27. B. W. Sheldon and V. B. Shenoy, Physical Review Letters, 106 (2011). 28. I. Kosacki, V. Petrovsky, H. U. Anderson and P. Colomban, Journal of the American Ceramic Society, 85, 2646 (2002). 29. S. Kim, R. Merkle and J. Maier, Surface Science, 549, 196 (2004). 30. A. Tschope, Journal of Electroceramics, 14, 5 (2005). 31. Y. Kuru, S. R. Bishop, J. J. Kim, B. Yildiz and H. L. Tuller, Solid State Ionics, 193, 1 (2011). 32. L. Zhao, N. H. Perry, T. Daio, K. Sasaki and S. R. Bishop, Chemistry of Materials, 27, 3065 (2015). 33. D. Chen, S. R. Bishop and H. L. Tuller, Advanced Functional Materials, 23, 2168 (2013). 34. B. W. Sheldon, S. Mandowara and J. Rankin, Solid State Ionics, 233, 38 (2013). 35. S. Bhatia and B. W. Sheldon, Journal of the American Ceramic Society, 91, 3986 (2008). 36. Y. Y. Lei, Y. Ito, N. D. Browning and T. J. Mazanec, Journal of the American Ceramic Society, 85, 2359 (2002). 37. A. Tschope, S. Kilassonia and R. Birringer, Solid State Ionics, 173, 57 (2004). 38. H. J. Avila-Paredes and S. Kim, Solid State Ionics, 177, 3075 (2006). 84 39. H. J. Avila-Paredes, K. Choi, C. T. Chen and S. Kim, Journal of Materials Chemistry, 19, 4837 (2009). 40. X. Guo, W. Sigle and J. Maier, Journal of the American Ceramic Society, 86, 77 (2003). 41. K. Amezawa, T. Kushi, K. Sato, A. Unemoto, S. Hashimoto and T. Kawada, Solid State Ionics, 198, 32 (2011). 42. S. Mandowara, PhD Dissertation, Brown University (2009). 43. S. R. Bishop, K. L. Duncan and E. D. Wachsman, Electrochimica Acta, 54, 1436 (2009). 44. J. Maier, Physical Chemistry of Ionic Materials, Wiley (2004). 85 CHAPTER 4 IN-SITU STRESS EVOLUTION IN Li1+xMn2O4 THIN FILMS DURING ELECTROCHEMICAL CYCLING IN Li-ION CELLS 4.1 Introduction A predictive understanding of degradation mechanisms in Li-ion battery electrodes is an essential step towards designing batteries with superior electrochemical performance and longer life. It is now a general consensus that mechanical degradation of electrodes is an important pathway for performance degradation of Li-ion cells during cycling. Consequently, there has been a surge of research efforts to explore and quantify the delithiation/lithiation induced mechanical degradation of Li-ion battery electrodes.1-16 As discussed in Chapter 1, this mechanical degradation primarily arises as a result of volume changes during the delithiation/lithiation process. Electrodes, such as silicon, germanium, tin that undergo significant volume changes upon lithiation/delithiation cycles (for example, silicon shows ~300% increase in volume upon full lithiation) have been studied extensively in this regard.2, 17-20 On the other hand, delithiation/lithiation induced volume changes in ceramic oxide electrodes (typically cathodes) are much lower and typically lies in the range of only a few percent. Nevertheless, owing to their brittle nature, even very small cycling induced strain could be severe and can have a significant 86 effect on electrode cycling performance. As such, severe intra-particle and inter-particle damage (micro-fracture, cracks) have been observed in cycled layered LiCoO2 (LCO), Li(Al0.05Ni0.8Co0.15)O2, LiNiO2 and in spinel LiMn2O4 cathodes.21-24 Spinel LiMn2O4 , along with layered LCO, is a canonical cathode material and has been studied extensively for Li-ion battery applications.25, 26 LiMn2O4 is more advantageous compared to any other cathode systems, such as LCO, because it is environmentally benign and has low cost. Even though delithiation/lithiation in LixMn2O4 can be achieved in the range 0≤x≤2, cycling of LixMn2O4 is generally restricted in the region with 0≤x≤1 (so called 4 V region). This restriction is a consequence of the severe capacity fading observed in the region 1≤x≤2 (so called 3 V region) arising from a structural phase transition (cubic ↔ tetragonal) mediated by the collective Jahn-Teller (J- T) effect of Mn3+ ions. Nonetheless, capacity of LixMn2O4 does fade upon cycling in the 4 V region, especially at higher temperatures (for example, at 55°C). The vast amount of work conducted to explore the causes of LixMn2O4 capacity fading in the 4 V region suggest the following reasons: manganese dissolution, onset of J-T distortion at higher potentials due to dynamic non-equilibrium conditions during cycling, non-stoichiometry of the starting composition etc.26-30 In addition, Hao et al.22 noted micro fractures in LMO particles cycled in the 4 V region and argued that the observed capacity fade was “tied to mechanical failure”. Owing to their direct effect on the performance loss of Li-ion batteries, studies on exploring the cycling induced mechanical properties of cathode materials are now being pursued both experimentally and theoretically.9-12, 31 Woodford et al. performed in-situ 87 acoustic emission experiments to study the C-rate dependent mechanical degradation of polycrystalline LiCoO2.10 Other studies have reported on the in-situ stress/strain evolution in cathode thin films. For example, Malav et al. recently reported the in-situ stress evolution in (003) oriented LiCoO2 thin films during the delithiation cycle by the substrate curvature method and concluded that these electrodes are relatively stable in the single phase regime but undergo mechanical degradation in the two phase coexistence region.16 Chung et al. employed a laser probe beam bending technique to qualitatively estimate the strain evolution in LiMn2O4 thin film electrodes.32, 33 Kim et al. also used a similar technique to estimate the stress evolution in LiMn2O4 thin films during electrochemical cycling.34 It should be noted, however, that the aforementioned studies on LiMn2O4 thin films mainly focused on stress/strain evolution in the second cycle and beyond. In the work reported in this chapter we highlight the irreversible stress response observed in LMO thin film cathodes during first delithiation in the 4 V region; we also note the reversible stress evolution behavior in subsequent cycles. The in-situ stress evolution data were obtained by monitoring the substrate curvature, using a multiple- beam optical stress sensing (MOSS) method, during electrochemical cycling.35 88 4.2 Experimental Film Preparation Thin films of nominal spinel LiMn2O4 were prepared using a solution deposition technique. The precursor materials used were Lithium acetate dihydrate [Li(CH3COO).2H2O, Alfa Aesar] and Manganese (II) acteate tetrahydrate [Mn(CH3COO)2.4H2O, Alfa Aesar]. Stoichiometric amounts of the precursors were first dissolved independently into a mixed solvent of DI water and acetic acid (Alfa Aesar). An excess of the lithium precursor was added to compensate for lithium loss during the high temperature annealing process. Afterwards, the solutions were mixed together and the mixture was left stirring at 60oC for 8 hours followed by stirring at room temperature for 12 hours; the resulting solution was stable for several days. The thin film electrode was prepared by spin-coating the precursor solution onto a substrate, which was prepared as follows. Quartz wafers (dia. 2″) were coated with a 15 nm Ti layer using an e-beam deposition (LESKER-PVD LAB18 Kurt J. Lesker Company) technique. A 150 nm Pt layer (which served as the current collector) was then deposited on the Ti using DC sputtering (LESKER-PVD LAB18 Kurt J. Lesker Company). Note that the intermediate Ti layer is needed to enhance adhesion between the quartz substrate and the Pt layer. Prior to spin coating, the solution mixture was filtered using a 0.2 m filter. During the thin film preparation, the solution was first spin coated at 3000 rpm for 30 seconds followed by drying at 400oC for 5 minutes in order to decompose the organics. The process was repeated till the desired thickness was achieved. After the final coat, the films were annealed in air at 750°C for 1 hour. 89 Film Characterization Microstructural characterization of the thin films was conducted using a LEO 1530 VP scanning electron microscope and FEI HELIOS 600 operated in the scanning electron mode. The thin film thickness was measured using cross-sectional SEM. X-ray diffraction (XRD) and Raman spectroscopy measurements were performed to check the crystal structure and phase purity of the as-prepared samples. XRD measurements were carried out using Cu Kα radiation (λ = 1.5406 Å), with a Bruker AXS D8 Discover diffractometer operated at 40 kV and 40 mA. A confocal Raman spectrometer (Witec Alpha 300, Ulm, Germany) was used to collect spectra at ambient temperature, using Nd:YAG 532 nm laser excitation. A 100x objective with a holographic grating of 600 grooves mm–1 (BLZ 500 nm) and a 100 mm diameter pinhole was used. Data were also obtained on samples after electrochemical cycling; the cycled samples were thoroughly washed with DMC before analysis. Electrochemical and MOSS Measurements To allow for in-situ stress measurements, a suitable beaker cell configuration (cross section schematically shown in Figure 4.1) was employed. The electrochemical cell was made of teflon with a stainless steel lid, which has a quartz window to allow for passage of incident and reflected laser beams for monitoring the substrate-curvature change. Electrochemical cells were assembled with a lithium metal foil (1.5 mm thick, 52 mm diameter disk, Alfa Aesar) as anode and LMO thin film as cathode using non- aqueous liquid electrolyte [1M LiPF6 in a mixture of ethylene carbonate and diethyl 90 carbonate (1:2 by wt.), BASF Selectilyte A6]. Note the cell was flooded with liquid electrolyte (i.e. the cathode film-substrate was completely submerged into the electrolyte). Electrochemical lithium extraction/insertion from/into thin film cathodes was performed galvanostatically using a Solartron 1470E MultiStat system (Solartron Analytical, Oak Ridge, TN), and data acquisition was done using the CellTest System (Solartron Analytical). The entire process of cell assembly and testing were performed inside an Ar atmosphere glovebox (H2O < 0.1 ppm; O2 < 0.1 ppm). Figure.4.1. Schematics of the Multi-beam Optical Stress Sensor (MOSS) set-up and the electrochemical cell (cross section). Note that the reflecting surface (i.e. substrate) is completely submerged into the electrolyte i.e. the beaker cell is filled with liquid electrolyte. Beaker cell assembly and MOSS measurements were performed in an Ar filled glove box. Also note that the refraction of the laser beams (for both incident/reflected), occurring before and after passing the optical window, is also shown in the schematic. In-situ stress evolution in LMO films was obtained by monitoring the changes in the elastic substrate curvature during electrochemical cycling. The substrate-curvature measurements were performed continuously using the multi-beam optical stress sensor (MOSS) technique (k-space Associates, Dexter, MI). A detailed description of the MOSS setup can be found elsewhere.2, 5, 7, 36-39 and a schematic of the experimental setup is 91 shown in Figure 4.1. A summary of the technique is as follows. An array of parallel laser beams is incident on the back side of the quartz substrate and the reflected beams are captured using a CCD camera. The spacing between the adjacent laser beams (d) is governed by the curvature of the substrate (κ) as follows: (d  do ) 1    (4.1) do Am where, d0 is the initial distance between the adjacent laser beams, Am is the mirror constant given as 2Lns/cos(θ) [L is the optical path length of the laser beam between the plane of the wafer substrate and the CCD array, ns is the refractive index of the electrolyte solution with respect to air,40 θ is the incident angle of the laser beam on the wafer substrate]. The mirror constant is measured by placing a flat mirror and a reference mirror of known curvature in the sample plane (submerged into the electrolyte) and measuring the relative change in the spot spacing. One advantage of using multiple beams is that it mitigates the problems associated with the system vibrations and improves the signal-to-noise ratio compared to conventional cantilever beam deflection methods. As such, the standard deviation associated with the relative change in the spot spacing is very small (less than 10-2). When the quartz substrate deforms elastically, the change in the curvature of the film-substrate system is proportional to the product of the thickness averaged stress in the film and its thickness (commonly referred to as the “stress-thickness” in the literature). Stress-thickness is related to curvature change through Stoney’s equation.41 92 M s hs2    hf  (4.2) 6 where, <> is the thickness averaged stress in the film, hf is the film thickness, Ms is the biaxial modulus of the substrate, hs is the substrate thickness and  is the curvature of the film- substrate system [obtained through Eqn. (4.1)]. Stress in the film can then be calculated by dividing measured stress-thickness with nominal thickness of the film. The back surface of the quartz wafer (substrate of the LMO films) is visible through a quartz window on top of the sealed cell, which makes it possible to monitor the substrate curvature (bending of the substrate/thin films system) during electrochemical cycling. The initial curvature of the substrate, with the current collector but without any active material, is measured to determine the initial stress. This value is then taken as a zero stress reference to measure the residual stresses in the annealed LMO films. Stress developed in the films during lithiation/delithiation (in-situ) is then measured by monitoring the changes in the spot spacing of the deflected beams during electrochemical cycling. The stiff substrate constrains expansions and contractions in the in-plane dimensions of the active thin film (i.e., LMO here) during delithiation/lithiation. This constraint leads to bending of the substrate/thin film system that alters the spacing between the beams that are reflected back from the substrate. The interpretation of the measurements is not significantly altered by the Pt film used as a current collector, as long as it is much thinner than the quartz substrate and is relatively inactive towards lithiation/delithiation. 93 XPS Measurements Surface compositional analysis was conducted using ex-situ XPS measurements (K-alpha, Thermo) with Al Kα X-ray source at a pass energy of 50 eV and measured spot size of 400 m. The electrodes were transferred from the glove box to the XPS analysis chamber using a special vacuum-sealed module (Thermo) without exposure to the air at any time. The binding energy was corrected based on the C 1s peak of hydrocarbon at 284.8 eV. 4.3 Results Figure 4.2 shows a representative SEM image of the surface of a pristine LMO film. As can be seen, the film is fairly dense with faceted primary particles in the 50 to 150 nm size range. 94 Figure.4.2. A representative SEM image of the surface of a pristine LMO film. Figure 4.3(a) shows a representative XRD pattern of an as prepared LMO thin film. Multiple peaks in the XRD pattern could be indexed based on a cubic spinel structure (with space group Fd-3m), suggesting the presence of dominant polycrystalline spinel LMO along with a minor impurity phase (Mn2O3). Figure 4.3(b) shows a representative Raman spectrum of an annealed LMO sample. The plot shows a broad band around 600-650 cm-1 which is characteristic of cubic spinels and arises due to the vibrations associated with the motion of oxygen atoms in the MnO6 octahedra.42 The Raman spectrum in Figure 4.3(b) is in good agreement with literature reports.43 95 (a) * Mn2O3 Pt (111) LMO (111) Intensity (a.u.) LMO (311) * pristine LMO film Pt coated substrate 10 20 30 40 50 60 70 80 2(deg) (b) LiMn2O4 Intensity (a.u.) 625 200 400 600 800 -1 Raman shift (cm ) Figure.4.3. Representative (a) XRD pattern (also showing the background from the annealed platinum coated quartz wafer) and (b) Raman spectra of a pristine LMO film on Pt/Ti/quartz substrate. 96 Figure 4.4(a) shows the charge-discharge profiles of a ~150 nm thick LMO film that was cycled 10 times galvanostatically in 3.5-4.3 V (vs. Li/Li+) range with a constant current density of 2.5 µA/cm2. The charge-discharge profiles show two step features in the 4 V region, which is characteristic of spinel LiMn2O4, and agree well with previous reports.26, 28, 32, 34, 44, 45 Moreover, a comparison of the charge discharge profiles in Figure 4.4(a) to those of typical stoichiometric and non-stoichiometric spinels suggests that the present samples are better described as non-stoichiometric spinels (Li1+xMn2O4+y; |x|>0, |y|>0).44 It is evident from Figure 4.4(a) that the films cycle well in this voltage region without substantial capacity fade. The concomitant evolution of delithiation/lithation induced stresses in the LMO film during cycling is shown in Figure 4.4(b). Note the residual tensile stress (~1.3 GPa) in the as-prepared LMO film in Figure 4.4(b). Of particular note is the stress evolution during the first delithiation cycle, which is quite distinct from the subsequent cycles; this data is shown in Figure 4.4(c) for clarity. As can be seen from Figures 4.4(b) and 4.4(c), there is a steady buildup of tensile stress with initial delithiation up to ~ 4.05 V reaching a maximum value of ~1.45 GPa. On further delithiation, however, the stress reverses direction and decreases steadily (termed as “anomalous drop”, hereafter) having a final value of ~1.3 GPa at 4.3 V. In the following lithiation step (i.e. first discharge), the stress shows a steady decrease with lithiation reaching a value of ~ 1.02 GPa at 3.5 V. Subsequent cycles do not show any anomalous drop during delithiation; there is a reversible evolution of the induced stress between 1.3 and 1.02 GPa with steady stress accumulation and release during delithiation and lithiation, respectively. These general trends in the induced stress evolution during delithiation/lithiation cycles were reproduced on more than 20 samples. 97 The inset in Figure 4.4(c) compares the dQ/dV vs. potential plots of the first three cycles of LMO film derived from the galvanostatic charge-discharge curve shown in Figure 4.4(a). Plateaus in the charge-discharge profiles correspond to the peaks in the dQ/dV plots. The presence of two well separated peaks both in anodic and cathodic directions are characteristic of spinel LMO indicating that lithium extraction/insertion proceeds in two stages for LMO in 4 V region.46, 47 Notably, the anodic peak shapes and positions during the first delithiation are somewhat different from those in the subsequent cathodic/anodic cycles. These observations suggest some irreversible structural changes of LMO during the first delithiation, which we believe are responsible, at least in part, for the observed anomalous drop in the stress response. The correlation between the observed anomalous drop and the irreversible structural changes along with its probable origin during first delithiation of LMO is discussed later. 98 Potential (V, vs. Li/Li ) + 4.4 (a) 4.1 4.05V 3.8 3.5 anomalous 1.4 (b) drop  (GPa) 1.2 1.0 0 20000 40000 60000 80000 100000 Time (s) 1.8 0.6 1st cycle 4.8 (c) 2nd cycle dQ/dV (mAh/V) 0.3 3rd cycle Potential (V, vs. Li/Li ) 0.0 1.6 4.5 -0.3 -0.6  (GPa) 3.5 3.7 3.9 4.1 4.3 + 4.2 1.4 Potential (V, vs. Li/Li ) region I region II 3.9 1.2 3.6 + delithiation lithiation 1.0 0 2000 4000 6000 8000 10000 Time (s) Figure.4.4. (a) Charge-discharge profiles and (b) accompanying stress evolution of a ~150 nm thick LMO film cycled in the 3.5-4.3 V (vs. Li/Li+) range with a constant current density of 2.5 µA/cm2. For clarity an expanded view of the first cycle is shown in panel (c). dQ/dV vs. potential plots for the first three cycles derived from the galvanostatic charge discharge profiles in panel (a) are shown as an inset in panel (c). 99 In an attempt to gain further insight into the origin of the anomalous drop during first delithiation cycle, an experimental scheme involving reannealing of cycled samples was devised. The results are given here and their implication towards the observed anomalous drop is discussed later. Figure 4.5(a) shows the charge-discharge profiles of a LMO film (fresh sample) along with the induced stress evolution for first two cycles in the 3.5-4.3 V range with a constant current density of 2.5 µA/cm2 (run 1). The electrochemical and stress profiles are quite similar to those in Figure 4.4 and the anomalous drop is clearly observed only at the later stages of first delithiation. After the second cycle was completed, the sample was recovered from the beaker cell, washed thoroughly with DMC and reannealed in air at 750°C for 1 hr (similar to the annealing condition of the fresh sample). The reannealed cathode sample was then placed back in the beaker cell and cycled twice using the same current density in the same voltage range (run 2). The curvature of the film-substrate system was monitored at each step. The charge-discharge profiles for run 2 with the accompanying stress evolution are shown in Figure 4.5(b). We note that both the electrochemical and stress evolution profiles in Figure 4.5(a) and 4.5(b) are very similar, except for the slight reduction in capacity for run 2. Not only did the anomalous drop reappear beyond 4.05 V in the first delithiation step during run 2, its magnitude also remained comparable to that in run 1 (35 GPa-nm vs. 32 GPa-nm). Additionally, the residual stress in the reannealed LMO film prior to run 2 was found to be the same as it was before run 1 (i.e. pristine sample). 100 320 Potential (V, vs. Li/Li ) (a) Run 1 4.4 300 35 GPa-nm *h~ *h (GPa-nm) 4.2 280 4.0 260 3.8 240 3.6 220 3.4 + 0 5000 10000 15000 20000 25000 30000 Time (s) 320 (b) Run 2 (reannealed) Potential (V, vs. Li/Li ) 4.4 300 32 GPa-nm *h~ *h (GPa-nm) 4.2 280 4.0 260 3.8 240 3.6 220 3.4 0 5000 10000 15000 20000 + Time (s) Figure.4.5. Charge/discharge profiles and accompanying stress evolution (a) for a pristine LMO film and (b) for a reannealed LMO film. Both tests were performed in the 3.5-4.3 V (vs. Li/Li+) range with a constant current density of 2.5 µA/cm2. See text for details. 101 4.4 Discussion In-situ stress evolution in the nominal LMO films may be examined in light of their crystal structure evolution during electrochemical cycling. Previous in-situ and ex- situ XRD studies have shown that structural changes in spinel LixMn2O4 as a function of lithium extraction/insertion in the range 0h (where h is the film thickness and <ζ> is magnitude of anomalous stress drop) is expected with varying film thickness during the anomalous drop if it resulted only from 106 the surface effects. However, if bulk effects are responsible, the value of <ζ>h should be proportional to the film thicknesses.8 The magnitudes of <ζ>h during the first cycle anomalous drop for ~75, 150 and 300 nm thick LMO films were measured to be ~16, 23 and 30 GPa-nm, respectively. Clearly, neither did the magnitude of <ζ>h during first cycle anomalous drop remain constant for various film thicknesses, nor did it scale linearly with film thickness. This data indicate that the first cycle anomalous drop did not arise solely from surface effects and contributions from some irreversible bulk structural changes during the first delithiation need to be considered. It should be noted that possible surface effects may include surface restructuring involving oxygen loss, similar to what has been observed in other cases,55 in addition to surface film formation. Bulk structural changes- First cycle irreversibility involving bulk electrode structural changes is not uncommon in lithium ion batteries. For example, the loss of oxygen from the bulk of Li- and Mn-rich layered-layered oxides, xLi2MnO3.(1-x)LiMO2 (M=Ni, Co), during first delithiation results in a stable structural configuration at the end of first delithiation that supports reversible lithiation/delithiation during subsequent cycling.56 As a consequence, the first delithiation profile in such materials is quite distinct from those of the subsequent cycles. As such, any first cycle structural irreversibility involving either surface or bulk of the electrode would manifest itself with a distinct feature in the lithiation/delithiation profile. In this context, comparisons of the peaks in the dQ/dV plot [inset of Figure 4.4(c)] for successive cycles suggest that some irreversible structural changes did occur during first delithiation of LMO samples studied here. However, mechanistic processes that partake in the irreversible structural changes are not completely known at present. Nevertheless, the experimental scheme used in 107 Figure 4.5 helps shed some insight into the possible origin of the irreversible electrode structural changes that result in the observed anomalous drop during first delithiation from the LMO films. Of particular note are the observations that the anomalous drop reappeared in the first delithiation step following the reannealing of a cycled sample [run 2, Figure 4.5(b)] and the anomalous drop magnitude during run 2 (~32 GPa-nm) was quite comparable to that during run 1 (~35 GPa-nm). Combining this with the fact that the residual stress in the LMO film after reannealing (i.e. before run 2) was similar to that in the pristine film (i.e. before run 1) suggest that the cycled LMO sample (after run 1) reverted back to its pristine state (from both surface and bulk perspective) after reannealing. Therefore, the irreversible structural changes in the LMO film that was incurred during the first delithiation (beyond 4.05 V) during run 1 were completely recovered upon reannealing the sample. From the surface point of view, this suggests that any surface film that might have formed during run 1 did not withstand the high temperature treatment and expectedly decomposed during the re-annealing process. From the bulk perspective, reannealing of the cycled LMO sample in air after run 1 is expected to regain the lost crystallinity and eliminate oxygen vacancies to take the cycled sample back to the pristine state before run 2. Therefore, we conjecture that the irreversible structural changes, responsible for the anomalous drop during first delithiation cycle of LMO, arises from a combination of i) delithiation induced loss of crystallinity and ii) electrochemically induced creation of oxygen vacancies. An irreversible loss of crystallinity in LMO samples at the end of first delithiation step has also been observed by Hao et al. in a recent study,22 which agrees well with our hypothesis. Regaining the crystallinity that was lost during first delithiation upon 108 reannealing is, perhaps, intuitively simple to understand. Delithiation induced creation of oxygen vacancies in LMO, on the other hand, is not a widely-known phenomenon. Support of this speculation, however, comes from a comparison of Mn2p XPS spectra of LMO at various stages of cycling as shown in Figure 4.7. Note that XPS gives surface specific information, and the evolution of the oxidation state in the bulk of the sample might not necessarily be the same as in the surface. Nonetheless, it is evident from Figure 4.7 that the peak positions of the Mn 2p3/2 spectra of sample A (pristine sample) and sample B (discharged at the end of two cycles) are quite similar, which is expected on the basis of Mn3+↔Mn4+ oxidation/reduction during delithiation/lithiation cycles. Slight difference in the peak shape between these two spectra, however, indicate minor differences in bonding environments around manganese between these two samples. On the other hand, both the peak position and the shape of Mn 2p3/2 spectra for sample C (reannealed after two cycles i.e. reannealed sample B) are exactly the same as that of the pristine sample. This fact strongly suggests that the atomic structure around Mn in sample C reverts to its pristine state upon reannealing. As such, this means that the oxygen coordination around Mn in the reannealed sample (sample C) is the same as in the pristine sample, but is slightly different than that in the cycled sample B (discharged at the end of 2 cycles). Based on this, we speculate that the irreversible structural changes in LMO during first delithiation involve, at least in part, creation of oxygen vacancies, which are replenished during reannealing process. Additionally, based on charge neutrality considerations, the creation of oxygen vacancies would require manganese reduction (from Mn4+ to Mn3+/Mn2+) or additional Li removal or both. This suggests that at the end of first delithiation, there would be more Mn3+ (and/or Mn2+) in the electrode 109 than what is expected based on capacity considerations only. Qualitatively similar results that support this hypothesis have been observed recently by Tang et al. on delithiated LMO samples.57 They report XPS and EELS measurements that show substantially enhanced Mn3+ (and Mn2+) content at the charged (4.3 V) LMO electrode surfaces. Even though XPS and EELS results are surface specific, these results are consistent with our hypothesis of oxygen vacancies’ contribution to the irreversible structural changes during first delithiation of LMO. Note that introduction of oxygen vacancies results in an increase in the lattice parameter of spinel LMO,58 which is also consistent with the anomalous drop. Additional efforts to understand the origin of the anomalous drop phenomenon are needed, possibly via DFT based computational studies. Mn2p1/2 Mn2p3/2 Intensity (a. u) (c) (b) (a) 660 655 650 645 640 635 Binding Energy (eV) Figure.4.7. Mn 2p XPS spectra of LMO films at different charge state (a) pristine (Sample A), (b) discharged at the end of two cycles i.e. run 1 (Sample B) and (c) reannealed Sample B. 110 In summary, observation of the anomalous drop in the stress response, in absence of apparent mechanical damage on cycled samples, indicates involvement of other (surface and bulk) effects including, but not limited to, oxygen loss and loss of crystallinity, surface film formation, surface reconstruction (by means of loss of manganese/oxygen). As such, combined effect of these additional processes outweighs the effect of lithium removal toward the induced stress evolution and results in a reversal of stress evolution direction giving rise to the anomalous drop during the later stages of first delithiation of LMO. Additionally, the absence of this anomalous drop in the subsequent cycles suggests that the irreversible structural changes (involving both surface and bulk) only occur during the first delithiation such that a stable configuration is achieved at the end of this step. It is this stable configuration that acts as a host for reversible lithium insertion/extraction during subsequent cycling. 4.5 Conclusions Electrochemical cycling induced stress evolution in spinel LMO thin films was measured by monitoring the changes in the curvature of an elastic substrate while cycling the sample galvanostatically in the 3.5-4.3 V range. The initial delithiation from spinel LMO induced tensile stress up to ~4.05 V (vs. Li/Li+) in agreement with the volume contraction during delithiation as suggested by XRD. Continued delithiation beyond 4.05 V, however, resulted in a reversal of the induced stress direction (termed as the “anomalous drop”), which is inconsistent with the reported monotonic decrease in the 111 lattice parameter (hence the unit cell volume) of LMO. During the first lithium insertion step there was steady buildup of compressive stress. In subsequent cycles the induced stress evolved reversibly with the stress becoming tensile during delithiation and compressive during lithiation in accordance with the XRD results. Absence of apparent micro-cracks/fracture in cycled LMO samples suggests that the anomalous drop did not arise from mechanical damage during cycling; irreversible changes in the electrode structure contribute to the anomalous drop. Stress measurements on LMO films with varying thicknesses showed that both surface and bulk effects contribute toward the first cycle anomalous drop. Interestingly, the anomalous drop reappeared for a cycled sample that was “reannealed”. Based on this observation, we conjecture that a combination of electrochemically induced creation of oxygen vacancies and delithiation induced loss of crystallinity in the bulk of the material during first delithiation (beyond 4.05 V) was responsible for the irreversible structural changes that resulted in the first cycle anomalous drop. 112 4.6 References 1. G. Bucci, S. P. V. Nadimpalli, V. A. Sethuraman, A. F. Bower and P. R. Guduru, Journal of the Mechanics and Physics of Solids, 62, 276 (2014). 2. M. J. Chon, V. A. Sethuraman, A. McCormick, V. Srinivasan and P. R. Guduru, Physical Review Letters, 107 (2011). 3. S. P. V. Nadimpalli, V. A. Sethuraman, G. Bucci, V. Srinivasan, A. F. Bower and P. R. 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Huang, Chemistry of Materials, 26, 3535 (2014). 58. Y. Xia, H. Wang, Q. Zhang, H. Nakamura, H. Noguchi and M. Yoshio, Journal of Power Sources, 166, 485 (2007). 116 CHAPTER 5 EFFECT OF INTERNAL STRESSES ON PHASE TRANSFORMATIONS IN VANADIUM OXIDE ELECTRODES 5.1 Introduction Due to their layered structure (which can host more Lithium ions), high cell potentials, high power densities and high capacities, vanadium pentoxide (V2O5) has been a candidate material for cathodes in secondary Li-ion batteries.1-4 When Li ions are incorporated into the host lattices, various structural changes take place.4, 5 These include i) change in interlayer spacing,5 ii) change in the stacking mode of the layers6 and c) formation of intermediate phases at low Li concentration thus exhibiting staging5, 7. Therefore, in analyzing these materials, one of the most critical parameters is stability to repeated electrochemical cycling. The degree of reversibility of the cycling depends on the extent of irreversible structural damage incurred by the active material during cycling. Crystalline V2O5 films have been widely studied in the past. Several authors have reported the formation of the two phase plateau regions at 3.3, 3.2, 2.3 and 1.9 V corresponding toand phases when these films are cycled galvanostatically.4, 8-10 McGraw et al., verified that when the crystalline V2O5 films are cycled beyond the threshold to 2 V, they exhibit an immediate and a continuous fade in 117 the capacity as well as a nearly 90% decrease in XRD peak intensity and a similar decrease in the raman signal intensity in as few as 10 cycles. The amorphous films on the other hand had a less capacity loss.11 Based on the Electrochemical Quartz Crystal Microbalance (EQCM) measurements, Koike et al., observed that during the initial galvanostatic cycling of the V2O5 films between 4-2 V, part of the inserted lithium irreversibly changes the surface film. In addition, a small amount of lithium molecules may survive in the V2O5 film following each cycle. As a result, the charge–discharge profiles change into amorphous-like curves with repeated cycling caused by the irreversible phase transformation.9 Thus, the insertion/extraction of Li ions from the active material (V2O5 in this case) during cycling leads to significant stresses in the films which may lead to mechanical failure of the electrode. From the literature, it has also been observed that the electrochemical properties reported from thick films exhibit in some cases a poor behavior in comparison with that of thin films.8, 12 In order to get more information on the relationship between the film performances and the microstructure and morphology of the film, it is crucial to characterize and to understand the stresses that are generated in these films during the growth process as well as during the electrochemical cycling of these films. For the study reported in this chapter, we prepared crystalline vanadium pentoxide thin films having different internal stress states (i.e., stress in the pristine film before electrochemical cycling) but similar grain structures and film thickness. This was achieved by varying the current collectors that were used for the active material in the electrochemical cycling. Wafer curvature measurements using Multi-beam Optical Stress Sensor (MOSS) technique (described in the previous chapters) was employed to measure 118 the internal stress in the films and to precisely measure the in-situ stresses that were generated in the films during the electrochemical cycling of the active material. The phase transitions were characterized by thorough X-Ray diffraction measurements on both the cycled and pristine films (annealed but not electrochemically cycled). Grain sizes, thickness of the film and the surface morphology were analyzed using the scanning electron microscope and the transmission electron microscopes. The experimental results were then compared to a modified Nerst equation which takes into account the effect of intrinsic stresses (stress state in the pristine material) and extrinsic stresses (stress generated as a result of electrochemical cycling) on the change in chemical potential of Lithium in the active material. Through these investigations, we found that by varying the internal stresses in the thin films, one could modify the phase transformations and degradation in a thin film cathode material during cycling. 5.2 Experimental Film Preparation Schematics showing the sample configuration and processing steps are shown in Figure 5.1. To summarize, 50 nm thick vanadium oxide layers were separately deposited on a 200 nm Aluminum(Al) coated SiO2 wafers (25.4 mm in diameter and 250 μm thick) and on 145 nm Gold (Au) coated SiO2 wafers (25.4 mm in diameter and 250 μm thick), respectively. The substrates were first ultrasonically cleaned in acetone, ethanol, and de- ionized water for 5 minutes each, and then separately mounted in a custom built e-beam 119 evaporation system for the deposition of the metal layers. The base pressure of this system was 3 ×10−6 Torr, and the current collectors were deposited at a fixed deposition rate of 0.1 nm/s, monitored with an Inficon QCM (Quartz Crystal Microbalance). For the Au specimens, 10 nm of Ti was first deposited on the SiO2 to improve adhesion between the Au and the quartz substrate. The vanadium oxide was produced with DC reactive sputtering (LESKER-PVD LAB18 Kurt J. Lesker Company) using vanadium targets (2 in. diameter, 0.125 in. thick discs, 99.5% pure, Kurt J. Lesker Company) in a mixed Ar + O2 atmosphere (Ar:O2= 9:1). The DC power and the total pressure during deposition were 180W and 2 mTorr, respectively. The as-deposited vanadium oxide films were amorphous. To crystallize and completely oxidize them, they were annealed at 550oC in air for 3 hours. Figure.5.1. Schematic showing the details of the film fabrication processes. 120 Film Characterization X-ray diffraction was carried out with a Bruker AXS D8 Discover diffractometer using Cu Kα radiation (λ = 1.5406 Å) at glancing angles with the films. The generator was operated at 40 kV and 40 mA. Microstructural characterizations of the thin films were done using a LEO 1530VP scanning electron microscopy (SEM). Some films were also characterized with transmission electron microscopy (TEM), using both FEI CM20 and JEOL 2010FS system for high resolution imaging. The TEM samples were prepared by cross sectional lift-outs using focused ion-beam (FEI HELIOS 600). The as-cycled samples were thoroughly soaked/cleaned in DMC before doing any post-cycling analysis. Electrochemical and MOSS Measurements The electrochemical behavior of the V2O5 films were investigated during galvanostatic and potentiostatic discharge/charge cycles against Li metal in a custom made electrochemical cell.13-18 The liquid electrolyte used was an equimolar mixture of ethylene carbonate (EC) and dimethyl carbonate (DMC) containing 1 M LiPF6 salt. For the galvanostatic cycling, a constant current density of 0.2 A/cm2 was used. The intrinsic stress (post-deposition and annealing) and the in-situ cycling induced stresses in the V2O5 films were measured using the MOSS technique as discussed in the previous chapters. During the measurements, the back surface of the quartz substrate was visible through a quartz window on top of the sealed custom made cell. This made it possible to monitor the substrate curvature (bending of the 121 substrate/thin films system) during electrochemical cycling using MOSS technique. As mentioned in the previous chapters, this technique employs an array of parallel laser beams that are focused on the back side of the quartz substrate.13, 17, 18 Since the quartz substrate deforms elastically, the thickness-average stress in the active film is proportional to the induced change in wafer curvature, which can be determined quantitatively with Stoney’s equation13, 17, 18: M s hs2    hf  (5.1) 6 where, <> is the average stress state of the film, hf is the thickness of the film, Ms is the biaxial modulus of the substrate, hs is the substrate thickness and  is the curvature change of the film- substrate system as a result of the electrochemical cycling. The initial curvature of the substrate (with the current collector) was measured without any active material on it. This was then taken as a zero stress reference to measure the intrinsic stresses in the as sputtered and annealed vanadium oxide films. Stress developed in the films during lithiation/delithiation (in-situ) was then measured by monitoring the changes in the spot spacing of the deflected beams during electrochemical cycling.13, 15, 17 During lithiation/delithiation, the stiff substrate constrains expansions and contractions in the in-plane dimensions of the active thin film (i.e., V2O5 here). This leads to bending of the substrate/thin film system. The interpretation of the measurements is not significantly altered by the Au and Al films used as a current collector, as long as they are much thinner than the quartz, deform elastically, and are relatively inactive towards lithiation/delithiation. These conditions are reasonable approximations for our 122 experiments, and thus the measured changes in the laser spots were interpreted as in- plane nominal stress in the active material.13, 14 5.3 Results Control of Film Stress The films on the two different current collectors exhibited significantly different stresses after crystallization. This discovery made it possible to explore the impact of changing the initial stress state on the electrochemical performance of the V2O5 films. From the XRD plots in Figure 5.2, it is evident that both types of film crystallize into orthorhombic V2O5 after annealing at 550oC. The dominant (001) peak indicates substantial texturing in both cases, since the only other peaks observed are from the Al and Au current collectors. The Al current collector shows an amorphous bump which could likely be due to formation of oxide on the surface during annealing. 123 V2O5 (001) Au (111) Au (200) V2O5 (002) Intensity V2O5 on Au Al (111) Al (200) V2O5 on Al Al (200) Al (111) Annealed Al coated substrate 10 20 30 40 50 2 Figure.5.2. Representative XRD measurement (also showing the background from the annealed Al coated quartz substrate) of the V2O5 film on Au and Al. Top surfaces of the crystallized V2O5 films are shown in Figure 5.3. This comparison clearly indicates that both the films have similar microstructures and grain sizes(~100 nm on Al and ~110 nm on Au). Cross-sectional TEM images verified the V2O5 film thicknesses of 50 nm on both the current collectors, EDS showed only the presence of V and O (i.e., any impurities were below the detection limit). The lattice fringe image in Figure 5.4 clearly shows the film crystallinity. 124 Figure.5.3. A representative SEM image of the surface of the pristine V2O5 films on (a) Al and (b) Au. Figure.5.4. Lattice fringe image confirming the crystallinity of the pristine V2O5 films. The biaxial stresses in the crystallized films are reported in Table 5.1. These stresses can be induced by both the film deposition process and by the post deposition annealing process. In general, the tensile stresses here are indicative of densification during crystallization (i.e., the crystalline films have higher densities than the initial amorphous films). As noted above, the difference observed with Al and Au current collectors made it possible to vary the initial stress state in these materials, which is a 125 principle effect that motivated the work reported here. The cause of this stress difference was not explored in detail, although one possibility is that the lower yield stress of the Au current collector accommodated more of the volume contraction that occurred during crystallization. Sample Intrinsic stress measured (pristine film) V2O5 on Al (as deposited amorphous film) 0.5 GPa (tensile) V2O5 on Au (as deposited amorphous film) 0.5 GPa (tensile) V2O5 on Al (post annealing) 2.12 GPa (tensile) V2O5 on Au (post annealing) 1.25 GPa (tensile) Table.5.1. Initial stress measured in the pristine and as deposited films using MOSS. Electrochemical Cycling Galvanostatic experiments: The as-deposited (sputtered but not annealed) amorphous vanadium oxide films were cycled at a C-rate of C/20 against Li metal in the range of 4–2 V. These amorphous films showed good reversibility with minimal capacity fading even at later cycles (Figure 5.5). The stress response of these films during cycling was also largely reversible. Here the insertion of Li (lithiation) into the active material during electrochemical cycling induces net compression (relative to the initial stress in the film), and the extraction of Lithium from the lithiated vanadium oxide (during de-lithiation) induces tensile stress. These observations are consistent with the expectation that Li insertion increases the film volume to accommodate the guest ions. Furthermore, the nearly linear and symmetric response during Li insertion and removal is indicative of 126 elastic deformation (i.e., the material expands during Li insertion and then undergoes an analogous contraction during Li removal). 4.0 0.8 Voltage (V) vs Li/Li + 0.7 3.5 0.6 Stress (GPa) 3.0 0.5 2.5 0.4 0.3 2.0 0.2 9000 9100 9200 9300 9400 9500 Capacity (mAh/gm) Figure.5.5. Charge-discharge profile and accompanying stress evolution for as-deposited amorphous VOx films (no annealing). Note that the plot shows the 31st and 32nd cycle. In order to probe the influence of the stress state on phase changes, the crystalline films were galvanostatically cycled against Li metal. As expected, the electrochemical response showed voltage plateaus that correspond to phase transitions (co-existence of two phases) between different Li-intercalation stages of the V2O5 (see Figure 5.6). These plateaus along with the XRD and TEM results confirm that the thin film electrodes are well crystallized. The voltage plateaus observed with both current collectors are summarized in Table 5.2. The measured values are in general agreement with the plateaus reported for crystalline V2O5 films by various authors (see Table 5.2).With the Au current collector, cycling between 4-2 V produced plateaus for all of the expected LixV2O5 phases, down to x = 3 (i.e., the omega phase). With the Al current collector, 127 cycling to lower potentials was needed to observe this final transition (Figure 5.6). Table 5.2 shows comparisons between the plateaus observed in our experiments and literature values. Further analysis of the shift in these voltage plateaus and the role of stress are provided in the Analysis and Discussion section. The measured stress responses exhibit features which are similar with both current collectors. As noted above, compressive stresses during Li insertion correspond to volume expansion while tensile stresses are indicative of volume contraction. The experimental measurements during initial cycling (Figure 5.6) are nominally consistent with the reported LixV2O5 transformations, most of which lead to volume expansions during lithiation (but with some exceptions as noted in Table 5.4). More quantitative assessments of the relationships between the measured stresses and the specific volume changes are beyond the scope of the current investigation, in part because these films are partially textured and the volume changes associated with the LixV2O5 transformations are known to be anisotropic. However, it is important to note that the stress signatures are generally similar for the two current collectors, with the following key features:  Up to x = 2, the stress is primarily compressive (reflecting volume expansion).  For x > 2, large tensile stresses occur in both cases. This could reflect the transformation to the omega phase where significant contraction occurs when the structure changes from orthorhombic (a = 9.8 Å, b = 3.6 Å and c = 10.24 Å for -Li2V2O5) to tetragonal (a = 9.23 Å, b = 9.23 Å and c = 128 4.11 Å for -Li3V2O5). The films may also be subject to amorphization at this point.  During initial delithiation, both the voltage and stress responses differ substantially from the corresponding portion of the lithiation cycle. In particular, the  to  voltage plateau is not observed and the stress is tensile (reversible elastic behavior here would have been compressive). These observations are consistent with the irreversible amorphization that is expected to occur here. 129 (a) 4.0 V2O5 on Al 2.4 1st cycle 3.5 3.33  + Voltage (V) vs Li/Li 3.175  2.2 Stress (GPa) 3.0 2.12 2.0 2.5  2.118 2.0  1.944 1.8 1.5 + Li insertion Li+ de-insertion 1.6 0 100 200 300 400 Capacity (mAh/gm) (b) 4.0 V2O5 on Au 1.4 1st cycle 3.5 + 1.25 Voltage (V) vs Li/Li  1.2 Stress (GPa) 3.202 3.0 1.0 2.5  2.312 0.8  2.038 + + 2.0 Li insertion Li de-insertion 0 200 400 600 Capacity (in mAh/g) Figure.5.6. In-situ voltage and stress measurements for crystalline a) V 2O5 film on Al (cycled galvanostatically against Li metal in 4-1.5 V range) and b) V2O5 film on Au current collectors (cycled galvanostatically against Li metal in the 4-2 V range). 130 S. No Phase Voltage plateau Reference 1  ~3.2 V 19  ~2.3 V  ~1.9 V 2  ~3.2 V 5  ~2.3 V  ~1.95 V 3  ~3.3 V 4  ~3.2 V  ~2.3 V  ~2-2.1 V 4  ~3.3 V 20  ~3.2 V  ~2.3 V  ~2.1 V 5  ~2.2-2.3 V 21  ~2-2.1 V 6  ~3.35 V 22  ~3.23 V  ~2.3 V  ~2.1 V 7  ~3.35 V 10  ~3.2 V  ~2.3 V  ~2-2.1 V 8  ~3.15 V 23  ~2.3 V  ~1.9 V 9  V2O5 film on V2O5 film on This study  Al Au  3.33 V  3.175 V 3.202 V  2.118 V 2.312 V  1.944 V 2.038 V Table.5.2. Variations in the two phase plateaus observed by different authors throughout the literature and those observed in this study. 131 During subsequent cycles (not shown here), the voltage plateaus become less pronounced. This can be attributed to the loss of crystallinity. Considerable irreversible capacities were also observed during the first few cycles, which others have attributed to irreversible structural damage and amorphization of V2O5 films.8, 23, 24 Thus, these amorphized materials resemble the results obtained with the amorphous films (Figure 5.5). Potentiostatic experiments: We employed constant voltage holds in order to ensure complete lithiation and delithiation of the active material in the two systems studied here. A typical voltage-current-time plot is shown in Figure 5.7. These holds were maintained until the films were equilibrated with the final potential (defined here as a current <4*10-8 A). -6 6.0x10 4.0 V2O5 on Al 1st cycle -6 3.5 3.0x10 + Voltage (V) vs Li/Li Current (A) 3.0 0.0 2.5 -6 -3.0x10 2.0 -6 -6.0x10 0 10 20 30 40 50 Time (in hrs) Figure.5.7. A typical current response of a V2O5 film on Al at constant voltage holds at 4, 3 and 2 V against Li metal. 132 Post cycling XRD measurements (Figure 5.8) were then conducted after three charge/discharge cycles with potentiostatic holds at 4, 3 and 2 V. For the film on Al, the active material gradually changes structure with subsequent cycles. This is confirmed by the broadening of the (001) peak, the decrease in the peak intensity, and the lowering of the theta value (maintaining the orthorhombic structure). In comparison, for the film on Au, the active film on Au has completely amorphized at the end of 3rd cycle (i.e., the (001) peak completely vanishes). 133 V2O5 on Al a) V2O5(001) Al (111) Al (200) annealed Al Intensity coated substrate * V2O5(002) * pristine film * FWHM=0.36 * after 3 cycles FWHM=0.42 after 5 cycles FWHM=0.49 10 20 30 40 50 2 (b) V2O5 on Au Au (111) Au (200) V2O5 (001) Intensity V2O5 (002) pristine film FWHM= 0.39 after 3 cycles 10 20 30 40 50 2 Figure.5.8. Post cycling XRD measurements of a) V2O5 film on Al and b) V2O5 film on Au cycled potentiostatically with voltage holds at 4, 3 and 2 V. 134 Figure.5.9. Voltage-capacity curves for a) V2O5 film on Al and b) V2O5 film on Au cycled galvanostatically between 4-2 V. Figure 5.8 and 5.9 further confirm that when the films on Al were cycled between 4-2 V they did not lead to the formation of the  phase and subsequent amorphization. This is consistent with the plateau for formation that was observed at 1.94 V in Figure 5.6. In contrast, for the films on Au, the  phase forms at 2.04 V and thus the film amorphizes after just one discharge cycle (also marked by less prominent two phase plateaus during the second discharge cycle in Figure 5.9(b)). Figure 5.10 shows the top surface of the V2O5 film on Al and Au after 3 potentiostatic cycles. It is clear that the film on Au undergoes a significant surface change compared to the film on Al. This further strengthens the previous observations i.e., the film on Au (with lower intrinsic stress state) undergoes a faster amorphization compared to the film on Al (with higher initial stress state). 135 Figure.5.10. SEM images comparing the top surfaces of the V2O5 films on (a) Al and (b) Au after 3 potentiostatic charge-discharge cycles. 5.4 Analysis and Discussion Stress evolution in crystalline V2O5 films may be interpreted in light of their lattice parameter evolution during lithiation/delithiation cycles. Tables 5.3 and 5.4 list respective lattice parameter values calculated using first principles study and found experimentally. The isotropic strains correspond to cases where the grains are randomly oriented. Whereas, the in-plane orthotropic strain corresponds to the ideal case of perfect texturing (i.e. grains oriented with the c-axis normal to the substrate). As observed from Tables 5.3 and 5.4, the isotropic strain values show significant volume expansions whereas the in-plane orthotropic strain values shows comparatively smaller contractions when Li is inserted in the active material. This along with Figure 5.2 and Figure 5.8 suggests that the texturing in the films is probably responsible for the lower measured stress values. 136 x in a (Å) b (Å) c (Å) Volume % strain Expected in- LixV2O5 [Ref. [Ref. [Ref. (Å3) plane 20] 20] 20] Isotropic In-plane orthotropic orthotropic stress (MPa) (Bi-axial modulus ~ 150 GPa) 0 11.69 3.59 4.48 188.0126 -- -- -- 0.5 11.42 7.17 4.72 386.4802 0.927 -0.012 - 18 1 11.35 3.63 9.97 410.769 3.080 -0.255 -382.5 2 9.9 3.73 10.48 386.995 0.972 -0.280 -420 20 Table.5.3. Lattice parameters (as calculated by Rocquefelte et al. ) and the volumetric strains corresponding to the values of x in LixV2O5. Note that the stress and strain are calculated with respect to x = 0. x in a (Å) b (Å) c (Å) Volume % strain Expected in- LixV2O5 (Å3) plane Isotropic In-plane orthotropic orthotropic stress (MPa) (assumed Bi- axial modulus ~ 150 GPa) 0 11.51 3.56 4.37 179.063 -- -- -- [Ref. 25] 0.5 11.41 7.13 4.52 367.716 0.893 -0.004 -6 [Ref. 26] 1 11.24 3.6 9.91 400.998 3.990 -0.253 -379.5 [Ref. 27] 2 9.8 3.6 10.24 361.267 0.292 -0.285 -427.5 [Ref 28] Table.5.4. Lattice parameters (as found experimentally from different references) and the volumetric strains corresponding to the values of x in LixV2O5. Note that the stress and strain are calculated with respect to x = 0. Simplified Two Phase Equilibrium The difference in the chemical potentials between the active material (i.e., V2O5 here) and the counter electrode (i.e., Li metal here) acts as the chemical driving force for lithium ion exchange in the active material. It can be expressed as the standard Gibbs free 137 energy change per mole of reaction, Gf. The balance between the chemical and electrical forces upon lithium exchange and under open circuit conditions can be expressed as: ∆𝐺𝑓 = −𝑧𝐹∆𝜙 (5.2) where F is the energy required to move the electrons from the positive to the negative electrode, z is the charge number of mobile ionic species (+1 in case of Li+ ions), F is the Faraday constant and  is the potential difference between the two electrodes. Upon lithiation/delithiation, crystalline V2O5 undergoes several phase transformations. As such, during the co-existence of two phases, the charge/discharge profiles of the material exhibits constant voltage plateaus (as seen in Figure 5.6). A schematic showing the expected two phase transformation (phase p  phase q) upon lithiation is shown in Figure 5.11(a). Other possible configurations are clearly possible (i.e., random nucleation of q grains in the p film). In the absence of specific information about way in which this phase transformation proceeds, the bi-layer configuration in the Figure 5.11 provides a useful basis for our basic analysis. 138 Figure.5.11. Schematic showing (a) the representative phase transformation (from phase p  phase q) upon lithiation of a material, and (b) graphical representation of the free energy curves of two phases, p and q with (solid lines) and without (dashed lines) strain energy contributions. The terms U po and U qo are the elastic strain energy terms as given in Equation 5.5 and 5.6, respectively. Note that the two phases p and q are pseudo 𝑝 𝑜𝑟 𝑞 𝑝 𝑜𝑟 𝑞 𝑝,𝑒𝑞𝑚 binary phases consisting of oxide (V2O5) and Li i.e., 𝑐𝐿𝑖 = 1 − 𝑐𝑜𝑥𝑖𝑑𝑒 . 𝑐𝐿𝑖 and 𝑞,𝑒𝑞𝑚 𝑐𝐿𝑖 are the equilibrium concentrations of Li in phase p and q, respectively in the two phase co-existence region. Also, the shape of these free energy curves are chosen at random. The exact shape of these curves is outside the scope of this work. 139 During the beginning of the voltage plateau, lithium addition to the host material results in formation of phase q. With further lithiation, the composition of the two phases does not change, but the relative amount of the phase with higher Li content (phase q) increases at the expense of the initial phase p; this results in the movement of the interface between the two phases, as illustrated in Figure 5.11(a). Towards the end of the voltage plateau, all of phase p is consumed and the host material transforms to phase q (Li-rich phase). Stress in the active material (intrinsic and/or extrinsic) can contribute to the difference in the chemical potential between the active material and the counter electrode for lithiation/delithiation, thereby causing shifts in the two-phase equilibrium voltage plateaus in the charge/discharge profiles.29,30 A representative schematic of the stress induced shift in the free energy curves of the two phases and the corresponding shifts in the two phase equilibrium voltage plateau is shown in Figure 5.11(b). This is consistent with the observation in the Results section where galvanostatic and potentiostatic cycling experiments indicate that the phase transformations occur at lower potentials with the Al current collector, for example,  to , voltage plateau occurs at 1.944 V for the film on Al compared to 2.038 V for the film on Au. In particular, the galvanostatic comparisons (Figure 5.6 and Table 5.2) provide a quantitative measure of the voltages where the two phase plateaus occur. The electrochemical and the corresponding stress measurements discussed in the Results section can be analyzed in this context using the model presented below. 140 Impact of Stress on Two Phase Equilibrium– Simplified Formulation The schematic for the basis of this model is shown in Figure 5.11. In the absence of any stress contributions, the free energy of two phases, p and q, can be given as: Gmo, p  cLip  Lip  coxide p oxide p (5.3) Gmo,q  cLiq  Liq  coxide q oxide q (5.4) where 𝐺𝑚𝑜,𝑝 and 𝐺𝑚𝑜,𝑞 are the molar gibbs free energy of phases p and q (in absence of strain energy contributions), respectively. Each phase here is treated as a pseudo-binary that consists of oxide (V2O5 in this case) and Li components, where c and 𝜇 are the molar fractions and chemical potentials, respectively, and the subscripts and superscripts are the component and phase, respectively such that, 𝑐𝑜𝑥𝑖𝑑𝑒 + 𝑐𝐿𝑖 = 1 in each of the phases. As mentioned earlier, elastic strain energies will modify thermodynamic equilibrium and thus alter the relationship between the equilibrium voltage and the composition of a material. Incorporating the elastic strain energy terms then modifies the free energies to: Gmp  Gmo, p  U po (5.5) Gmq  Gmo,q  U qo (5.6) where U po and U qo are elastic strain energy terms given as, U po  Vmp M p [ op ]2 and U qo = Vmq M q [ op   op q ]2 and 𝑉𝑚 ’s, M’s, and 𝜀𝑜 ’s are the molar volumes, bi-axial 141 𝑝 moduli, and the reference strains in the phases (i.e., 𝜀𝑜 is the initial strain in phase pin absence of any phase transformation due to lithiation and similarly for phase q), 𝑝 𝑞 𝑉𝑚 −𝑉𝑚 respectively and 𝜀𝑜𝑝→𝑞 is the corresponding phase transformation strain (𝜀𝑜𝑝→𝑞 = 𝑞 ). 3𝑉𝑚 In a binary system, the two phase equilibrium voltage plateau can be represented by drawing common tangents to the free energy curves of the two phases (Figure 5.11(b)). The standard construction for two phase equilibrium corresponds to equating the chemical potentials for the two phases: 𝑝 ,𝑒𝑞𝑚 𝑝 ,𝑒𝑞𝑚 𝑞,𝑒𝑞𝑚 𝑞 ,𝑒𝑞𝑚 𝑒𝑞𝑚 𝑝,𝑒𝑞𝑚 𝑞,𝑒𝑞𝑚 𝑐𝑜𝑥𝑖𝑑𝑒 𝐺𝑚 −𝑐𝑜𝑥𝑖𝑑𝑒 𝐺𝑚 𝜇𝐿𝑖 = 𝜇𝐿𝑖 = 𝜇𝐿𝑖 = 𝑝 ,𝑒𝑞𝑚 𝑞,𝑒𝑞𝑚 (5.7) 𝑐𝑜𝑥𝑖𝑑𝑒 −𝑐𝑜𝑥𝑖𝑑𝑒 Assuming, the impact of stress on the equilibrium composition of the phases to be small and Mp=Mq=M, we get: 𝑝,𝑒𝑞𝑚 𝑞 𝑞,𝑒𝑞𝑚 𝑝 𝑝 𝑒𝑞𝑚 𝑐 𝑉𝑚 − 𝑐𝑜𝑥𝑖𝑑𝑒 𝑉𝑚 𝑝 2 −FΔ𝜙 𝜀𝑜 = 𝜇𝐿𝑖 𝑜 = 𝜇𝐿𝑖 + 𝑀[ 𝑜𝑥𝑖𝑑𝑒 𝑝,𝑒𝑞𝑚 𝑞,𝑒𝑞𝑚 [𝜀𝑜 ] 𝑐𝑜𝑥𝑖𝑑𝑒 − 𝑐𝑜𝑥𝑖 𝑑𝑒 𝑝 ,𝑒𝑞𝑚 𝑞 𝑐𝑜𝑥𝑖𝑑𝑒 𝑉𝑚 𝑝 +( 𝑝 ,𝑒𝑞𝑚 𝑞 ,𝑒𝑞𝑚 2𝜀𝑜 𝜀 𝑝→𝑞 + 𝜀 𝑝→𝑞 )2 ] (5.8) 𝑐𝑜𝑥𝑖𝑑𝑒 −𝑐𝑜𝑥𝑖𝑑𝑒 Equation 5.8 can be rearranged as follows to calculate the potential difference between the films on Al and Au (i.e., films with different initial stress states), for any of the two phase equilibrium plateaus: 𝑝,𝑒𝑞𝑚 𝑞 𝑞,𝑒𝑞𝑚 𝑝 1 𝑐𝑜𝑥𝑖𝑑𝑒 𝑉𝑚 − 𝑐𝑜𝑥𝑖𝑑𝑒 𝑉𝑚 Δ𝜙 𝐴𝑙 𝜀𝑜𝑝,𝐴𝑙 − Δ𝜙 𝐴𝑢 𝜀𝑜𝑝,𝐴𝑢 =− [ 𝑝,𝑒𝑞𝑚 𝑞,𝑒𝑞𝑚 ([𝜎𝑜𝑝,𝐴𝑙 ]2 − [𝜎𝑜𝑝,𝐴𝑢 ]2 ) 𝐹𝑀 𝑐𝑜𝑥𝑖𝑑𝑒 − 𝑐𝑜𝑥𝑖𝑑𝑒 𝑝 ,𝑒𝑞𝑚 𝑞 𝑐 𝑉 𝑝,𝐴𝑙 𝑜𝑥𝑖𝑑𝑒 𝑚 + (𝑐 𝑝 ,𝑒𝑞𝑚 −𝑐 𝑞,𝑒𝑞𝑚 2(𝜎𝑜 − 𝜎𝑜𝑝,𝐴𝑢 )𝜎 𝑝→𝑞 ] ] (5.9) 𝑜𝑥𝑖𝑑𝑒 𝑜𝑥𝑖𝑑𝑒 142 where Δ𝜙 𝐴𝑙 and Δ𝜙 𝐴𝑢 are the two phase equilibrium plateau for the film on Al and Au, respectively and 𝜎𝑜𝑝,𝐴𝑙 (= 𝑀𝜀𝑜 )and 𝜎𝑜𝑝,𝐴𝑢 (= 𝑀𝜀𝑜 𝑝,𝐴𝑙 𝑝,𝐴𝑢 ) are the intrinsic stresses in the films deposited on Al and Au, respectively. Substituting the value of M from reference [31], 𝜎𝑜𝑝,𝐴𝑙 , 𝜎𝑜𝑝,𝐴𝑢 and 𝜎 𝑝→𝑞 as measured by MOSS, and 𝑉𝑚𝑝 and 𝑉𝑚𝑞 as calculated using a theoretical density of V2O5 as 3.36 gm/cc in Equation 5.9, one can determine the difference in the equilibrium potential values for the two phase plateaus. For example, using Equation 5.9 to calculate the difference in the equilibrium potential values for the  phase transformation for the films on Al and Au gives a difference of -0.25 V apart (i.e., the film on Al should show the  plateau at a potential 0.25 V lower than the film on Au). Similar calculations for the  phase transformation predict that the film on Al should show the  plateau at a potential 0.17 V lower than the film on Au. These values were calculated using the respective 𝜎𝑜𝑝,𝐴𝑙 , 𝜎𝑜𝑝,𝐴𝑢 and 𝜎 𝑝→𝑞 values from Figure 5.6 and the values tabulated in Table 5.6. The differences in the calculated and the experimentally measured values as listed in Table 5.5 could arise from uncertainties associated with the values of the thermodynamic parameters such as molar volumes of each phases, mechanical constants, texturing of the film and/or configuration of the material system. However, the magnitude of the predicted stress-induced voltage shifts are similar to those measured experimentally in this study (Table 5.5). It is important to note here that, in the current study, the initial stress state (i.e., before electrochemical cycling) for the V2O5 films on Al and Au current collectors are tensile. Moreover, the film on Al has a higher initial stress than the film on Au (2.12 and 1.25 GPa for the films on Al and Au, respectively). These stresses are much 143 higher than the stress generated in the V2O5 films due to lithiation induced phase transformation. Also, these phase transformation induced stress are similar for both films. For example, the stress induced by the  phase transformation in both the films is ~ 270 MPa. As such, at any given state of charge, the film on Al has a higher net tensile stress than the film on Au. Therefore, the strain energy contributions to the free energy for the film on Al will always be higher than that for the film on Au. The schematic in Figure 5.12 shows this relative position, along with the corresponding tangent construction. This shows that the larger strain energy in the Al film causes a larger shift in the voltage plateau. This conclusion is the same, regardless of whether the phase transformation produces compressive or tensile stress (i.e., the two cases shown in Table 5.5). On the other hand, for the case when the stress induced due to the phase transformation is comparable or higher than the initial stress state (for example, in the bulk geometries), then depending on the stress states (compression or tension) and magnitudes of the initial and phase transformation induced stresses, strain energy contributions to the free energy curves may vary and cause a different response to these two phase equilibrium voltage shifts. 144 Figure.5.12. A graphical representation of the free energy curves of V2O5 film on Al (solid line) and Au (long dash dot line) for two phases, p and q with and without (dashed lines) strain energy contributions. The shape of these free energy curves are chosen at random. The exact shape of these curves is outside the scope of this work. Two Equilibrium plateau Potential drop (Al(op,Al)Au(op,Al)) phases position present Film on Al Film on Au measured calculated using Eqn. 5.9 experimentally  2.118V 2.312V -0.194V -0.25 V  1.944V 2.038V -0.094V -0.17 V Table.5.5. Equilibrium plateau positions for the film on Al and the film on Au and the potential drop calculated using Equation 5.9. 145 𝑝𝑕𝑎𝑠𝑒 ,𝑒𝑞𝑚 𝑝𝑕𝑎𝑠𝑒 ,𝑒𝑞𝑚 𝑝𝑕𝑎𝑠𝑒 Phase Chemical 𝑐𝐿𝑖 𝑐𝑜𝑥𝑖𝑑𝑒 Density of 𝑉𝑚 Composition the phase (cm3) (gm/cc)  Li0.1V2O5 0.09 0.91 3.36 54.33  Li0.5V2O5 0.33 0.67 3.36 55.16  LiV O 2 5 0.5 0.5 3.36 56.19  Li2V2O5 0.67 0.33 3.36 58.26  Li3V2O5 0.75 0.25 3.36 60.32 Table.5.6. Details about individual phases of lithiated V2O5. Note that, the density of each phase is taken to be the same as V2O5.As such, Vm of each of the phases is calculated using this value. As mentioned earlier, the model outlined above is a basic formulation which is designed to show that stress contributions can have a significant impact on the two phase equilibrium thermodynamics. It assumes that the phase propagation takes place in accordance with the schematic in Figure 5.11. Moreover, it assumes that the impact of stress on the equilibrium composition of each of the phases is negligible. Also, the above model assumes that the lithiation induced volume changes in both the phases are compatible. These are acceptable assumptions for the bi-layer configuration used here, but would be invalid in the bulk electrode where lithiation induced stress fields are more complex and where the equilibrium Li concentration in the new phase is dependent on the stress state of the particle. As such, there is a need to develop an evolved model that is not limited by the aforementioned assumptions and takes into account the chemical and stress contributions to the Gibb's free energy. With this in mind, we attempted to formulate a preliminary model, using which one can calculate the total change in the Gibb’s free energy in the two phases p and q, by summing the chemical component, Gchem, given by Equation E.1.5 and the stress component, G (adapted from Bucci et al.30). This model is discussed in Appendix E. 146 In summary, the effect of stress on two phase equilibrium differs from that for a single phase equilibrium. For a single phase equilibrium case, tensile and compressive stresses will always produce opposite effects i.e., when the stresses are tensile, incorporating the stress contribution to the standard Nerst equation will lower the equilibrium potential and the opposite is true for the case of compressive stresses. However, as discussed in this chapter, this is not necessarily true for the two phase equilibrium case (especially when the two phases have a narrow Li composition range). In such cases, magnitudes and sign of the initial and phase transformation induced stresses in the active material can affect the two phase equilibrium voltage shifts in different ways (differs when the net stress in the film results in tension or in compression). Therefore, it is paramount to study the strain energy shifted free energy curves of both the phases that are involved in the phase transformation to completely understand stress induced equilibrium voltage shifts. 5.5 Conclusions Vanadium oxide thin films were sputter deposited on Al and Au current collectors. Annealing these as-deposited films in the same annealing atmosphere resulted in crystalline V2O5 films that had different initial internal stress states. Electrochemical cycling induced stress evolution in these films were measured by MOSS technique while Li ions were inserted/extracted from the films either galvanostatically or potentiostatically in a custom built half cell. Comparison of the electrochemical cycling behavior of the two films reveal that the two phase equilibrium voltage plateaus for the 147 film on Al (with relatively higher initial tensile stress state) forms at lower voltages compared to that for the film on Au (with lower initial tensile stress state).To gain further insight into such a dependence of two phase equilibrium kinetics on the stress state of the films, a thermodynamic model was employed that takes into account the impact of intrinsic stresses (i.e., stress state of the pristine film) and extrinsic stresses (i.e., stress induced due to electrochemical cycling). The experiments and analysis reveal that stress in the electrode can significantly alter the voltage plateaus associated with two phase equilibria. This indicates that the initial stress states in crystalline thin films can be used as a tunable parameter to control the cycling induced phase transformation/amorphization of the active host material. 148 5.6 References 1. M. S. Whittingham, Journal of the Electrochemical Society, 123, 315 (1976). 2. J. G. Zhang, J. M. McGraw, J. Turner and D. Ginley, Journal of the Electrochemical Society, 144, 1630 (1997). 3. E. J. Jeon, Y. W. Shin, S. C. Nam, W. I. Cho and Y. S. Yoon, Journal of the Electrochemical Society, 148, A318 (2001). 4. Y. Wang and G. Z. Cao, Chemistry of Materials, 18, 2787 (2006). 5. J. Scarminio, A. Talledo, A. A. Andersson, S. Passerini and F. Decker, Electrochimica Acta, 38, 1637 (1993). 6. R. Schöllhorn, in, p. 149, Chemical Physics of Intercalation, NATO Series B, Plenum, New York (1987). 7. J. M. Cocciantelli, J. P. Doumerc, M. Pouchard, M. Broussely and J. Labat, Journal of Power Sources, 34, 103 (1991). 8. Y. J. Park, K. S. Ryu, K. M. Kim, N. G. Park, M. G. Kang and S. H. Chang, Solid State Ionics, 154, 229 (2002). 9. S. Koike, T. Fujieda, T. Sakai and S. Higuchi, Journal of Power Sources, 81, 581 (1999). 10. C. Delmas, H. Cognacauradou, J. M. Cocciantelli, M. Menetrier and J. P. Doumerc, Solid State Ionics, 69, 257 (1994). 11. J. M. McGraw, J. D. Perkins, J. G. Zhang, P. Liu, P. A. Parilla, J. Turner, D. L. Schulz, C. J. Curtis and D. S. Ginley, Solid State Ionics, 113, 407 (1998). 12. Y. J. Park, K. S. Ryu, N. G. Park, Y. S. Hong and S. H. Chang, Journal of the Electrochemical Society, 149, A597 (2002). 13. A. Mukhopadhyay, A. Tokranov, K. Sena, X. C. Xiao and B. W. Sheldon, Carbon, 49, 2742 (2011). 14. S. K. Soni, B. W. Sheldon, X. C. Xiao and A. Tokranov, Scripta Materialia, 64, 307 (2011). 15. S. K. Soni, B. W. Sheldon, X. C. Xiao, M. W. Verbrugge, D. Ahn, H. Haftbaradaran and H. J. Gao, Journal of the Electrochemical Society, 159, A38 (2012). 16. J. A. Floro, E. Chason and S. R. Lee, Material Research Society Symposium Proceedings, 406, 491 (1996). 17. E. Chason and B. W. Sheldon, Surface Engineering, 19, 387 (2003). 149 18. L. B. Freund and S. Suresh, Cambridge University Press, Cambridge (2003). 19. A. Benayad, H. Martinez, A. Gies, B. Pecquenard, A. Levasseur and D. Gonbeau, Journal of Physics and Chemistry of Solids, 67, 1320 (2006). 20. X. Rocquefelte, F. Boucher, P. Gressier and G. Ouvrard, Chemistry of Materials, 15, 1812 (2003). 21. P. Rozier, J. M. Savariault and J. Galy, Solid State Ionics, 98, 133 (1997). 22. J. M. McGraw, C. S. Bahn, P. A. Parilla, J. D. Perkins, D. W. Readey and D. S. Ginley, Electrochimica Acta, 45, 187 (1999). 23. A. Shimizu, T. Tsumura and M. Inagaki, Solid State Ionics, 63-5, 479 (1993). 24. S. Oukassi, R. Salot and J. P. Pereira-Ramos, Applied Surface Science, 256, 149 (2009). 25. R. Enjalbert and J. Galy, Acta Crystallographica Section C-Crystal Structure Communications, 42, 1467 (1986). 26. J. M. Cocciantelli, Caracte´risation physico-chimique d’e´lectrodespositives de composition LixV2O5, in, Bordeaux (1990). 27. R. J. Cava, A. Santoro, D. W. Murphy, S. M. Zahurak, R. M. Fleming, P. Marsh and R. S. Roth, Journal of Solid State Chemistry, 65, 63 (1986). 28. J. M. Cocciantelli, M. Menetrier, C. Delmas, J. P. Doumerc, M. Pouchard and P. Hagenmuller, Solid State Ionics, 50, 99 (1992). 29. V. A. Sethuraman, V. Srinivasan, A. F. Bower and P. R. Guduru, Journal of the Electrochemical Society, 157, A1253 (2010). 30. G. Bucci, S. P. V. Nadimpalli, V. A. Sethuraman, A. F. Bower and P. R. Guduru, Journal of the Mechanics and Physics of Solids, 62, 276 (2014). 31. T. Reeswinkel, D. Music and J. M. Schneider, Journal of Physics-Condensed Matter, 21 (2009). 150 CHAPTER 6 CONCLUSIONS AND FUTURE DIRECTIONS 6.1 Conclusions This thesis primarily examines the in-situ evolution of the compositional stresses, obtained by wafer curvature measurements, in three material systems; 10% Praseodymium doped ceria (PCO), spinel Li1+xMn2O4 (LMO), and V2O5, in thin film configuration. This chapter summarizes our contributions by highlighting the key results and discussing the potential research extension of this thesis. PCO system PCO thin films used in Chapters 2 and 3 were prepared on elastic substrates (sapphire or YSZ) by pulsed laser deposition system. The study discussed in Chapter 2 revealed that the PCO films supported on sapphire exhibit similar oxygen content to films supported on YSZ. Moreover, comparison of oxygen content with prior film and bulk defect modeling uncovered a trend of shifting defect formation energy from lower values (consistent with the thin film model) at 700 and 750oC to higher values (consistent with the bulk model) at 800 and 850oC. It was also found that the thin film chemical expansion coefficients decrease with increasing temperature, and were about 18% less than in the bulk solid. On one hand, the wafer curvature measurements performed on PCO films 151 supported on YSZ substrates were not reversible; on the other hand, films supported on sapphire substrates exhibited reproducible behavior. We believe that the stress relaxation observed for the PCO films on YSZ may be associated with differences in the grain boundary structures (as observed by TEM). Comparison of the measurements conducted on the PCO films on YSZ and sapphire substrates revealed that the choice of the substrate plays a crucial role in determining the film morphology and thereby governs the properties of the oxide thin film. In Chapter 3 we discussed the dependence of stress and strain evolution on the average grain size of PCO films on sapphire. Comparison of the stress and strain measurement with varying oxygen partial pressure at 750oC revealed that the compositional stress and the lattice parameter increases with decreasing grain sizes for the PCO films. These results demonstrate that the grain boundary effects dominate the compositional stresses in these films. Also, it was found that the average elastic constants are similar for the PCO films with different grain sizes. We used an existing analytical model that assumes the polycrystalline PCO films to have a brick-layer topology to explain the experimental findings. The calculations from the model indicate that space charge effects can substantially enhance stresses due to chemical expansions. LMO system In Chapter 4, we discussed the electrochemical cycling induced stress evolution in spinel LMO thin films. These films were prepared using a solution-derived technique. In this study, it was observed that initial delithiation from spinel LMO (in 4.3-3.5 V range) induced tensile stress up to ~4.05 V (vs. Li/Li+); however, continued delithiation beyond 152 4.05 V, resulted in a reversal of the induced stress direction (termed as the “anomalous drop”). During the first lithium insertion step, there was a steady buildup of compressive stress. In subsequent cycles the induced stress evolved reversibly with the stress becoming tensile during delithiation and compressive during lithiation. Absence of apparent micro-cracks/fracture in cycled LMO samples suggested that the anomalous drop did not arise from mechanical damage during cycling. Stress measurements on LMO films with varying thicknesses showed that both surface and bulk effects contribute toward the first cycle anomalous drop. Based on the experiments described in the chapter, we conjectured that a combination of electrochemically induced creation of oxygen vacancies and delithiation induced loss of crystallinity in the bulk of the material during first delithiation (beyond 4.05 V) was responsible for the irreversible structural changes that resulted in the first cycle anomalous drop. V2O5 system In Chapter 5, we discussed the impact of stress (intrinsic and extrinsic) on electrochemically induced phase transformations in V2O5 thin films. Vanadium oxide thin films were sputter deposited on Al and Au current collectors. Annealing these as- deposited films in the same annealing atmosphere resulted in crystalline V2O5 films that had different initial internal stress states. Comparison of the electrochemical cycling behavior of the two films revealed that the two phase equilibrium voltage plateaus for the film on Al (with relatively higher initial tensile stress state) forms at lower voltages compared to that for the film on Au (with lower initial tensile stress state). A thermodynamic model was employed that takes into account the impact of intrinsic 153 stresses (i.e., stress state of the pristine film) and extrinsic stresses (i.e., stress induced due to electrochemical cycling). The experiments and analysis revealed that stress in the electrode can significantly alter the voltage plateaus associated with two phase equilibria. This indicates that the initial stress states in crystalline thin films can be used as a tunable parameter to control the cycling induced phase transformation/amorphization of the active host material. 6.2 Future Work In this thesis, we introduced multiple techniques and analytical models to study the interdependence of the electrical-chemical-mechanical properties of oxide thin films used for SOFC and LIB applications. The ideas presented in this dissertation could be extended through the following possible research directions:  Additional MOSS and TEM experiments could be planned to gain insight into the stress relaxation mechanisms observed for the PCO films on YSZ in Chapter 2.  The analytical model used in Chapter 3 could be extended to other non- stoichiometric oxides used as electrodes and solid electrolytes in electrochemical energy storage and conversion devices. A detailed chemo-mechanical model that separates the stress contributions in the grain boundary core and that in the space charge regions could be developed to reveal important contributions from the space charge effects. 154  Studies exploring the dependence of stress and strain evolution in ceria over a broad range of temperature and as a function of dopant concentration could also be undertaken.  In order to get a better understanding of the phenomena that led to the anomalous drop in LMO (as discussed in Chapter 4), computational (DFT based) and TEM based studies could be undertaken. These studies could provide insights into any structural anomalies (for example, secondary phases) present in the active material and could also shed light into the possibility of lithiation induced structural change in LMO (at the surface and/or in the bulk of the electrode).  The studies discussed in Chapters 4 and 5 are an essential step toward an in-depth understanding of the stress evolution in thin film cathodes used in Li-ion batteries. In these chapters the in-situ studies were only focused on LMO and V2O5 thin film cathodes. Such studies could be extended to other more practical cathode materials such as Li1+x(NiyCozMn1-x-y-z)O2, LiCoO2, Li(AlxNiyCo1-x-y)O2, etc. Moreover, the analytical model discussed in Chapter 5 could also be extended to these cathodes as well as anodes in order to get a comprehensive understanding of the impact of stress on the electrochemical cycling of the battery electrodes. 155 APPENDIX A ADDITIONAL MEASUREMENTS ON PCO SAMPLES A.1 Determination of Coefficient of Thermal Expansion (CTE) of PCO One of the advantages of the MOSS technique employed in this thesis (described in Chapters 2-5) is that one can determine the thickness averaged stress state of the film without knowing the values of the mechanical constants like the elastic modulus, poisson’s ratio, etc. for the film under study. The above statement is true as long as the film-substrate system satisfies the following assumptions of the Stoney’s equation: i) The film thickness (hf) is much smaller than the thickness of the substrate (hs). ii) Both hs and hf are very small compared to the lateral extent of the film substrate system. iii) The substrate material is homogeneous, elastic and isotropic. The PCO (Pr0.1Ce0.9O2) film on sapphire substrate used in our study (Chapters 2 and 3) do satisfy these assumptions and so, it is possible to employ the MOSS technique to measure the film-substrate curvature,  and relate it to the thickness average stress state in the PCO film by applying Stoney’s equation.1 156 Besides being able to measure the stress state of the film, MOSS can also be used to predict the mechanical properties (e.g., coefficient of thermal expansion, elastic modulus etc.) of the film. In the present work, we attempted to determine the CTE value of the PCO film by measuring the thermal stress that the film (avg. grain size of 72 nm) undergoes when heated from room temperature to desired experimental temperatures. As described in Chapter 3, the standard experimental protocol for our HTMOSS measurements of the PCO films included heating the sample from room temperature to the desired experimental temperature under 0.13 atm. of oxygen. Given that the PCO film and the sapphire substrate have different CTE values, this increase in temperature would result in the PCO film experiencing a thermal stress. The value of this thermal stress is then given by the difference in the steady state stress (i.e., the equilibrated stress at desired temperature and 0.13 atm. O2) from the reference stress (i.e., the stress at room temperature). A typical time dependent in-situ MOSS measurement for measuring the thermal stress experienced by a PCO film is shown in Figure A.1.1 ((a) at 750oC and (b) at 800oC). As seen in Figure A.1.1, the film experiences a thermal stress of 1465 MPa and 1597 MPa when heated from room temperature to 750oC and 800oC respectively. The measured thermal stresses are in the compressive direction due to the larger CTE value of the film compared to the substrate. These thermal stress values can be related to the CTE difference between the film and the substrate as follows: 157 T1 E  thermal   ( sapphire   film )dT (1   ) 298 A.1.1 where thermal is the thermal stress that the film experiences, E is the elastic modulus of the film,  is the poisson’s ratio, T1 is the desired experimental temperature and sapphire and film are the CTE values for the sapphire substrate and the PCO film respectively. The room temperature is 298K. 158 (a) 1000 Heated from room temp 900 o Temperature and stress allowed to equilibrate 500 to 750 C at before the pO step change) Change in Stress (MPa) 2 0.13 atm 750 of O2 o Temp= 750 C Temperature ( C) 0 600 -500 450 300 -1000 o 150 -1465 -1500 0 0 5000 10000 15000 20000 Time (sec) (b) 1000 Heated from Temperature and stress allowed to equilibrate 900 room temp before the pO2 step change) Change in Stress (MPa) o 500 to 800 C at 0.13 atm Temp= 800 C 750 o of O2 Temperature ( C) 0 600 -500 450 300 -1000 o 150 -1500 -1597 0 0 5000 10000 15000 20000 Time (sec) Figure A.1.1. MOSS measurement of a PCO film (avg. grain size of 72 nm) heated from room temperature (25oC) to (a) 750oC and (b) 800oC. Note that the room temperature stress is taken as the reference stress state and so the change in stress at room temperature in the plots shown in (a) and (b) has a value of zero MPa. 159 As per Bates et al.,2 the CTE value of sapphire is a function of temperature (T) and is given as follows:  sapphire  3.796 * 106  4.2185 * 108 T  5.33586 * 1011T 2  2.45519 * 1014T 3 K 1 A.1.2 Using the values of the thermal stress measured at 750oC and 800oC, E= 174 GPa,  = 0.33 (values of E and  for PCO films were determined in Chapters 2 and 3) and sapphire as given by equation A.1.2, equation A.1.1 can then be analyzed at 750oC and 800oC to determine the CTE value of the PCO film. Note that we assume that the CTE of PCO is independent of temperature. The calculated values of film are tabulated in Table A.1.1. Our calculated values are in good agreement with the CTE values reported by Chiba et al.3 for PCO. They employed high temperature XRD to determine these values. T1 (in K) Thermal Stress Thermal Strain T1 film (inK-1) (MPa) (MPa)  298 dT sapphire 1023 (750oC) -1465 -0.00564 0.0055519 1.54*10-5 1073 (800oC) -1597 -0.00614 0.0060569 1.68*10-5 Average film (in K-1) 1.61*10-5 Table A.1.1. CTE values of PCO film determined using the thermal stress values as measured by the HTMOSS system. To summarize, the CTE value of the PCO film was determined to be ~1.61*10-5 K-1. The thermal stress values were measured at 750oC and 800oC by employing the wafer curvature measurements. The samples were heated from room temperature to the desired temperature and at 0.13 atm. O2. The calculated values of the CTE of PCO match well with those reported in the literature. This technique can therefore be used to estimate 160 the CTE values of any other materials as long as the deposited film and the substrate satisfy the assumptions for the Stoney’s equation. A.2 Stress Reversal in PCO at High Temperatures and Very Low pO2 As discussed in Chapters 2 and 3, in PCO, at relatively high pO2 (0.13- 10-6 atm. O2), a decrease in pO2 causes oxygen vacancies to form which is accompanied by the reduction of Pr4+ to Pr3+(as given by equation A.2.1): × 1 2Pr× ′ ∙∙ Ce + OO ↔ 2PrCe + VO + 2 O2 (g) (A.2.1) In the intermediate pO2 range (10-6 and 10-18 atm.), the oxygen non-stoichiometry is fixed and no further oxygen vacancy creation or cation reduction takes place with a further decrease in the pO2. At pO2 < 10-18 atm., oxygen vacancies are created which is accompanied by the reduction of Ce4+ to Ce3+ (as given by equation A.2.2): 1 2Ce× × ′ ∙∙ Ce + OO ↔ 2CeCe + VO + 2 O2 (g) (A.2.2) Such creation/annihilation of point defects results in significant build up of stress in the material. In Chapters 2 and 3, we studied the composition induced stress evolution at 750oC and in the high pO2 range (0.13-10-6 atm. of O2). In this appendix, we investigate the in-situ compositional stress evolution in PCO film (average grain size of 72 nm) at high temperatures (750–800oC) and in the very low pO2 range (~10-17–10-24 atm. of O2). 161 The low pO2 environments were generated using a mixture of CO/CO2 in N2 and H2 gas. Details of the gas compositions used to generate the desired oxidizing and reducing environments are given in Table A.2.1. The in-situ compositional stresses on PCO for isothermal oxidation-reduction- reoxidation cycles were measured through MOSS as described in details in Chapters 2 and 3. A typical in-situ stress profile for PCO film at different reducing environments for higher temperature oxidation-reduction cycle is shown in Figure A.2.1. As observed from this plot, during reduction cycle, at high pO2s, the stress evolves in the compressive direction which is consistent with the discussion in Chapters 2 and 3. However, at very low pO2 (8.7×10-21 atm.), during the reduction cycle, stresses first evolve in compressive direction, and then at a later point in the cycle the stresses reverse their direction and become tensile (Figure A.2.1). This observation is in contradiction to the bulk and nanocrystalline PCO behavior, as the reduction process should lead to compressive stresses.4 Despite the fact that the stresses evolve in the opposite direction during the reduction cycle, they are still completely reversible for a redox cycle i.e., steady state stress during oxidation and re-oxidation cycle is the same, and therefore the stress change during the reduction cycle is attributed to non-stoichiometry induced effects only. 162 oxidation o -1.2 pO = reduction 800 C 2 0.13 atm -1.5 -3 pO2 = 10 atm  (in GPa) -1.8 -5 pO2 = 10 atm -2.1 -2.4 stress reversal -21 -2.7 pO2 = 8.7*10 atm -3.0 0 25000 50000 75000 100000 125000 150000 Time (in secs) Figure A.2.1. In-situ stress measurements for the PCO film on sapphire substrate cycled at 800oC in indicated reducing and oxidizing atmospheres. At low pO2, the film shows a stress reversal during reduction. Similar stress reversal observations during reduction cycle were made by Sunil (Chapter 7 in reference [5]) on undoped ceria at high temperatures and very low pO2s. He conducted a systematic temperature study to see the gradual changes in compositional stress direction from compressive to tensile during the reduction cycle. Through these experiments, he hypothesized that the reversal of compositional stress direction at high temperatures and very low pO2s is because the grain boundary region in pure ceria undergoes phase transformation. The initial move into the compressive regime is expected through combined bulk and grain boundary phase expansion for ceria and is consistent with observations for nanocrystalline ceria at lower temperatures. However, as the oxygen ions continue to be extracted from the bulk and grain boundary region during reduction, for very large defect concentrations it becomes thermodynamically 163 advantageous for the grain boundary region or crystal to transform to a new phase and thus result in the stress reversal. Interestingly, for undoped ceria, at higher temperatures and in extremely reducing conditions several different phases have been reported.6-10 By employing in-situ TEM analysis in extremely reducing and high temperature conditions, Sharma et al.,11 reported that the new ceria phases were stable only at higher temperatures and the cubic fluorite phase of ceria is recovered once the sample is cooled below 400oC. It is important to note that reduction of Ce4+ to Ce3+ takes place at low pO2 in both undoped and doped ceria systems. But, it is only in the case of doping ceria with an aliovalent dopant (like Pr) that results in reduction of the cations (Pr in this case) at relatively high pO2s (0.13- 10-5 atm.). Given that the mechanism responsible for chemical expansion at very low pO2 is the same in undoped and Pr doped ceria, similar argument as made by Sunil for stress reversal in ceria could be used to explain the stress reversal observed for PCO at very low pO2s as is the case in this study. Unfortunately, we did not collect any in-situ XRD data to observe the phase transformation at high temperatures and low pO2s that might be occurring in PCO. We also conducted a systematic study to investigate the onset of stress reversal and its dependence on temperature and pO2 during the reduction cycle. This allowed us to see the gradual changes in compositional stress direction from compressive to tensile during the reduction cycle. The isothermal pO2 dependent compositional stress profiles for a PCO film on sapphire substrate are shown in Figure A.2.2. This figure gives direct evidence of the onset of the stress reversal and its dependence on pO2 and temperature. For 750 and 775oC, the stress reversal occurs when the reducing environment is ~ 4.3×10-24 atm. of O2 whereas, at 800oC it occurs much earlier ~ 3.5×10-18 atm. of O2. The 164 understanding of the phenomena behind such dependence is not clear at the moment and therefore needs further investigation. (a) Reduction o 0 at 750 C -500 (in MPa) -1000 -22 pO2= 5.1*10 atm -1500 -24 -2000 pO2= 4.3*10 atm -2500 0 20000 40000 60000 80000 Time(in secs) (b) Reduction o 0 at 775 C -21 pO2= 8.73*10 atm  (in MPa) -500 -22 pO2= 5.1*10 atm -1000 -24 pO2= 4.3*10 atm -1500 0 80000 160000 240000 Time (in secs) 165 (c) Reduction o at 800 C 0 -17 pO2= 3.62*10 atm -500 -18 pO2= 3.5*10 atm  (in MPa) -1000 -21 pO2= 8.7*10 atm -24 pO2= 4.3*10 atm -1500 -2000 -2500 0 80000 160000 240000 Time (in secs) Figure A.2.2. pO2 dependence of the onset of the stress reversal during reduction cycle for a PCO film on sapphire substrate at (a) 750oC, (b) 775oC and (c) 800oC. pO2 Gas compositions Total Pressure = 100 Torr Temperature Reduction Oxidation Reduction Oxidation (oC) (atm.) (atm.) 750 5.1*10-22 0.13 0.59% CO, 5.9% CO2, 40.6% H2 in N2 Pure O2 4.3*10-24 0.13 0.11% CO, 1.1% CO2, 89% H2 in N2 Pure O2 775 8.73*10-21 0.13 0.75% CO, 7.5% CO2, 25% H2 in N2 Pure O2 5.1*10-22 0.13 0.4% CO, 4% CO2, 60% H2 in N2 Pure O2 4.3*10-24 0.13 0.055% CO, 0.55% CO2, 94.5% H2 in N2 Pure O2 800 3.62*10-17 0.13 1% CO, 10% CO2, 0% H2 in N2 Pure O2 3.5*10-18 0.13 0.98% CO, 9.8% CO2, 2.4% H2 in N2 Pure O2 8.7*10-21 0.13 0.59% CO, 5.9% CO2, 40.6% H2 in N2 Pure O2 4.3*10-24 0.13 0.03% CO, 0.3% CO2, 97% H2 in N2 Pure O2 Table A.2.1. Details of the gas compositions used during oxidation and reduction and the corresponding equilibrium oxygen partial pressures. 166 A.3 Full Brick Layer Model (3-D) Schematic of the grain structure used to evaluate the model is shown in Figure 3.6. For simplicity, the grains are treated as cubes of size L and the grain boundary core and the SC region is considered as one region denoted as the grain boundary (gb) region. The width of the grain boundary region is denoted as b. The model considers three different orientations of the grain boundaries namely b1 (lying along the YZ plane), b2 (lying along the XZ plane and b3 (lying along the XY plane). Both the bulk and the gb region are assumed to have an isotropic behavior. Small strain approximations are expected to be valid for the PCO films under study. The elastic modulus, Poisson ratio and linear strain induced in the bulk is represented as Ebulk, bulk and fbulk. Similarly, these quantities in the grain boundary region are represented as Egb, gb and fgb. To begin with, we start by evaluating the stresses in a layer of grain between two b3 oriented boundaries. From the symmetry of the structure, the following equalities hold true:   xx bulk   yy bulk   bulk  (A.3.1)   xx b1   yy b2   ||gb  (A.3.2)   yy b1   xx b2   gb  (A.3.3)   zzb1   zzb 2   zzgb  (A.3.4) 167 where,   bulk  is the mean in-plane equi-biaxial stress in the bulk,   ||gb  is the mean strain along the b1 and b2 boundaries and   gb  is the mean strain across these boundaries. The boundaries need to be in mechanical equilibrium which requires the following equality:   bulk   gb  (A.3.5) As the film is constrained by a thick substrate, the mean strain along each boundary is zero. Mean strain along b1 = 0 would thus give the following: 1 [  xxb1   gb (  yy b1     zzb1 )]  f gb  0 (A.3.6) Egb Applying the equalities from above we get: 1 [  ||gb   gb (  gb     zzgb )]  f gb  0 (A.3.7) Egb The mean strain through the grain (perpendicular to the boundary) in the y direction is also zero: ( L  b) [  yy bulk   bulk (  xxbulk     zzbulk )]  ( L  b)  f bulk  E bulk (A.3.8) b  [  yy b1   gb (  xxb1     zzb1 ]  b  f gb  0 E gb 168 Applying the equalities from above we get: ( L  b) [  gb   bulk (  gb     zzbulk )]  ( L  b)  f bulk  E bulk (A.3.9) b  [  gb   gb (  ||gb     zzgb ]  b  f gb  0 E gb For the given configuration, assuming that b/L is small enough to neglect any force that is associated with the intersection of the b1 and b2 boundaries, the net force in the z direction is equal to zero: 4( L  b) 2 2 Lb 2   zzbulk   2   zzgb  0 (A.3.10) 4L L Applying the equalities then yields: ( L  b) 2   zzbulk  2Lb   zzgb  0 (A.3.11) Also, the strain in the z direction for the grain and for the boundary should be equal: 1 [  zzbulk   bulk (  xxbulk     yy bulk )]  f bulk  Ebulk (A.3.12) 1  [  zzb1   gb (  xxb1     yy b1 ]  f gb  E gb Applying the equalities from above we get: 1 [  zzbulk  2 bulk   gb ]  f bulk  Ebulk (A.3.13) 1  [  zzgb   gb (  gb     ||gb ]  f gb  E gb 169 For a given oxygen non-stoichiometry, fbulk can be determined from Equation 3.2. By inputting a pre-determined set of values of Ebulk, Egb, bulk, gb, b and fbulk the above equations can be solved for four stress values:   bulk  ,   zzbulk  ,   ||gb  and   zzgb  . To account for the contribution from the b3 oriented grain boundaries, the requirement that the out of plane stress is zero gives   zzb3  0 . Given the constrained geometry of the film, the mean strain along b3 is also equal to zero which yields: 1 [  yy b3   gb (  xx b3     zzb3 )]  f gb  0 (A.3.14) Egb Applying the equalities gives: Egb  f gb    b 3   (A.3.15) (1   gb ) With this, the mean in-plane stress in the thin film, <>, can then be described as the sum of the contribution from the b3 boundaries and the bulk layers between them. This gives: ( L  b) b      bulk     b3  (A.3.16) L L The MOSS measurement gives the values for    and L is determined by applying a linear intercept method on the SEM images for various PCO films. The thickness of the SC region is typically considered to be twice the Debye length and so the 170 value of b is selected to be in the range of 1-3 nm for the films studied here. Thus, for a given set of data at a constant temperature and pO2, the above equations can be evaluated for fgb. 171 A.4. References 1. L. B. Freund, Journal of the Mechanics and Physics of Solids, 48, 1159 (2000). 2. B. Yates, R. F. Cooper and A. F. Pojur, Journal of Physics Part C Solid State Physics, 5, 1046 (1972). 3. R. Chiba, H. Taguchi, T. Komatsu, H. Orui, K. Nozawa and H. Arai, Solid State Ionics, 197, 42 (2011). 4. J. Sheth, D. Chen, J. J. Kim, W. J. Bowman, P. A. Crozier, H. L. Tuller, S. T. Misture, S. Zdzieszynski, B. W. Sheldon and S. R. Bishop, Nanoscale, 8, 16499 (2016). 5. S. Mandowara, in engineering, brown university (2009). 6. M. Zinkevich, D. Djurovic and F. Aldinger, Solid State Ionics, 177, 989 (2006). 7. O. T. Sorensen, Journal of Solid State Chemistry, 18, 217 (1976). 8. R. Korner, M. Ricken, J. Nolting and I. Riess, Journal of Solid State Chemistry, 78, 136 (1989). 9. S. P. Ray, A. S. Nowick and D. E. Cox, Journal of Solid State Chemistry, 15, 344 (1975). 10. E. A. Kummerle and G. Heger, Journal of Solid State Chemistry, 147, 485 (1999). 11. P. A. Crozier, R. Wang and R. Sharma, Ultramicroscopy, 108, 1432 (2008). 172 APPENDIX B MEASUREMENTS ON AMORPHOUS ALUMINUM OXIDE FILMS DEPOSITED BY MOCVD B.1. Determination of Coefficient of Thermal Expansion (CTE) Amorphous aluminum oxide is a material of wide technological importance because of its use in optical and microelectronic components, catalyst supports, as protective coatings in the metal cutting tools and for protection against corrosion and high temperature oxidation. Coating aluminum oxide thin films on complex shape or temperature sensitive materials is a challenging process. For such applications, Metal Organic Chemical Vapor Deposition (MOCVD) systems are used. Aluminum oxide films deposited using MOCVD are often found to be amorphous in nature.1 The composition, allotropic form, microstructure and crystallinity of deposited films may vary depending on the MOCVD experimental conditions. It has been shown that the composition of the aluminum oxide coating deposited using MOCVD is dependent on the processing temperature.2 Films prepared at 350oC are composed of amorphous aluminum oxy-hydroxide, AlO(OH). Films deposited between 415 - 700oC are shown to form stoichiometric, amorphous and compact Al2O3 films. Between 350oC - 415oC, with an increase in temperature, the film composition changes gradually from 173 AlO(OH) to Al2O3 (while the films still remains amorphous). Films that were deposited at 710oC showed wide diffraction peaks attributed to partially crystallized -Al2O3. Annealing these films for one hour is shown to improve the crystallization of the -Al2O3 as verified by XRD.3 This clearly shows that the microstructure of alumina varies with temperature and as such, the film properties like coefficient of thermal expansion (CTE) would also be temperature dependent. This appendix investigates the dependence of CTE of amorphous alumina on temperature. The work was carried out in collaboration with Prof. Constantin Vahlas’s group from ENSIACET, France. They deposited 500 nm thick amorphous alumina films on sapphire and YSZ substrates (25.4 mm diameter) using the MOCVD system and at a deposition temperature of 480oC. The details of the MOCVD deposition parameters are provided in Table B.1.1. The deposition was carried out in a horizontal hot wall reactor using aluminum tri-isopropoxide (ATI) as the metal-organic precursor. ATI is a convenient precursor for the processing of aluminum oxide coatings. The initial curvatures of the substrates were measured prior to deposition, using the HTMOSS technique (as described earlier). This provided a reference curvature value for the subsequent residual/growth stress measurements of the films. Post deposition, the residual stresses were measured as described in Chapters 2 and 3. The residual stress in the pristine amorphous alumina film on sapphire was found to be 2.14 GPa (tensile) and that for the film on YSZ was found to be 1.1 GPa (tensile). The mechanism responsible for such large tensile residual/growth stress is not clear at this point. However, the tensile stress implies that there is some type of densification of the film material, either after or as material is added to the growth surface. 174 QN2,ATI 20 sccm QN2,dilution 631.5 sccm QATI 1.5 sccm Qtotal 653 sccm Pressure 5 Torr Deposition temperature 480oC ATI Temperature (precursor) 90oC Table B.1.1. Deposition parameters for MOCVD grown amorphous alumina films. The MOCVD deposited film-substrate systems were exposed to different heat treatments, as a result of which, the amorphous alumina film experiences thermal stresses (as discussed earlier in Appendix A.1). Standard heat treatments involved heating the sample from room temperature to the desired temperature, dwell at that temperature for two hours and then cool the sample back to room temperature. These measurements were conducted at 0.13 atm. of oxygen and at 420oC (lower than the deposition temperature), 480oC (same as the deposition temperature) and 600oC (greater than the deposition temperature); given that the alumina densifies and changes its microstructure with an increase in temperature, the measurements were first conducted at lower temperatures i.e., 420oC, followed by 480oC and then at 600oC. Note that, we did not carry out measurements at higher temperatures. The reason being that the film starts crystallizing at ~700oC, which means that we exceed the structural stability domain foreseen for technical applications (amorphous coatings are generally used). In other words, the coating is destroyed with regard to its targeted property (barrier to prevent oxidation/corrosion of the underlying material). The stress values were recorded during heating, dwelling, and cooling of these samples using the HTMOSS system (as described in Chapters 2, 3 and Appendix A.1). The objective was to measure the stress change during heating and cooling and use that to calculate the CTE values of the amorphous 175 film at that particular temperature; the procedure used to calculate the CTE values is described in more details in Appendix A.1. The stress profiles of the above mentioned alumina coating on sapphire and YSZ and at different temperatures are shown in Figure B.1.1 and B.1.2 respectively. All films demonstrated large tensile stresses at room temperature. In many cases, heating and cooling of these specimens led to little or no change in the room temperature stress (see Figure B.1.1 and B.1.2). Heating to higher temperatures resulted in lowering the room temperature stresses at the end of the experiment i.e., once the sample is cooled back to room temperature (Figure B.1.1 (c) and B.1.2 (d) and (e)). These stress reduction values were usually less than 0.2 GPa, and thus they did not significantly alter the large room temperature stress. Such lowering of stress at higher temperatures suggests some modest change in the amorphous structure of the film. It is important to note that such stress relaxations were also observed during the initial portion of the dwell cycles (see Figure B.1.1 and B.1.2). The exact understanding of the phenomena leading to such relaxations in not known at the moment and requires more experiments. Interestingly, these relaxations disappear when the samples are exposed to the desired temperature for the second time i.e. when the measurements are repeated at a particular temperature (see Figure (B.1.2 (a), (c) and (d)). This might suggest that amorphous alumina film, when exposed to a particular temperature for the first time, undergoes some kind of structural/compositional changes that leads to a stabilized structure and hence, the stress relaxations (during the initial dwell cycle) are absent when the film is exposed to that temperature for the second time. 176 Amorphous Al2O3 on sapphire 2800 (a) o 420 C 2400  (MPa) cooling 2000 heated held o cooled to rt to at 420 C o 420 C 1600 1200 0 5000 10000 15000 20000 Time (secs) Amorphous Al2O3 on sapphire (b) 2600 o 480 C 2400 2200  (MPa) 2000 cooling heated to held at cooled to rt o 1800 480 C o 480 C 1600 1400 0 5000 10000 15000 20000 25000 Time (secs) 177 Amorphous Al2O3 on sapphire 2600 (c) o 600 C 2400 2200  (MPa) 2000 cooling 1800 heated to held at o cooled to rt 600 C o 600 C 1600 1400 1200 0 10000 20000 30000 Time (secs) Figure B.1.1. MOSS measurement of an amorphous alumina film on sapphire substrate heated from room temperature (25oC) to (a) 420oC, (b) 480oC and (c) 600oC. Note that the stress change during cooling (cooling) is used to calculate CTE values of the films at any given temperature. Amporphous Al2O3 on YSZ 1600 (a) o 420 C 1400 1200  (MPa) cooling 1000 heated held at cooled to rt to o 420 C 800 o 420 C 600 0 10000 20000 30000 Time (secs) 178 Amporphous Al2O3 on YSZ 1600 (b) o 480 C 1400 1200  (MPa) 1000 cooling 800 heated held at o cooled to rt to 480 C o 480 C 600 400 0 10000 20000 30000 Time (secs) Amporphous Al2O3 on YSZ 1600 (c) o 480 C 1400 repeat 1200  (MPa) cooling 1000 heated held at 800 to o cooled to rt 480 C 480 C o 600 400 0 10000 20000 30000 40000 Time (secs) 179 Amporphous Al2O3 on YSZ 1600 (d) o 600 C 1400 1200  (MPa) 1000 cooling 800 heated held at cooled to rt 600 to o 600 C o 600 C 400 200 0 10000 20000 30000 Time (secs) Amporphous Al2O3 on YSZ 1600 (e) o 600 C 1400 repeat 1200  (MPa) 1000 cooling 800 heated held at cooled to rt 600 to o 600 C o 600 C 400 200 0 10000 20000 30000 40000 Time (secs) Figure B.1.2. MOSS measurement of an amorphous alumina film on YSZ substrate heated from room temperature (25oC) to (a) 420oC, (b) 480oC (c) measurement repeated at 480oC, (d) 600oC and (e) measurement repeated at 600oC. Note that the stress change during cooling (cooling) is used to calculate CTE values of the films at any given temperature. Also, the stress relaxations during the initial dwell cycles are absent when the measurements are repeated at a particular temperature ((c) and (e)). 180 CTE calculations The plots in Figure B.1.1 and B.1.2 suggests that the thermal equilibrium during the heating step is delayed likely due to convection related heat loss, which occurs at fairly low temperatures (used in this study). This might be causing the stress relaxations observed during the initial dwell cycles. So, the average CTE values of the alumina films were calculated using the cooling values (as tabulated in Table B.1.2) measured at the corresponding temperatures. Figure B.1.3 (a) and (b) plots the CTE values against the annealing temperatures for the amorphous alumina films on sapphire and YSZ respectively. The calculated CTE values are also tabulated in Table B.1.2. These calculations were carried out using equation A.1.1. The value of elastic modulus of the amorphous alumina film was taken as 390 GPa,4 poison's ratio as 0.25, sapphire as given by equation A.1.2, YSZ as 10.3×10-6 K-1 and thermal as cooling measured from the experiments. Interestingly, the calculated CTE values for the film on YSZ are higher (~40%) than that for the film on sapphire at any given temperature. The cause for the observed differences in the CTE values is not well understood at this point. One possibility could be that the two amorphous alumina films that are being compared here have different structure and/or composition. 181 Amorphous Al2O3 on Sapphire -5 1.2x10 (a) -5 1.0x10 )-1 -6 8.0x10 CTE (in K -6 6.0x10 -6 4.0x10 -6 2.0x10 400 450 500 550 600 Temperature (in C) o Amorphous Al2O3 on YSZ (b) -5 1.20x10 -5 1.05x10 ) -1 CTE (in K -6 9.00x10 -6 7.50x10 -6 6.00x10 400 450 500 550 600 Temperature (in C) o Figure B.1.3. CTE values plotted against the annealing temperatures for amorphous alumina films deposited on (a) sapphire and (b) YSZ. 182 T1 cooling  Temperature (T1 in Sample dT substrate film (in K-1) K) (in MPa) 298 Amorphous 693 (420oC) 150 0.0027 6.10*10-6 alumina on 753 (480oC) 119 0.0032 6.53*10-6 sapphire 873 (600oC) 162 0.0042 6.76*10-6 693 (420oC) 152 0.00406 9.54*10-6 753 (480oC) 160 0.00468 9.60*10-6 Amorphous 753 (480oC) repeat 207 0.00468 9.41*10-6 alumina on YSZ 873 (600oC) 250 0.00592 9.46*10-6 873 (600oC) repeat 265 0.00592 9.41*10-6 Table B.1.2. CTE values of amorphous alumina film deposited on sapphire and YSZ substrates. The values were determined using the thermal stress values as measured by the HTMOSS system. 183 B.2. References 1. D. Samélor, M. M. Sovar, A. Stefanescu, A. N. Gleizes, P. Alphonse and C. Vahlas, in Fifteenth European Conference on Chemical Vapor Deposition (EUROCVD-15), A. Devi, R. Fischer, W. Parala, M. D. Allendorf and M. Hitchmer Editors, p. 1051, Pennington, NJ (2005). 2. B. Castel, Les alumines et leurs applications, Nathan (1990). 3. A. N. Gleizes, C. Vahlas, M. M. Sovar, D. Samelor and M. C. Lafont, Chemical Vapor Deposition, 13, 23 (2007). 4. A. M. Huntz, M. Andrieux, C. Vahlas, M. M. Sovar, D. Samelor and A. N. Gleizes, Journal of the Electrochemical Society, 154, P63 (2007). 184 APPENDIX C ADDITIONAL MEASUREMENTS ON LMO SAMPLES C.1 In-situ Atomic Force Microscopy (AFM) on LMO Films During First Delithiation Cycle As observed in Chapter 4, the initial delithiation (1st cycle) from spinel LMO induced tensile stress up to ~4.05 V (vs. Li/Li+). Continued delithiation beyond 4.05 V, however, resulted in a reversal of the induced stress direction (termed as the “anomalous drop”). During the first lithium insertion step there was steady buildup of compressive stress. In subsequent cycles the induced stress evolved reversibly with the stress becoming tensile during delithiation and compressive during lithiation in accordance with the XRD results. This behavior can be seen in Figure 4.4(b) . As pointed out in Chapter 4, the unexpected anomalous drop in the first delithiation cycle might indicate some structural instability arising from the mechanical damage (e.g. microcracking) of the cathode film. To gain further insight into this possibility, we attempted to do an in-situ AFM measurement on the LMO films during the first delithiation cycle. The purpose of this measurement was to see if the surface morphology changes or if any form of mechanical damage occurs to the film during the first delithiation cycle (i.e., when the 185 anomalous drop occurs). These measurements were conducted by Ravi Kumar during one of his ARL visits. The LMO sample for AFM investigations was prepared on 500 μm thick quartz wafer (double-side polished, 40 mm × 40 mm in size). The LMO film was deposited on platinized quartz wafer using the solution based technique as discussed in section 4.2. The in-situ AFM measurements were conducted with a Dimension ICON electrochemical AFM setup inside of an argon-filled glovebox (at ARL), where both H2O and O2 were below 1 ppm. The unique PeakForce tapping mode was used with MLCT tips (Bruker AFM Probes), composed of a silicon nitride cantilever with a sharp silicon nitride tip (spring constant: 0.6 N/m; nominal tip radius: 20 nm). The electrolyte was a mixture of ethylene carbonate (EC) and diethyl carbonate (DEC) (1:1 vol. ratio with 1M LiPF6). The sample was cycled against Li metal foil in an in-house electrochemical cell designed for Li ion battery materials and sealed during AFM operation. Figure C1.1(a) shows the charge-discharge profile of a ~120 nm thick LMO film that was cycled 2 times in 3.5-4.3 V (vs. Li/Li+) range with a constant current of 4.6A . The electrochemical cycling was conducted with potentiostatic holds at 3.5 and 4.3 V. The cell was held at these potential until the current reached an asymptotic value that was less than 10% of the value at the start of the hold. Continuous AFM scans were performed during the first delithiation cycle. Each scan took ~ 2640 seconds. The corresponding scan numbers are shown in Figure C.1.1(b). 186 (a) 4.4 -6 4.0x10 4.2 Potential (V, vs. Li/Li ) + 4.0 Current (A) 0.0 3.8 3.6 -6 -4.0x10 3.4 0 25000 50000 75000 100000 125000 150000 Time (sec) Scan No. (b) 4.4 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 -6 4.60x10 4.2 Potential (V, vs. Li/Li ) + 4.0 0.00 Current (A) 3.8 3.6 -6 -4.60x10 1st de-lithiation cycle 3.4 0 5280 10560 15840 21120 26400 31680 36960 42240 Time (sec) Figure C.1.1. (a) Charge-discharge profile of a 120 nm thick LMO film cycled between 3.5-4.3 V (vs. Li/Li+). (b) First delithiation cycle and the corresponding AFM scan numbers for the LMO film shown in panel (a). Note that the shaded region corresponds to the scan numbers shown in Figure C.1.2. 187 Figure C.1.2 shows the AFM topographs of an LMO film during the first delithiation cycle. The scan numbers in the figure corresponds to those shown in the shaded region in Figure C.1.1(b). As can be observed from the figure, the morphology of the LMO film does not change throughout the first delithiation cycle, including when the anomalous drop occurs i.e., for potential > 4.05 V. Moreover, no apparent mechanical damage was observed on the LMO surface during these in-situ AFM measurements. Figure C.1.2. AFM topographs of a LMO film during the first delithiation cycle at (a) Scan No. 0, (b) Scan No. 5, (c) Scan No. 10 and (d) Scan No. 15. The scan numbers are in accordance to the ones shown in Figure C.1.1(b). Note that scan numbers 5, 10 and 15 are the voltage regions where the anomalous drop is observed. 188 These in-situ AFM measurements are in accordance with the post cycling SEM images shown in Figure 4.6. Both of these measurements indicate that there was no apparent mechanical damage on the surface of the cycled LMO samples. As such, we conclude that the observed anomalous drop in the LMO films was not a manifestation of mechanical damage arising from volume change and/or transformation strain in LMO during first delithiation. Based on this, we conjecture that some irreversible changes in the electrode structure (surface and/or bulk) during the later stages of the first delithiation from LMO contribute to the observed anomalous drop (as observed in Chapter 4). C.2 Surface XPS Measurement of LMO Films at Different Open Circuit Potentials As discussed in Chapter 4, the absence of apparent micro-cracks/fracture in cycled LMO samples suggests that the anomalous drop did not arise from mechanical damage during cycling; irreversible changes in the electrode structure contribute to the anomalous drop. Stress measurements on LMO films with varying thicknesses showed that both surface and bulk effects contribute toward the first cycle anomalous drop (section 4.4). Interestingly, the anomalous drop reappeared for a cycled sample that was re-annealed (Figure 4.5(b)). Based on this observation, we conjectured that the observed anomalous drop could partly be explained in terms of creation of oxygen vacancies in the bulk of the material during first delithiation (beyond 4.05 V) from LMO. Additionally, based on charge neutrality considerations, the creation of oxygen vacancies would require 189 manganese reduction (from Mn4+ to Mn3+/Mn2+) or additional Li removal or both. This suggests that at the end of first delithiation, there would be more Mn3+ (and/or Mn2+) in the electrode than what is expected based on capacity considerations only. To support this speculation, we conducted surface XPS scans and analyzed the Mn2p spectra of LMO at various stages of cycling. These measurements were conducted at University of Rhode Island (URI) in collaboration with Prof. Brett L. Lucht’s group. The LMO samples for the XPS measurements were prepared using the solution based technique as discussed in Chapter 4; for consistency, the samples were prepared from the same batch of the LMO solution. These samples were galvanostatically cycled to different charge/discharge states using a Solartron 1470E MultiStat system and inside an Ar filled glove box (H2O < 0.1 ppm; O2 < 0.1 ppm). More details about the experimental setup for the electrochemical lithium extraction/insertion from/into LMO films could be found in section 4.2. Once cycled, the films were thoroughly rinsed with DMC; this was done in order to clean the LMO surface of any decomposition products that might have formed during the electrochemical cycling. The samples were then stored in the antechamber for 30 minutes in order to dry them. The dried samples were stored inside the glove box until the XPS measurements were performed on them. Surface compositional analysis was conducted using ex-situ XPS measurements (K-alpha, Thermo) with Al Kα X-ray source at a pass energy of 50 eV and measured spot size of 400 μm. The electrodes were transferred from the glove box to the XPS analysis chamber using a special vacuum-sealed module (Thermo) without exposure to the air at any time. The binding energy was corrected based on the C1s peak of hydrocarbon at 190 284.8 eV. Quantitative analysis of the Mn2p peaks were carried out using the XPSPEAK41 software and following the peak fitting protocol as described by Nesbitt el al.1 and Biesinger et al.2 Table C.2.1 lists the sample IDs and the corresponding open circuit potentials (OCVs) of the LMO films that were used for the XPS measurements. For the ease of visualization, Figure C.2.1 shows these sample IDs superimposed on a typical charge/discharge profile of the LMO films. Note that the XPS measurements were conducted on separate LMO samples that were charged or discharged to the OCV of interest for e.g., sample (b) was galvanostatically cycled to 3.9 V and then thoroughly cleaned to perform the XPS measurements, whereas, sample (d) was a separate LMO sample that was galvanostatically cycled to 4.3 V followed by a thorough cleaning of the sample for the XPS measurements. The Mn2p XPS spectra (surface scans) of LMO films at various stages of cycling are shown in Figure C.2.2. Note that XPS gives surface specific information, and the evolution of the oxidation state in the bulk of the sample might not necessarily be the same as in the surface. Specific information at a certain depth could be obtained by sputtering off desired thickness from the surface of the LMO film and conducting the XPS measurement on the sputtered surface. But, when performed, the absence of C1s peak makes it difficult to correct the XPS spectra for any shift that might be caused by charging of the sample. As such, the XPS measurements at different depths for the LMO samples were not pursued. 191 Sample ID Open circuit potential Cycle stage A 3.6 V Pristine st B 3.9 V 1 delithiation C 4.16 V 1st delithiation D 4.3 V 1st delithiation E 3.6 V 2nd lithiation F 3.6 V Re-annealed sample E Table C.2.1. Sample IDs and the corresponding OCVs of the LMO films used for the XPS measurements. 320 *h (GPa-nm) 300 280 260 240 220 200 Potential (V, vs Li/Li ) + 4.4 4.2 (D) (C) 4.0 (B) 3.8 3.6 (A) (E) 3.4 0 5000 10000 15000 20000 25000 Time (secs) Figure C.2.1. Sample IDs for the XPS measurements superimposed to the corresponding charged state on a typical charge/discharge profile of the LMO film. Note that, the XPS measurements were conducted on separate LMO samples that were separately charged or discharged to different OCVs. 192 Mn2p1/2 Mn2p3/2 (f) Normalized Intesity (e) (d) (c) (b) (a) 660 655 650 645 640 635 Binding Energy (eV) Figure C.2.2. Mn2p XPS spectra of LMO films at different charge state (a) pristine (Sample A), (b) charged to 3.9 V (sample B), (c) charged to 4.16 V (sample C), (d) charged to 4.3 V (sample D), (e) discharged to 3.6 V at the end of two cycles (sample E) and (f) re-annealed sample E (Sample F). The vertical line in the plot is shown to provide a visual guide in order to observe the relative change in the Mn2p3/2 peak shape and position for various LMO samples. Qualitative analysis of Mn2p3/2 surface scans of various LMO samples It is evident from Figure C.2.2 that the peak positions of the Mn2p3/2 spectra of sample A (pristine sample) and sample E (discharged at the end of two cycles) are quite similar, which is expected on the basis of Mn3+↔Mn4+ oxidation/reduction during delithiation/lithiation cycles. Slight difference in the peak shape between these two spectra, however, indicate minor differences in bonding environments around manganese between these two samples. On the other hand, both the peak position and the shape of Mn2p3/2 spectra for sample F (re-annealed after two cycles i.e. re-annealed sample E) are 193 exactly the same as that of the pristine sample. This fact strongly suggests that the atomic structure around Mn in sample F reverts to its pristine state upon re-annealing. As such, this means that the oxygen coordination around Mn in the re-annealed sample (sample F) is the same as in the pristine sample, but is slightly different than that in the cycled sample E (discharged at the end of 2 cycles). This supports our speculation that the irreversible structural changes in LMO during first delithiation involve, at least in part, creation of oxygen vacancies, which are replenished during re-annealing process. As mentioned earlier, charge neutrality considerations require that the creation of oxygen vacancies be accompanied by Mn reduction (from Mn4+ to Mn3+/Mn2+). This can be ascertained by comparing the peak positions of the Mn2p3/2 spectra of sample A (pristine sample) and sample D (charged to 4.3 V during the first delithiation cycle). The Mn2p3/2 peak position of sample D shifts to a lower binding energy. Moreover, the peak shape also changes when compared to sample A. This peak shift qualitatively suggests that sample D (at the end of first delithiation) has more Mn3+ (and/or Mn2+) in the electrode than what is expected (in an ideal situation, complete delithiation of LMO would result in formation of -MnO2 in which the Mn exists as Mn4+). This is also consistent with our earlier speculations. These observations are also qualitatively consistent with Tang et al.,3 who report XPS and EELS measurements that show substantial enhancement of Mn3+ and Mn2+ content at the charged (4.3 V) LMO electrode surfaces. 194 Quantitative analysis of Mn2p3/2 surface scans of various LMO samples The change in the manganese valence states in samples A-F were quantified by de-convoluting the Mn2p3/2 peak in terms of contributions from Mn2+, Mn3+ and Mn4+ peaks. This was done for each sample using the XPSPEAK41 software and the calculated values are presented in Table C.2.2. The presence of multiplet splitting and shakeup features within the Mn2p spectra complicates the analysis of the XPS data. In simple terms, multiplet splitting can be described as an energy coupling interaction between unpaired electrons in the valence shell and unpaired electrons within the core level which occurs following the excitation of core level electrons during the photoemission process.1, 4 The result of this energy coupling for manganese is that Mn2p spectra taken from a single chemical species contain several multiplet peaks over a broad energy range (~10eV). Another spectral feature known to affect the analysis of Mn2p spectra are shake-up features that arise from photoelectrons that have lost energy through the promotion of valence electrons from an occupied energy to a higher unoccupied level. While these factors greatly complicate the analysis, Nesbitt et al.1 outlined curve fitting parameters that can be used for the deconvolution of Mn2p photoemission spectra taken from a number of specific Mn-based chemical species. In this study these curve fitting parameters were used to curve fit Mn2p3/2 spectra taken from various LMO films at different OCVs. The XPS spectra were curve fitted using 100% Gaussian line shapes and using a Shirley-type background. Because of the limitations of the peak fitting software (can fit maximum of 10 peaks at a time), the fitting was carried out by selecting three peaks (of highest intensities) for each valence state of manganese (this gives us 9 peaks in total; three each for Mn2+, Mn3+ and Mn4+) and a shake-up peak. The full width at half- 195 maximum (fwhm) of all curve fitted peak were fixed to 1.3 eV, with permission of slight adjustment. The binding energy differences between any two peaks were also fixed with permission of slight adjustment. Figure C.2.3 shows the best fits obtained for samples A- F using the above mentioned method. In general, the average oxidation state of manganese in pristine LiMn2O4 spinel is +3.5 (comprised of 50% Mn3+ and 50% Mn4+). The common expectation is that as lithium is extracted from LMO, the oxidation state of Mn increases to +4.0 (at the end of delithiation) and decreases back to +3.5 with re-insertion of lithium (at the end of lithiation). As discussed in the previous section and based on the values reported in Table C.2.2, the surface XPS measurements on LMO at different charged states suggests that this trend is not followed by the LMO samples during the first de-lithiation cycle. It is important to note that our pristine LMO film has higher concentrations of Mn2+ and Mn3+ than expected. This could be explained by the fact that we use excess lithium during the fabrication of the films and that the pristine films contain some impurities in the form of manganese oxides (as seen in Figure 4.3(a)). The qualitative analysis of the Mn2p3/2 peaks (as discussed earlier) agrees well with the values reported in Table C.2.2. To summarize, the tabulated values suggest that sample A (pristine) and sample F (re-annealed sample E) have exactly the same average oxidation states of Mn which indicates that re-annealing sample E, reverted the irreversible structural changes that took place in LMO during the first de-lithiation cycle. Sample A and E (at the same OCV) have somewhat different average oxidation states of manganese. On the other hand, Sample D has more Mn3+ and Mn2+ than expected. The 196 tabulated values for sample B and C do not agree well with any of the observed trend and hence are outliers to our proposed hypothesis. This could be due to uncertainties associated with the peak fitting procedure as discussed later. Nevertheless, the tabulated values for samples A, D, E and F supports our hypothesis that during the later stages of first delithiation, oxygen loss is accompanied by the reduction of the Mn ions in LMO; this results in irreversible structural changes in the LMO that lead to a stable configuration by the end of the first delithiation. It is this stable structure that acts as a host for reversible lithiation and delithiation during the later cycles. Re-annealing of the cycled sample in air and at 750oC (as discussed in Chapter 4), reverts the irreversible structural changes and replenishes the lost oxygen, thereby, returning the sample back to its pristine state. It is important to note here that XPS mainly reflects the surface information on the sample; this suggests that the valence change of manganese ions near the surface may differ from that in the bulk region. Moreover, because 10 peaks are being curve fitted to the XPS Mn2p3/2 spectra, a large number of fitting parameters (different binding energies corresponding to the peaks of different manganese oxidation states, fwhm values of all the 10 peaks, the behavior of the line (Gaussian vs. Lorentzian or a mix of both), percentage of the total area covered by each of the peaks etc.) are involved in the peak fitting procedure. A small tweak to either of these parameters could significantly alter the overall results. As such, the uncertainty associated with the reported values is quite high. This renders the tabulated values in Table C.2.2 to be unreliable. Therefore, more work is needed in terms of better quantification of the surface XPS measurements. 197 Sample A Sample B Sample C Sample D Sample E Sample F (pristine) (OCV = (OCV= (OCV= (OCV = (re-annealed 3.9 V) 4.16 V) 4.3 V) 3.6 V) sample E) Mn2+ 8.57% 9.36% 8.78% 14.93% 10.29% 8.63% Mn3+ 52.87% 58.88% 55.67% 25.71% 61.89% 53.67% Mn4+ 38.56% 31.76% 35.55% 59.36% 27.82% 37.70% Table C.2.2. Change in the manganese oxidation states in the LMO films at different OCVs. These values are obtained by resolving the Mn2p3/2 peak in terms of contributions from the Mn2+, Mn3+ and Mn4+ peaks using the fitting protocol as described in the text. Sample A (pristine) (a) Scan Fit Shirley background Intensity (a.u.) 2+ Mn 3+ Mn 4+ Mn Shake-up peak 2+ Mn = 8.57% 3+ Mn = 52.87% 4+ Mn = 38.56% 648 646 644 642 640 638 Binding Energy (eV) 198 Sample B (OCV= 3.9 V) (b) Scan Fit Shirley background Intensity (a.u.) 2+ Mn 3+ Mn 4+ Mn Shake-up peak 2+ Mn = 9.36% 3+ Mn = 58.88% 4+ Mn = 31.76% 648 646 644 642 640 638 Binding Energy (eV) Sample C (OCV= 4.16 V) (c) Scan Fit Shirley Intensity (a.u.) background 2+ Mn 3+ Mn 4+ Mn Shake-up peak 2+ Mn = 8.78% 3+ Mn = 55.67% 4+ Mn = 35.55% 648 646 644 642 640 638 Binding Energy (eV) 199 Sample D (OCV= 4.3 V) (d) Scan Fit Shirley background 2+ Mn Intensity (a.u.) 3+ Mn 4+ Mn Shake-up peak 2+ Mn = 14.93% 3+ Mn = 25.71% 4+ Mn = 59.36% 648 646 644 642 640 638 Binding Energy (eV) Sample E (OCV= 3.6 V) (e) Scan Fit Shirley background 2+ Intensity (a.u.) Mn 3+ Mn 4+ Mn Shake-up peak 2+ Mn = 10.29% 3+ Mn = 61.89% 4+ Mn = 27.82% 648 646 644 642 640 638 Binding Energy (eV) 200 Sample F (re-annealed sample E) (f) Scan Fit Shirley background 2+ Mn Intensity (a.u.) 3+ Mn 4+ Mn Shake-up peak 2+ Mn = 8.63% 3+ Mn = 53.67% 4+ Mn = 37.70% 648 646 644 642 640 638 Binding Energy (eV) Figure C.2.3. Fitted Mn2p3/2 XPS spectra of LMO films at different charge state (a) pristine (Sample A), (b) charged to 3.9 V (sample B), (c) charged to 4.16 V (sample C), (d) charged to 4.3 V (sample D), (e) discharged to 3.6 V at the end of two cycles (sample E) and (f) re-annealed sample E (Sample F). The peak fits are obtained using the fitting protocols as described in the text. C.3 High Temperature MOSS Measurements on LMO Films As proposed in Chapter 4, in an attempt to gain further insight into the origin of the anomalous drop during first delithiation cycle, an experimental scheme involving re- annealing of cycled LMO samples was devised. The details about this modified experimental scheme could be found in section 4.3. Based on the re-annealing and XPS measurements, it was observed that the irreversible structural changes in the LMO film that incurred during the first delithiation (beyond 4.05 V) during run 1 were completely recovered upon reannealing the sample. Therefore, we conjectured that the irreversible structural changes, responsible for the anomalous drop during first delithiation cycle of 201 LMO, partly arises from the electrochemically induced creation of oxygen vacancies (accompanied by the reduction of the Mn ions) during the later stages of the first delithiation cycle. These oxygen vacancies were replenished during re-annealing of a cycled sample in air, this therefore, reverts the LMO sample back to its pristine state. This is also consistent with the observation that the residual stress in the LMO film after re-annealing was similar to that in the pristine film (before run 1; as described in Chapter 4). In order to understand the phenomena that results in the recovery of the irreversible structural change in cycled LMO samples, stress evolution in the LMO films were monitored by employing the HTMOSS system during the re-annealing step. To prevent the furnace tube from lithium contamination, the sample was placed in a quartz container which was then loaded inside the HTMOSS system for the re-annealing measurements. Figure C.3.1 shows the image of the LMO sample inside the quartz container. Figure C.3.1. LMO sample placed in a quartz container. It was then loaded into the HTMOSS system for the re-annealing measurements. 202 This appendix is divided into two parts. Part I deals with distinguishing between the contributions from the thermal stress in LMO and the irreversible stress recovery that is observed during the re-annealing step. Part II, on the other hand, deals with understanding the stress evolution in LMO when the cycled film is re-annealed at 750oC in a wide range of pO2s (0.13 - 10-6 atm.). This was believed to give us a better understanding of the dependence of the anomalous drop on the oxygen non-stoichiometry in LMO. Note that, in contrast to Chapter 4, the LMO samples used for these set of measurements were deposited on 25.4 mm diameter platinized quartz wafers. Part I Figure C.3.2 (a) shows a pristine LMO sample that was re-annealed at 750oC at 0.13 atm. of O2 (similar to air). The stress evolution in this sample during the re- annealing process was found to be reversible i.e., the room temperature stress in the sample, before and after the re-annealing step, is the same. It is important here to point out that the LMO film studied here was pristine i.e., the film was not electrochemically cycled which means that there were no stress contributions from the recovery of the structural irreversibility in the LMO during the re-annealing step. Thus, the thermal stress experienced by the LMO-quartz system can be given as the stress change during heating and/or cooling of the pristine sample; this value for our film when heated to 750oC is ~1.24 GPa. Evaluating equation A1.1 using E= 160 GPa, = 0.33, LMO = 7.5*10-6 K-1 5 and quartz = 0.5*10-6 K-1 yields a very similar value of the thermal stress for a LMO- quartz system (~ 1.23 GPa). Figure C.3.2 (b) and (c) shows the XRD and Raman measurements respectively, performed before and after the re-annealing measurements on 203 the pristine LMO sample. These plots suggest that re-annealing a pristine sample did not cause any apparent structural or compositional changes in the LMO film. Pristine LMO re-annealed in 0.13 atm. O2 1.6 (a) o 800 750 C 1.4 700 1.2 600 Temperature ( C) 1.0 500  (GPa) 0.8 400 0.6  = 1.24 GPa 300 0.4 200 0.2 o 100 0.0 0 -0.2 0 5 10 15 20 25 30 Time (hr) (b) * * LMO (c) re-annealed Raman Intensity (a.u) in 0.13 atm O2 Intensity (a.u) * reannealed in pO2=0.13 atm pristine pristine 10 20 30 40 50 60 70 80 100 200 300 400 500 600 700 800 2 (deg) Raman Shift (cm ) -1 Figure C.3.2. (a) Stress evolution in a pristine LMO sample measured at 750oC and at 0.13 atm. of O2. (b) and (c) shows the corresponding XRD and Raman measurements respectively of the sample in (a). Another pristine LMO sample was cycled using the experimental scheme shown in Figure 4.5. The HTMOSS system was used to monitor the stress evolution during the re-annealing step. The stress-thickness evolution profile and the corresponding 204 electrochemical cycle for this sample are shown in Figure C.3.3 (a) and (b) respectively. For the purpose of this appendix, we will only focus on the stress evolution during the re- annealing step. This is shown in Figure C.3.3 (c) for clarity. During this step, heating the cycled LMO sample results in a change in stress of ~ 0.59 GPa and the same value for the cooling cycle was ~ 1.23 GPa. Interestingly, the stress change observed during cooling is same as the thermal stress measured for the LMO-quartz system (as discussed above). This suggests that the difference in the stress change during heating and cooling is due to the structural recovery of LMO during the heating cycle and is described later in this appendix. 205 (a) 280 h(GPa-nm) 240 200 160 120 run 1 re-annealed at run 2 80 750C in air Potential (V, vs. Li/Li ) 40 + (b) 4.4 4.2 4.0 3.8 3.6 3.4 0 10 20 30 40 50 60 70 Time (hr) (c) 1.8 cooled to room temp 1.6 cooling = 1.23 GPa (GPa) 1.4 1.8 750 1.2 1.6 0.59 GPa  600 Temperature ( C) 1.4 1.0 1.2 450  (GPa) heating = 1.8 1.0 0.8 300 1.6 0.8 150 1.4 o 0.6 0.6  (GPa) 1.2 0.4 0 1.0 0 1 2 3 4 0.4 Time (hr) 0.8 0 3 6 9 12 15 18 21 24 27 0.6 0.4 Time (hr) 0 1 2 Figure C.3.3. (a) Stress evolution and (b) the corresponding charge/discharge for a LMO film cycled using the experimental scheme as shown in Figure 4.5. For clarity, the stress evolution during the re-annealing step of the LMO film in (a) is shown in (c). The inset shows an expanded view of the stress evolution during the heating and dwelling cycles. 206 Comparing Figure C.3.2 (a) and C.3.3 (c), it can be clearly observed that heating/cooling the pristine LMO sample to/from 750oC from/to room temperature results in change in stress of ~ 1.24 GPa (consistent with the calculated thermal stress value). However, for a cycled LMO sample (i.e., after run 1; Figure C.3.3 (a)), the stress change during heating is ~ 0.59 GPa and that during cooling is ~ 1.23 GPa. Based on the above comparison, the stress change during heating and cooling can be given as: |  heating/ cooling ||  thermal   re cov ery | C.3.1 where heating and cooling are the change in stress during heating and cooling steps respectively, thermal is the contribution from the thermal stress and recovery is the stress contribution from the recovery of the irreversible structural change. The above equation then explains the differences in the heating and cooling stresses that are observed in the two samples. For the pristine sample in Figure C.3.2, since it did not undergo any structural irreversibility during the electrochemical cycling,  re cov ery  0 for the re-annealing step. Thus, |  heating ||  cooling ||  thermal | . For the cycled sample in Figure C.3.3, on the other hand,  re cov ery  0 and corresponds to the recovery of the irreversible changes that took place during run 1 (1st de-lithiation cycle; Figure C.3.3 (a)). As suggested in Chapter 4, these irreversible changes in the LMO film could be due to oxygen incorporation (along with Mn oxidation) and/or densification of the film and/or regaining crystallinity at higher temperatures. During re- annealing, recovery results in a tensile stress thus relaxing the expected thermal stress 207 due to CTE mismatch. During cooling, since, the lost oxygen and/or crystallinity have already been replenished in the film at high temperatures, the contribution from recovery becomes zero and thus the stress evolution during cooling can be given by equation C.3.2 and is also what is observed in Figure C.3.3 (c). |  cooling ||  thermal | C.3.2 Part II Earlier studies have reported the dependence of oxygen non-stoichiometry and defect structures of LMO on annealing temperatures and oxygen partial pressures.6-11 In this part of the appendix, we re-annealed the cycled and pristine LMO samples in different oxygen partial pressures. The idea here was that by re-annealing a cycled sample (i.e., after run 1) in different pO2s, one could vary the oxygen non-stoichiometry of the sample; this should then vary the magnitude of the anomalous drop that is observed during the later stages of the first delithiation cycle during run 2. If in the experiments conducted, the magnitude of the change in h during the anomalous drop observed in run 2 shows a dependence on the oxygen partial pressures used for re-annealing, the oxygen loss hypothesis would get further validated. The pristine LMO samples were cycled using the experimental scheme shown in Figure 4.5. The difference here is that the samples were electrochemically cycled at a current density of 1.58 A/cm2 and were re-annealed in pO2 values ranging from 0.13 – 10-6 atm. The samples were exposed to the specified pO2 value throughout the re- annealing process i.e., for heating, dwelling and cooling cycles. The stress change during 208 the heating and cooling step during re-annealing was defined as heating and cooling respectively and is shown in Figure C.3.3 (c) for clarity. The stress and electrochemical cycling profiles of different LMO samples that were re-annealed at different pO2s are shown in Figure C.3.4. These plots were used to study the following: 1. The change in the electrochemical performance of the re-annealed samples during run 2. 2. The dependence of the OCV (vs. Li/Li+) of the re-annealed films (i.e., before run 2) on the pO2 used for re-annealing. This is plotted in Figure C.3.7. 3. The dependence of the heating and cooling on the re-annealing pO2s. The plot is shown in Figure C.3.8. (a) 280 h(GPa-nm) 240 200 160 120 re-annealed at run 1 run 2 80 o 750 C in air 40 Potential (V, vs. Li/Li ) 4.4 + 4.2 4.0 OCV against Li/Li+ 3.8 before run 1 = 3.65V 3.6 before run 2= 3.65V 3.4 0 10 20 30 40 50 60 70 time (hr) 209 (b) 280 o re-annealed at 750 C 240 h (GPa-nm) -2 and pO2=10 atm 200 160 120 80 run 1 run 2 Potential (V, vs. Li/Li ) 40 4.4 + 4.2 4.0 OCV against Li/Li+ 3.8 before run 1 = 3.65V before run 2= 3.52V 3.6 3.4 0 10 20 30 40 50 60 70 Time (hr) (c) 280 240 h (GPa-nm) 200 160 120 o 80 re-annealed at 750 C; Run 1 -3 Run 2 40 pO2= 10 atm Potential (V, vs. Li/Li ) + 4.4 4.2 4.0 OCV against Li/Li+ 3.8 before run1= 3.65V 3.6 before run 2= 3.43V 3.4 0 5 10 15 20 25 30 35 40 45 50 55 60 65 Time (hr) 210 (d) 280 240 h (GPa-nm) 200 st lo 160 s ot 120 sp o 80 re-annealed at 750 C; 40 Run 1 -4 Run 2 Potential (V, vs. Li/Li ) pO2= 10 atm 4.5 + 4.0 OCV against Li/Li+ before run1= 3.65V 3.5 before run 2= 2.95V 3.0 0 5 10 15 20 25 30 35 40 45 50 55 Time (hr) (e) 350 300 h (GPa-nm) 250 200 150 100 o re-annealed at 750 C; 50 Run 1 -6 Run 2 0 pO2~ 10 atm (pure Ar) Potential (V, vs. Li/Li ) + 4.5 4.2 3.9 3.6 OCV against Li/Li+ 3.3 before run 1 = 3.65V before run 2 = 2.91V 3.0 2.7 0 10 20 30 40 50 60 Time (hr) Figure C.3.4. Stress evolution and the corresponding charge/discharge for LMO films cycled using the experimental scheme as shown in Figure 4.5 and re-annealed at 750oC and at (a) in air, (b) pO2= 10-2 atm., (c) pO2= 10-3 atm., (d) pO2= 10-4 atm., (e) pO2~ 10-6 atm. (in pure Argon gas). 211 Evaluating the electrochemical and stress profiles during run 2 of LMO samples that were re-annealed in different pO2 environments (from Figure C.3.4) suggests that the sample reannealed in air shows similar electrochemical and stress profiles as in run 1. Similar behavior is also seen for the sample re-annealed at pO2= 10-2 atm. For a re- annealing pO2 <10-2 atm. (Figure C.3.4 (c) to (e)), the samples show poor electrochemical performance during run 2 i.e., upon lowering the pO2 during the re-annealing process from 10-2 to 10-6 atm., the capacity of the re-annealed films during run 2 drastically reduces and the film eventually does not electrochemically cycle at all (as seen in Figure C.3.4 (e)). This could be explained in terms of irreversible phase transformations that take place in LMO films when they are annealed at different pO2s.6 Using thermogravimetric analysis, chemical titration and XRD techniques on bulk LMO, it has been shown by Sugiyama et al. that LMO can withstand a critical non-stoichiometry (cr) value of 0.2 (occurs around a pO2 value of 10-3 atm.), beyond which, the material starts to decompose into secondary phases including Mn3O4 and LiMnO2. The cubic spinel phase completely decomposes into these secondary phases for = 0.67 (occurs at pO2 ~10-4 atm.). For 0.07≤≤0.2, the cubic spinel phase distorts to tetragonal phase. Such secondary phase formation at different re-annealing environments (pO2s) was also observed in our experiments. Figure C.3.5 shows the XRD measurements carried out on the LMO samples after they were re-annealed at 750oC and at different pO2s. The XRD measurements were carried out before run 2. Consistent with the observations of Sugiyama et al., our samples also starts to form secondary phases at pO2~ 10-3 atm. and completely transform into these phases when the re-annealing is carried out in Ar gas (pO2~10-6 atm.) as evidenced by the absence of XRD peaks for LMO for 212 sample re-annealed in Ar. These secondary phases are inactive towards Li insertion/extraction and as such they fail to cycle against Li metal. This explains the poor cycling performance during run 2 for samples re-annealed at low pO2s. Interestingly, we failed to see any XRD peaks corresponding to the Mn3O4 phase. Instead, the secondary phases that were found to form in our samples (as per Figure C.3.5) were LiMnO2 and Mn2O3. The fact that these secondary phases are present after cooling the samples to room temperature in the corresponding pO2 environments indicates that the phase changes that occur at high temperatures are irreversible. This is also evident from the change in the color of the LMO film before and after the re-annealing step (see Figure C.3.6). * o * LMO + o/+ * o Mn2O3 + LiMnO2 (f) Intensity (a.u) (e) (d) (c) (b) (a) annealed new Pt substrate annealed old Pt substrate 10 20 30 40 50 60 70 80 2 (degrees) Figure C.3.5. XRD measurements performed on the LMO films (a) pristine and those that were re-annealed at 750oC and at (b) in air, (c) pO2= 10-2 atm., (d) pO2= 10-3 atm., (e) pO2= 10-4 atm., (f) pO2~ 10-6 atm. (in pure Argon gas). Note that the substrates used for sample d and the other samples were from different batches and hence XRD plots corresponding to annealed platinized substrates from two different batches (new and old) are also shown in the plot. 213 Figure C.3.6. LMO samples re-annealed at 750oC and (a) in air and (b) in pure Ar (pO2~ 10-6 atm.). These images were taken after re-annealing (before run 2). The samples that were re-annealed at pO2 < 10-2 atm. all showed similar color changes which indicate towards possible irreversible phase transformations taking place in LMO during the re- annealing step. OCV’s of the LMO films re-annealed at different pO2s were measured before run 2. These values are plotted against the pO2 used for re-annealing in Figure C.3.7. As can be seen, the film re-annealed in air, has an OCV of 3.65 V which is the same as that of the pristine film. This also indicates that re-annealing the cycled LMO sample in air does not cause any additional phase changes in the film. As the re-annealing pO2 is decreased (i.e., the re-annealing environment is made more reducing), the OCV of the film (before run 2) decreases. This suggests that the re-annealed film has a different composition/structure than the pristine film and that this film has a lower average oxidation state of Mn; this is consistent with the secondary phases that are observed in these films at lower pO2s. 214 3.6 OCV (V, vs. Li/Li ) + 3.4 3.2 3.0 2.8 2.6 -6 -5 -4 -3 -2 -1 0 log10(pO2[atm]) Figure C.3.7. Open circuit potentials (vs. Li/Li+) as measured before run 2 of the LMO films re-annealed at different pO2s. The samples re-annealed at a pO2 of 10-3, 10-4 and 10- 6 atm., undergo phase transformation and therefore have lower OCV values before run 2. As discussed earlier in part I, for a cycled LMO film that was re-annealed in air, the recovery of the irreversible structural change take place during the heating step. As such, the stress change during heating is less than the measured thermal stress value (since, recovery is tensile and relieves the thermal stress). Upon cooling, since the irreversible structural change (that occurred during run 1) has already been reverted at high temperatures, the stress change during cooling is measured to be same as the expected value of the thermal stress for LMO-quartz system (~1.23 GPa). Similarly, for the samples re-annealed in different pO2s, stress change during heating could be because of contributions from: i) thermal mismatch between the film-substrate system, ii) induced non-stoichiometry at low pO2s and corresponding phase changes and (iii) recovery of the irreversible structural change in the cycled sample. The change in stress during cooling 215 could be due to the thermal mismatch between the substrate and the overall phases present in the film (primary + secondary). The heating and cooling as measured from the re-annealing measurements (in Figure C.3.4) carried out at different pO2s are plotted in Figure C.3.8. The cooling values for the sample re-annealed in air and at 10-2 atm. of O2 were found to be very similar to the expected thermal stress values for the LMO-quartz system. This indicates that the LMO samples re-annealed at these pO2s did not undergo any secondary phase formation at high temperatures (consistent with Sugiyama et al.). As the re-annealing pO2 is decreased (< 10-2 atm.), both the heating and cooling values increase. The increase in the heating values could be explained by the increase in the stress contributions from the induced non-stoichiometry at low pO2s and the phase transformations associated with it. During cooling, the sample has a mixture of phases (primary: LMO and secondary: LiMnO2 and Mn2O3) in varying proportions (will be different at different pO2’s). As a result, the stress change during the cooling arises because of the differences in the average CTE value of the transformed film (with primary + secondary phases) and that of the quartz substrate. An increase in the cooling with reducing pO2s would then indicate that the net CTE value of this transformed film is higher than that of the pristine LMO film and as such, the thermal stress experienced by the film at lower pO2s is higher than the expected thermal stress for LMO-quartz system. 216 2.4 heating 2.1 cooling 1.8  (GPa) 1.5 expected thermal stress 1.2 0.9 0.6 phase change 0.3 observed with XRD 0.0 -6 -5 -4 -3 -2 -1 0 log10(pO2[atm]) Figure C.3.8. heating and cooling values measured for the cycled samples re-annealed at different pO2s. The dashed line shows the measured thermal stress values for LMO- quartz system at 750oC (1.23 GPa). Additionally, a control experiment was carried out where a pristine LMO sample was annealed in a series of oxidizing and reducing environments as shown in Figure C.3.9. Experimental conditions during different stages are tabulated in Table C.3.1. The purpose of this experiment was to study how the stress evolution takes place when the pristine LMO sample is exposed to different oxidizing and reducing environments. The XRD measurement of the sample after the re-annealing measurement is shown in Figure C.3.9 (b). It is observed that at 750oC, the stress values do not change much when the gaseous environment is changed from oxidizing to reducing (pO2s in the range of 0.13 – 10-6 atm.) and back to oxidizing. The cooling value on the other hand, is much larger than heating. The XRD measurement (Figure C.3.9 (b)) of this sample after re-annealing shows that several secondary phases are present in the film at room temperature; it is 217 important to note here that because the cooling of the sample is carried out in an oxidizing environment (0.13 atm. of O2), some LMO phase still exists even after the sample is exposed to pure Ar. This suggests that the LMO film did undergo irreversible phase transformations at high temperatures and low pO2s but there is no stress change associated with these transformations, which is quite surprising to see. More careful set of experiments needs to be conducted to better understand such a behavior. Stage Experimental conditions I Heated from room temperature to 750oC in 0.13 atm. of O2 II At 750oC and pO2= 10-2 atm. III At 750oC and pO2= 0.13 atm. IV At 750oC and pO2= 10-3 atm. V At 750oC and pO2= 0.13 atm. VI At 750oC and pO2= 10-4 atm. VII At 750oC and pO2= 0.13 atm. VIII At 750oC and pO2~ 10-6 atm. (pure Ar) IX At 750oC and pO2= 0.13 atm. X Cooled to room temperature from 750oC in 0.13 atm. of O2 Table C.3.1. Experimental conditions at different stages for the experiment in Figure C.3.9 (a). 218 3.5 (a) o 750 C 3.0 2.5 I IIIII IV V 2.0 VI X VII VIII IX  (GPa) 1.5 1.0 0.5 0.0 -0.5 0 80000 160000 240000 320000 Time (secs) (b) s- substrate LMO(111) Intensity (a.u) LMO(311) Mn2O 3/ LiMnO 2 Mn2O 3 LiMnO 2 s s s 10 20 30 40 50 60 70 80 2 (deg) Figure C.3.9. (a) Stress evolution during the control experiment as described in the text and (b) the XRD measurement carried out on the sample after the control experiment. Stages I-X in figure (a) corresponds to the experimental conditions tabulated in Table C3.1. 219 To summarize, the LMO film undergoes irreversible phase transformations for pO2s < 10-2 atm. The secondary phases that are formed are inactive towards (de)lithiation and as a result, the electrochemical performance during run 2 is significantly affected. This limits our re-annealing pO2 range between 0.21 – 10-2 atm. of O2 (only differs by an order of magnitude) and as such, it becomes extremely difficult for us to probe the effect of non-stoichiometry on the magnitude of the anomalous drop during the first de- lithiation cycle during run 2 because the number of data points are limited. Hence, these set of experiments did not provide any additional/conclusive insight into the oxygen loss phenomena that is hypothesized to take place during the later stages of the first delithiation cycle in LMO (as discussed in Chapter 4). C.4. Additional Electrochemical and MOSS Measurements on LMO Films Besides the experiments discussed in Chapter 4 and in appendices C.1-C.3, some additional measurements were conducted on the LMO films: 1. Stress evolution during deep-discharge cycles (4.3–2 V). 2. Voltage range in which the anomalous drop occurs during the first delithiation cycle of LMO. 220 Stress evolution during deep discharge cycles (4.3-2 V) of LMO Although all the electrochemical measurements carried out on LMO in Chapter 4 and in Appendix C were limited to 4.3-3.5 V range, delithiation/lithiation in LixMn2O4 can be achieved in the range 0 ≤ x ≤ 2. Cycling is generally restricted to the region with 0 ≤ x ≤ 1 (i.e., 4.3-3.5 V range; called the “4 V region”). This restriction is a consequence of the severe capacity fading observed in the region 1 ≤ x ≤ 2 ( 3 V region) arising from a structural phase transition (cubic ↔ tetragonal) resulting from the Jahn-Teller (J-T) effect of Mn3+ ions. In an attempt to study the stress evolution in the deep discharge region, a 100 nm thick pristine LMO sample was cycled between 4.3-2 V at a current density of 25A/cm2 using the experimental setup as described in Chapter 4 (Figure C.4.1). As expected, tensile stress evolves in the LMO films with lithium extraction and compressive stress evolves during lithium insertion. An anomalous drop during the later stages of the first delithiation cycle was also observed. Interestingly, the stress profile shows a plateau around the 3 V region which is where the J-T distortions are known to occur. Significant build-up of compressive stress during the first five cycles is evident from the lowering of the stress state of the film at the end of each lithiation/delithiation cycle. The XRD measurement of the LMO sample after the electrochemical cycling shown in Figure C.4.1 (b) is consistent with the amorphization that is believe to take place in LMO when it is repeatedly cycled to low voltages. The fact that the capacity fades and that the electrochemical profile changes (voltage plateaus become less prominent) with subsequent lithiation/delithiation cycles suggests that the J-T distortion occurring around 3V are inducing irreversible phase change and amorphization in the LMO film. As these 221 measurements were preliminary, no experiments in the deep discharge region were further pursued. Nevertheless, it would be interesting to conduct a detailed study to understand these phase transformations and the corresponding stress evolution during the deep discharge cycles. (a) 2.1 1.8  (GPa) 1.5 1.2 0.9 4.5 0 2000 4000 6000 8000 10000 12000 14000 Potential (V, vs. Li/Li ) (b) + 4.0 3.5 3.0 2.5 2.0 0 2000 4000 6000 8000 10000 12000 14000 Time (sec) (c) 800 LMO (311) s 600 LMO (111) Intensity (a.u.) Mn2O 3 400 before cycling 200 after cycling 0 20 40 60 80 2 Figure C.4.1. (a) Stress evolution and (b) the corresponding charge-discharge profiles of a ~100 nm thick LMO film cycled in the 4.3-2 V (vs. Li/Li+) range with a constant current density of 25 µA/cm2. The XRD measurement of the LMO sample before and after the electrochemical cycling in (a) is shown in (c). 222 Occurrence of the anomalous drop at higher voltages To study the voltage range at which the anomalous drop during the first delithiation cycle takes place, two separate LMO samples were cycled as follows: The first sample, “Sample I”, was cycled between 4.3-3.5 V for two cycles. During the third and the fourth cycle, the sample was delithiated to 4.4 and 4.5 V respectively. Finally it was delithiated to 4.3 V (Figure C.4.2 (a) and (b)). It was seen here that the anomalous drop only takes place during the first delithiation cycle during which the irreversible structural changes take place resulting in a stable configuration. Once, this stable configuration is obtained, no further oxygen loss takes place (even when delithiated to higher voltages during cycle 3) and thus, the stress evolution is reversible. A second sample, “Sample II”, was cycled with a modification to the standard experimental protocol (Figure C.4.3 (a) and (b)). Starting with a cutoff voltage of 4.15 V, the voltage limit was increased incrementally by 0.05 V each cycle i.e., for cycle 1, the sample was delithiated to 4.15 V, for cycle 2, it was delithiated to 4.2 V, and so on till a final cutoff voltage of 4.5 V. The sample was held at these voltages for 2 hours to allow for the stress to stabilize. Figure C.4.3 (a) suggests that the anomalous drop begins at 4.05 V and continues until 4.35 V. The anomalous drop ceases to occur beyond 4.35 V. The magnitude of the drop decreases with increasing voltage steps. Interestingly, the drop happens in an irreversible fashion i.e. during subsequent cycles, the drop only occurs at V > Vprevious cycle. For example, in cycle 3 (discharged to 4.25 V), the drop only starts after V > 4.2 V. 223 These measurements suggest that the anomalous drop due to the irreversible structural change occurs between 4.05-4.35 V and only when the film is delithiated to these potentials for the first time. Once the irreversible structural changes have taken place at a particular potential and the structure has attained a stable configuration, no further anomalous drop is observed. 220 (a) h (GPa-nm) 200 180 160 140 Potential (V, vs. Li/Li ) + 4.6 4.5 4.4 (b) 4.3 4.2 4.0 3.8 3.6 3.4 0 10000 20000 30000 40000 50000 60000 Time (secs) Figure C.4.2. (a) Stress evolution and (b) the corresponding charge-discharge profiles for sample I cycled as per the experimental protocol described above and with a constant current density of 2.5 µA/cm2. 224 240 (a) h (GPa-nm) 220 200 180 160 140 120 100 Potential (V, vs. Li/Li ) + 4.6 4.5 4.4 4.35 4.4 4.45 (b) 4.3 4.2 4.25 4.2 4.15 4.03 4.0 3.8 3.6 3.4 0 50000 100000 150000 Time (secs) Figure C.4.3. (a) Stress evolution and (b) the corresponding charge-discharge profiles for sample II cycled as per the experimental protocol described above and with a constant current density of 2.5 µA/cm2. C.5. Nanoscale Electrochemomechanical Spectroscopy (NECS) Technique: Application to LMO Thin Films This work is done in collaboration with Jessica G. Swallow (Van Vliet Group, MIT). She proposed a technique called “Nanoscale Electrochemomechanical Spectroscopy (NECS)” to directly measure the dynamic chemomechanical expansion/contraction of a material as a response to electrochemical driving forces under operando conditions. Depending on the sample design, this technique could be used to detect stress-amplified actuation or pure film strain on the scale of nm, including at high temperatures and in gas environments. In her experiments, she applies a sinusoidal voltage bias at different frequencies and temperatures and measures the corresponding mechanical response of Pr0.1Ce0.9O2- (PCO) thin films by employing a non-conductive 225 probe tip. As discussed in Chapters 2 and 3, PCO films undergo volume changes upon oxygen vacancy creation/annihilations. Applying a voltage bias drives the oxygen atoms in and out of the PCO film, which results in the expansion and contraction of the film, respectively. Using an equivalent circuit model, she analyzed these results to show that NECS could also be used to estimate changes in activation energies and oxygen exchange mechanisms in PCO and other functional oxides. As such, she suggested that this technique could facilitate new understanding of materials and conditions that maximize or minimize stress, strain, and fracture under redox cycling or gas interruption for applications in fuel cells, batteries, and gas sensors, or in response to electrical signals or environmental stimuli for sensor and actuator applications. In this appendix, we extend her NECS technique to battery materials to study the frequency dependent stress response of LMO films (cathodes for Li-ion batteries) upon lithium insertion/extraction. For the current set of experiments, the LMO films were prepared on a 25.4 mm diameter platinized quartz wafers using the film deposition technique as described in Chapter 4 (Figure C.5.1(a)). The samples were electrochemically cycled against Li metal using a Biologic VMP3 Potentiostat (LASV mode). Sinusoidal electrical bias signals were applied in three different voltage regimes (3.5-4.1 V, 3.6-4.2 V and 3.7-4.3 V against Li metal) at frequencies of 10-4, 5×10-4, 10-3, 5×10-3, 10-2, 5×10-2 and 10-1 Hz. The sample was cycled at a particular frequency for more than 10 cycles before moving on to the next frequency. The mechanical response of the sample to the applied voltage bias was measured using the MOSS technique. Before the sample was cycled in the LASV mode, it was first galvanostatically charged and discharged at 8A between 3.5-4.3 V for two delithiation-lithiation cycles. This was done 226 to allow for the irreversible structural changes to occur so that the film attains a stable configuration (as discussed in Chapter 4). A typical input sinusoidal voltage bias and the corresponding stress response for the LMO film is shown in Figure C.5.1(b). (b) 4.5 -3 -155 4.4 f= 10 Hz (4.2-3.6V) -160 4.3 phase lag () -165 Potential (V, vs. Li/Li ) + 4.2 -170 2*Amplitude (2A) 4.1 *h (GPa-nm) 4.0 -175 3.9 -180 3.8 -185 3.7 -190 3.6 3.5 -195 3.4 -200 0.0 0.1 0.2 0.3 0.4 0.5 Time (hr) Figure C.5.1. (a) Schematic of the LMO films used for the measurements. (b) A typical sinusoidal voltage input and the corresponding stress response of the LMO film in the voltage range of 4.2-3.6 V and at a frequency of 10-3 Hz. By analyzing the experimental results using a suitable model (not discussed here) one can describe the measured phase lag () and amplitude (A) of the mechanical response of the LMO films and its relation to the fundamental processes occurring within the material in response to frequency dependent lithiation/delithiation. Due to conflict of interest, this appendix only reports the MOSS data collected on the LMO thin films. The 227 model used to analyze the experimental data and the corresponding discussions will be included in a later publication. Figures C.5.2 – C.5.4 shows the input voltage and the corresponding stress response at seven different frequencies. As expected, a positive applied bias causes stresses to evolve in tensile direction (indicative of volume compression due to Li extraction), while a reduction in bias results in compressive stress evolution (corresponding to volume expansion due to Li insertion). Given sufficient time to relax following a change in lithium activity, the sample can equilibrate fully. Accordingly, with decreasing frequency, the amplitude should approach a maximum value, whereas the phase lag should approach zero. This is exactly what is observed in Figures C.5.2-C.5.4 i.e., as the frequency is decreased from 0.1 to 0.0001 Hz, the amplitude (magnitude of stress-thickness change) increases and the phase lag, , between the voltage peak and the stress-thickness peak approaches zero. -163 -162 (b) 4.1 -2 (a) -1 10 Hz 5*10 Hz -163 4.0 4.0 Potential (V, vs. Li/Li ) + Potential (V, vs. Li/Li ) + 3.9 -164 -164 *h (GPa-nm) *h (GPa-nm) -165 3.8 3.8 3.7 -165 -166 3.6 3.6 -167 3.5 -168 -166 76.889 76.890 76.891 76.892 76.893 76.894 76.842 76.844 76.846 76.848 76.850 76.852 time (hr) time (hr) 228 (c) -160 4.1 -2 4.1 10 Hz (d) -3 5*10 Hz -156 4.0 4.0 Potential (V, vs. Li/Li ) Potential (V, vs. Li/Li ) -158 + + -162 3.9 3.9 *h (GPa-nm) *h (GPa-nm) -160 3.8 3.8 -164 -162 3.7 3.7 -164 3.6 3.6 -166 -166 3.5 3.5 -168 76.60 76.61 76.62 76.63 76.64 76.10 76.12 76.14 76.16 76.18 76.20 time (hr) time (hr) 4.1 -145 4.1 -135 (e) -3 (f) -4 10 Hz 5*10 Hz 4.0 4.0 -140 Potential (V, vs. Li/Li ) -150 + Potential (V, vs. Li/Li ) + 3.9 3.9 -145 *h (GPa-nm) *h (GPa-nm) -155 3.8 3.8 -150 -160 3.7 3.7 -155 3.6 -165 3.6 -160 3.5 3.5 -170 -165 73.8 73.9 74.0 74.1 74.2 74.3 68.4 68.6 68.8 69.0 69.2 time (hr) time (hr) -120 (g) 4.1 -4 10 Hz 4.0 Potential (V, vs. Li/Li ) -130 + 3.9 *h (GPa-nm) 3.8 -140 3.7 -150 3.6 3.5 -160 60 61 62 63 64 time (hr) Figure C.5.2. LMO films electrochemically cycled in the voltage range of 4.1-3.5 V vs. Li/Li+ at a frequency of (a) 10-1, (b) 5×10-2, (c) 10-2, (d) 5×10-3, (e) 10-3, (f) 5×10-4 and (g) 10-4 Hz. The sample was cycled at each frequency for more than 10 cycles. 229 -184 -180 (a) 4.2 -2 (b) 4.2 10 Hz -3 5*10 Hz -182 4.1 -186 4.1 Potential (V, vs. Li/Li ) Potential (V, vs. Li/Li ) + + -184 4.0 4.0 *h (GPa-nm) *h (GPa-nm) -188 -186 3.9 3.9 -188 -190 3.8 3.8 -190 3.7 -192 3.7 -192 -194 3.6 3.6 -194 38.89 38.90 38.91 38.92 38.93 38.94 38.42 38.44 38.46 38.48 38.50 38.52 time (hr) time (hr) -165 -160 (c) 4.2 -3 (d) 4.2 10 Hz 5*10 Hz -4 -170 -165 4.1 4.1 Potential (V, vs. Li/Li ) + Potential (V, vs. Li/Li ) + -175 -170 4.0 *h (GPa-nm) 4.0 -175 *h (GPa-nm) -180 3.9 3.9 -180 -185 3.8 -185 3.8 -190 3.7 -190 3.7 -195 -195 3.6 3.6 -200 -200 37.7 37.8 37.9 38.0 38.1 38.2 32.8 33.0 33.2 33.4 33.6 33.8 time (hr) time (hr) -140 (e) 4.2 -4 10 Hz 4.1 -150 Potential (V, vs. Li/Li ) + 4.0 -160 *h (GPa-nm) 3.9 -170 3.8 -180 3.7 -190 3.6 14 15 16 17 18 time (hr) Figure C.5.3. LMO films electrochemically cycled in the voltage range of 4.2-3.6 V vs. Li/Li+ at a frequency of (a) 10-2, (b) 5×10-3, (c) 10-3, (d) 5×10-4 and (e) 10-4 Hz. The sample was cycled at each frequency for more than 10 cycles. At frequencies < 10 -2 Hz, the MOSS data was very noisy and so, is not shown here. 230 -182 -185 (b) 4.3 -2 (a) 10 Hz -1 5*10 Hz 4.2 -183 4.2 Potential (V, vs. Li/Li ) + -186 Potential (V, vs. Li/Li ) + 4.1 *h (GPa-nm) *h (GPa-nm) -184 4.0 4.0 -187 -185 3.9 -188 3.8 -186 3.8 3.7 -187 -189 39.840 39.841 39.842 39.843 39.844 39.770 39.775 39.780 time (hr) time (hr) -180 (c) 4.3 -2 (d) 4.3 -3 10 Hz 5*10 Hz -177 4.2 -182 4.2 -180 Potential (V, vs. Li/Li ) Potential (V, vs. Li/Li ) + + 4.1 4.1 -183 *h (GPa-nm) *h (GPa-nm) -184 4.0 -186 4.0 -186 -189 3.9 3.9 -192 3.8 -188 3.8 -195 3.7 3.7 -190 -198 39.60 39.61 39.62 39.63 39.64 39.65 39.16 39.18 39.20 39.22 39.24 39.26 time (hr) time (hr) -160 (f) (e) 4.3 10 Hz -3 4.3 -4 -165 5*10 Hz -160 4.2 -170 4.2 Potential (V, vs. Li/Li ) + Potential (V, vs. Li/Li ) + -175 -170 4.1 4.1 *h (GPa-nm) *h (GPa-nm) -180 4.0 4.0 -180 -185 3.9 -190 3.9 -190 -195 3.8 3.8 -200 -200 3.7 3.7 -205 38.1 38.2 38.3 38.4 38.5 38.6 30.8 31.0 31.2 31.4 31.6 time (hr) time (hr) 231 -140 (g) 4.3 -4 10 Hz -150 4.2 Potential (V, vs. Li/Li ) + 4.1 -160 *h (GPa-nm) 4.0 -170 3.9 -180 3.8 -190 3.7 -200 9 10 11 12 13 time (hr) Figure C.5.4. LMO films electrochemically cycled in the voltage range of 4.3-3.7 V vs. Li/Li+ at a frequency of (a) 10-1, (b) 5×10-2, (c) 10-2, (d) 5×10-3, (e) 10-3, (f) 5×10-4 and (g) 10-4 Hz. The sample was cycled at each frequency for more than 10 cycles. As mentioned earlier, these results will be discussed and analyzed in a future publication. 232 C.6. References 1. H. W. Nesbitt and D. Banerjee, American Mineralogist, 83, 305 (1998). 2. M. C. Biesinger, B. P. Payne, A. P. Grosvenor, L. W. M. Lau, A. R. Gerson and R. S. Smart, Applied Surface Science, 257, 2717 (2011). 3. D. Tang, Y. Sun, Z. Yang, L. Ben, L. Gu and X. Huang, Chemistry of Materials, 26, 3535 (2014). 4. P. Casey, A. P. McCoy, J. Bogan, C. Byrne, L. Walsh, R. O'Connor and G. Hughes, Journal of Physical Chemistry C, 117, 16136 (2013). 5. K. Mukai, Y. Kishida, H. Nozaki and K. Dohmae, Journal of Power Sources, 224, 230 (2013). 6. J. Sugiyama, T. Atsumi, T. Hioki, S. Noda and N. Kamegashira, Journal of Power Sources, 68, 641 (1997). 7. M. Molenda, R. Dziembaj, E. Podstawka and L. M. Proniewicz, Journal of Physics and Chemistry of Solids, 66, 1761 (2005). 8. P. Strobel, G. Rousse, A. Ibarra-Palos and C. Masqueller, Journal of Solid State Chemistry, 177, 1 (2004). 9. P. Endres, B. Fuchs, S. KemmlerSack, K. Brandt, G. FaustBecker and H. W. Praas, Solid State Ionics, 89, 221 (1996). 10. J. M. Paulsen and J. R. Dahn, Chemistry of Materials, 11, 3065 (1999). 11. X. Q. Yang, X. Sun, M. Balasubramanian, J. McBreen, Y. Xia, T. Sakai and M. Yoshio, Electrochemical and Solid State Letters, 4, A117 (2001). 233 APPENDIX D SiC OXIDATION MEASUREMNTS D.1. High Temperature Oxidation of SiC and the Corresponding Curvature Change Measured by HTMOSS Silicon Carbide possesses properties like high thermo-chemical stability, high hardness, high fracture toughness etc. It is therefore, widely used in the making of refractory, semiconductor devices, combustion engines, etc. SiC has a tendency to get oxidized at elevated temperature under oxidizing atmosphere. In most of the cases, SiC oxidation is passive with wide variation in the reaction rates and the morphology of the reaction products.1 It proceeds according to the following reaction: 2SiC s + 3O2 g → 2SiO2 g + 2CO(g) D.1.1 During passive oxidation, liberated SiO2 forms a dense layer on the surface of SiC which acts as an anti-oxidation protective layer.2 In this appendix, we made an attempt to study the high temperature oxidation of SiC by measuring the curvature change of SiC/SiO2 system using the MOSS technique. This work was done in collaboration with Ram Krishnamurthy et al., UES Inc. They prepared a 500 m thick SiC substrate. The sample was made from polycrystalline SiC 234 and was oxidized on all sides other than a polished side. The schematic of the sample is shown in Figure D.1.1. The oxidation was carried out at 800oC. The furnace was ramped up from room temperature to 800oC at 10oC/min. It was then held at this temperature for 20 hours. Finally, the sample was furnace cooled to the room temperature. The furnace environment was fixed at 160 Torr of O2 (0.21 atm., similar to air) throughout the experiment. The laser spots for the MOSS measurement were reflected from the polished (un-oxidized) side. Figure D.1.1. Schematic of the SiC/SiO2 sample used for the HTMOSS measurement. The laser spots during the MOSS measurement were reflected from the polished (un- oxidized) side. The change in curvature, , with respect to a flat mirror during the high temperature oxidation of the sample as measured by the MOSS technique is shown in Figure D.1.2. The curvature change observed during the measurement could be interpreted as follows: the sample is initially bent convex outward. During the initial heating to oxidation temperature, the SiC would want to expand more than the silica and consequently the initial curvature gets reduced; from the perspective of the un-oxidized side, it will appear as if the layers below the neutral axis want to expand more compared to those above, resulting in the reduction of the curvature (can be interpreted as compressive stress) as observed. Following oxidation of the un-oxidized side at the 235 oxidation temperature, the initial curvature is reduced further (as the newly formed oxide has a compressive stress), or from the perspective of the un-oxidized side, the layers below the neutral axis want to expand more compared to those above which is consistent with the small, but noticeable stress drop observed during the isothermal hold in the experiment. During the cooling cycle, the SiC would want to contract more than both the thicker oxide that was initially present and the newly formed oxide. However, since the newly formed oxide provides an additional constraint to the contraction of SiC, the initial heating stress is not fully recovered. The difference may be interpreted as the stress contribution (thermal and growth) of the new oxide. 0.01 800 0.00 cooled to -0.01 room lost Temperature ( C) temperature 600 MOSS spots -0.02  (m ) -0.03 400 -1 -0.04 200 -0.05 o -0.06 0 -0.07 0 5 10 15 20 25 30 35 Time (hr) Figure D.1.2. Curvature of the SiC/SiO2 sample as measured by MOSS technique during the high temperature oxidation. A flat mirror was used as reference for the measurement. The laser spots during the MOSS measurement were reflected from the polished (un- oxidized) side. 236 D.2. References 1. H. H. Du, R. E. Tressler and K. E. Spear, Journal of the Electrochemical Society, 136, 3210 (1989). 2. P. J. Jorgensen, M. E. Wadsworth and I. B. Cutler, Journal of the American Ceramic Society, 42, 613 (1959). 237 APPENDIX E MODEL: STRESS CONTRIBUTION TO TWO PHASE EQUILIBRIUM E.1 Complete Formulation In a homogeneous thin film consisting of a single phase p, the equilibrium voltage can be expressed with the following modified form of the Nernst equation: 2 ℱΔ𝜙 𝑜 ≅ −𝑅𝑇 ln 𝛾𝐿𝑖𝑝 𝑐𝐿𝑖 𝑝 + 𝑉𝑝 𝜎𝑝 (E.1.1a) 3 𝐿𝑖 𝑝 𝑝 𝑐𝐿𝑖 𝑉𝐿𝑖 𝜎 𝑝 = 𝑀𝑝 𝜀 𝑝 ≅ 𝑀𝑝 𝜀𝑜𝑝 + 𝑝 𝑐𝑜 3 𝑉𝑚𝑝 𝑑𝑐 (E.1.1b) where Δ𝜙 𝑜 is the modified cell potential, R is the gas constant, T is the temperature, 𝛾𝐿𝑖𝑝 is 𝑝 the activity coefficient of Li in phase p, 𝑐𝐿𝑖 is the concentration of Li in phase p, 𝑉𝐿𝑖𝑝 is the molar volume of Li in phase pand 𝜎 𝑝 and 𝜀 𝑝 are the net stress state and strain (i.e., contributions from intrinsic and extrinsic stress and strain) in the thin film at a cell potential of Δ𝜙 𝑜 . It is also convenient to express the impact of this stress with difference between Δ𝜙 𝑜 (i.e., stress contributions included) and ∆𝜙𝑒𝑞 𝑜 (the unstressed equilibrium state), via: 238 𝑜 𝑝 𝑝 ℱΔ𝜙𝑒𝑞 = −𝑅𝑇ln 𝛾𝐿𝑖,𝑒𝑞 𝑐𝐿𝑖,𝑒𝑞 (E.1.2a) 𝑝 𝑝 𝑝 𝑝 𝑝 𝛾𝐿𝑖 𝛿𝑐𝐿𝑖 2 𝑉𝐿𝑖 𝛿𝑐𝐿𝑖 −𝛿𝑐𝑜 ℱΔ𝜙 𝑜 − ℱΔ𝜙𝑒𝑞 𝑜 ≅ −𝑅𝑇 ln 𝑝 1+ 𝑝 + 𝑉 𝑝 𝑀𝑝 𝜀𝑜𝑝 + 𝑝 (E.1.2b) 𝛾𝐿𝑖 ,𝑒𝑞 𝑐𝐿𝑖 ,𝑒𝑞 3 𝐿𝑖 3 𝑉𝑚 𝑝 where 𝛾𝐿𝑖,𝑒𝑞 is the activity coefficient of Li in phase p when stress contributions are 𝑝 𝑝 𝑝 and 𝛿𝑐𝑜𝑝 = 𝑐𝑜𝑝 − 𝑐𝐿𝑖,𝑒𝑞 𝑝 neglected, 𝛿𝑐𝐿𝑖 = 𝑐𝐿𝑖 − 𝑐𝐿𝑖,𝑒𝑞 . The configuration in Figure 5.11 was used to evaluate two phase equilibrium. The description of the phase that is being created (𝑞 here) is the same as that in Equation 5.11, with an additional volume change due to the phase transformation (∆𝑉 𝑝→𝑞 ). 𝑜 𝑞 𝑞 ℱΔ𝜙𝑒𝑞 = −𝑅𝑇ln 𝛾𝐿𝑖,𝑒𝑞 𝑐𝐿𝑖,𝑒𝑞 (E.1.3a) ℱΔ𝜙 𝑜 − ℱΔ𝜙𝑒𝑞 𝑜 ≅ 𝑞 𝑞 𝑝 𝑝 𝑝 𝛾𝐿𝑖 𝛿𝑐 2 𝑉𝐿𝑖 𝛿𝑐𝐿𝑖 −𝛿𝑐𝑜 ∆𝑉 𝑝 →𝑞 −𝑅𝑇 ln 𝑞 1 + 𝑐 𝑞 𝐿𝑖 + 𝑉 𝑞 𝑀𝑞 𝜀𝑜𝑝 + 𝑝 + 𝑞 (E.1.3b) 𝛾𝐿𝑖 ,𝑒𝑞 𝐿𝑖 ,𝑒𝑞 3 𝐿𝑖 3 𝑉𝑚 3 𝑉𝑚 𝑞 𝑞 𝑞 where 𝛿𝑐𝐿𝑖 = 𝑐𝐿𝑖 − 𝑐𝐿𝑖,𝑒𝑞 . For a full description of equilibrium the other component of the pseudo-binary must also be considered (the subscript 𝑜𝑥 refers to V2O5 in our experiments): 239 𝑞 𝑞 𝑞 𝑝 𝛾𝑜𝑥 1−𝑐𝐿𝑖 2 𝑞 𝑝 𝛤𝑜𝑥 − 𝛤𝑜𝑥 = 0 = 𝑅𝑇𝑙𝑛 𝑝 𝑝 − 𝑉𝑜𝑥 𝜎 𝑞 − 𝑉𝑜𝑥 𝜎 𝑝 (E.1.4a) 𝛾𝑜𝑥 1−𝑐𝐿𝑖 3 𝑉𝐿𝑖𝑝 𝛿𝑐𝐿𝑖 𝑝 − 𝛿𝑐𝑜𝑝 ∆𝑉 𝑝→𝑞 𝑉𝑜𝑥𝑞 𝜎 𝑞 − 𝑉𝑜𝑥𝑝 𝜎 𝑝 = 𝑉𝑜𝑥𝑞 𝑀𝑞 𝜀𝑜𝑝 + + 3 𝑉𝑚𝑝 3 𝑉𝑚𝑝 𝑝 𝑝 𝑝 𝑉𝐿𝑖 𝛿𝑐𝐿𝑖 −𝛿𝑐𝑜 −𝑉𝑜𝑥𝑝 𝑀𝑝 𝜀𝑜𝑝 + 𝑝 (E.1.4b) 3 𝑉𝑚 If all of the thermodynamic properties for both phases are specified (𝛾’s, 𝑀’s, and 𝑉’s), then Equations E.1.2 to E.1.4 can be solved to obtain the Li concentration in both 𝑝 𝑞 phases (𝑐𝐿𝑖 and 𝑐𝐿𝑖 ) and Δ𝜙 𝑜 , as a function of the initial strain (𝜀𝑜𝑝 ). Even when 𝜀𝑜𝑝 = 0, this solution will deviate from the standard equilibrium case because the thin film constraint leads to stress in the material. Although this analysis is straight forward, a precise quantitative evaluation of our experiments is limited by several factors. First, the thermodynamic properties are not fully known. As described below, variations in these properties can lead to significant variations in the voltage plateau. Structures that differ from the bi-layer assumed here will also lead to more complex stress fields. A large variety of configurations are possible, however, these are not considered in the current treatment. In the absence of more precise information about the nature of the transformation in our films, the relatively simple configuration in Figure 5.11 is employed to provide general insight into the stress-induced shifts in the voltage plateaus. The solution thermodynamics are described by the activity coefficients, however, these are not accurately known for the phases of interest. Thus, to provide some insight into these effects it is convenient to employ the empirical Redlich-Kister form that is often used to describe the behavior of real solutions: 240 ∆𝐺𝑚𝑖𝑥 𝑐 = 𝑅𝑇 𝑐𝐿𝑖 ln 𝑐𝐿𝑖 + 1 − 𝑐𝐿𝑖 ln 1 − 𝑐𝐿𝑖 𝑛 + 𝑐𝐿𝑖 1 − 𝑐𝐿𝑖 𝑘=0 𝐿𝑘 (1 − 2𝑐𝐿𝑖 )𝑘 (E.1.5) where 𝐿𝑘 are the coefficients of the power series. Using a simple two parameter version of this for each phase then leads to the following evaluation of the chemical terms in Equation E.1.3(b) and E.1.4(a): 𝑝 𝛿𝑐𝐿𝑖 𝑅𝑇𝑙𝑛 𝛾𝐿𝑖𝑝 𝑐𝐿𝑖 𝑝 𝑝 𝑝 𝛾𝐿𝑖,𝑒𝑞 𝑐𝐿𝑖,𝑒𝑞 = 𝑅𝑇𝑙𝑛 1 + 𝑝 𝑐𝐿𝑖,𝑒𝑞 2 3 + −2𝐿𝑝𝑜 − 6𝐿𝑝1 1 − 2𝑐𝐿𝑖,𝑒𝑞 𝑝 𝑝 + 6𝐿𝑝1 𝑐𝐿𝑖,𝑒𝑞 𝑝 𝑝 + 2𝐿𝑝1 𝛿𝑐𝐿𝑖 𝑝 𝛿𝑐𝐿𝑖 𝛿𝑐𝐿𝑖 (E.1.6a) 𝑞 𝛿𝑐𝐿𝑖 𝛾𝐿𝑖𝑞 𝑐𝐿𝑖 𝑞 𝑞 𝑞 𝑅𝑇𝑙𝑛 𝛾𝐿𝑖,𝑒𝑞 𝑐𝐿𝑖,𝑒𝑞 = 𝑅𝑇𝑙𝑛 1 + 𝑞 𝑐𝐿𝑖,𝑒𝑞 2 3 + −2𝐿𝑞𝑜 − 6𝐿𝑞1 1 − 2𝑐𝐿𝑖,𝑒𝑞 𝑞 𝛿𝑐 𝑞 + 6𝐿𝑞1 𝑐𝐿𝑖,𝑒𝑞 𝑞 𝑞 + 2𝐿𝑞1 𝛿𝑐𝐿𝑖 𝑞 𝛿𝑐𝐿𝑖 (E.1.6b) One constraint on this model is that it must be consistent with the measured 𝑜 equilibrium potential, Δ𝜙𝑒𝑞 . For the two phase equilibrium that is of interest here, this gives: 𝑜 𝑝 𝑝 𝑝 2 𝑝 𝑝 𝑝 𝑝 −ℱΔ𝜙𝑒𝑞 = 𝑅𝑇ln 𝛾𝐿𝑖,𝑒𝑞 𝑐𝐿𝑖,𝑒𝑞 = 1 − 𝑐𝐿𝑖,𝑒𝑞 𝐿𝑜 + 𝐿1 1 − 4𝑐𝐿𝑖,𝑒𝑞 + 𝑅𝑇ln 𝑐𝐿𝑖,𝑒𝑞 (E.1.7a) 𝑜 𝑞 𝑞 𝑞 2 𝑞 𝑞 𝑞 𝑞 −ℱΔ𝜙𝑒𝑞 = 𝑅𝑇ln 𝛾𝐿𝑖,𝑒𝑞 𝑐𝐿𝑖,𝑒𝑞 = 1 − 𝑐𝐿𝑖,𝑒𝑞 𝐿𝑜 + 𝐿1 1 − 4𝑐𝐿𝑖,𝑒𝑞 + 𝑅𝑇ln 𝑐𝐿𝑖,𝑒𝑞 (E.1.7b) 241 These conditions are equivalent to determining one of the solution parameters for each phase. The equilibrium condition for the other component in the unstressed state (i.e., Equation E.1.4 with 𝜎𝑜𝑝 = 𝑀𝑝 𝜀𝑜𝑝 = 0), then implies that only one of the four solution parameters is unknown. One additional constraint on the material properties is that the molar volume of each phase can be expressed in terms of the partial molar volumes via: 𝑉𝑚𝑝 = 𝑐𝐿𝑖 𝑝 𝑝 𝑝 𝑉𝐿𝑖 + 1 − 𝑐𝐿𝑖,𝑒𝑞 𝑉𝑜𝑥𝑝 (E.1.8a) 𝑉𝑚𝑞 = 𝑐𝐿𝑖 𝑞 𝑞 𝑞 𝑉𝐿𝑖 + 1 − 𝑐𝐿𝑖,𝑒𝑞 𝑉𝑜𝑥𝑞 (E.1.8b) For the phases of interest, only the full molar volumes, 𝑉𝑚𝑝 and 𝑉𝑚𝑞 , are known quantities. This combined with Equation E.1.8 implies that there is one unknown volume for each phase, which we express as: 𝑝 𝑞 𝑉𝐿𝑖 𝑉𝐿𝑖 𝑓𝑝 = 𝑝 ; 𝑓𝑞 = 𝑞 (E.1.9) 𝑉𝑚 𝑉𝑚 The elastic properties for the phases of interest have also not been reported (𝑀𝑝 and 𝑀𝑞 for the film configuration). 242 Impact of Key Thermodynamic Properties To evaluate the model outlined above, five unknown thermodynamic quantities must be specified: 𝑓 𝑝 , 𝑓 𝑞 , 𝑀𝑝 , 𝑀𝑞 , and one of the four solution parameters (i.e., this 𝑝 𝑞 𝑜 assumes that Δ𝜙𝑒𝑞 , 𝑐𝐿𝑖,𝑒𝑞 , 𝑐𝐿𝑖,𝑒𝑞 , 𝑉𝑚𝑝 , 𝑉𝑚𝑞 , ∆𝑉 𝑝→𝑞 , and 𝜎𝑜𝑝 are specified). The solution of 𝑝 𝑞 the governing equations then gives values for Δ𝜙 𝑜 , 𝛿𝑐𝐿𝑖 , and 𝛿𝑐𝐿𝑖 . It is instructive to explore how the unknown thermodynamic properties will alter the position of the voltage plateau, Δ𝜙 𝑜 , before considering the impact of the initial stress in the film. As a starting point, the degree of freedom associated with the additional solution parameter can be evaluated by setting the curvature𝜅 of the Gibbs free energy of one of the phases: 𝑝 𝑝 𝜕𝐺𝐿𝑖 ,𝑥𝑠 = −2𝐿𝑝𝑜 − 6𝐿𝑝1 1 − 2𝑐𝐿𝑖,𝑒𝑞 𝑝 𝑝 𝑝 𝜅𝑒𝑞 = − 𝑅𝑇𝑙𝑛 𝑐𝐿𝑖,𝑒𝑞 1 − 𝑐𝐿𝑖,𝑒𝑞 (E.1.10) 𝜕𝑐 𝑝 𝑝 𝑐𝑒𝑞 𝑝 For example, with the delta phase (𝑐𝐿𝑖,𝑒𝑞 = 0.5), this leads to a relatively simple result: 1 𝐿𝑝𝑜 = − 2 𝜅𝑒𝑞 𝑝 + 3.317 𝑘𝐽 𝑚𝑜𝑙𝑒 (E.1.11) In this case, setting curvature determines 𝐿𝑝𝑜 directly and the other three solution 𝑜 𝑝 𝑞 parameters are determined by setting Δ𝜙𝑒𝑞 , 𝑐𝐿𝑖,𝑒𝑞 , and 𝑐𝐿𝑖,𝑒𝑞 . For the other phases of interest here (i.e., gamma and omega, etc), the same logic applies, but Equation E.1.10 does not lead directly to an explicit relationship between 𝐿𝑝𝑜 and 𝜅𝑒𝑞 𝑝 . 243 𝑝 To understand the implications of different curvature values, note that as 𝜅𝑒𝑞 increases the Li solubility range decreases (i.e., 𝑝 behaves more like a “line compound”). 𝑞 In the current formulation, the curvature of the other phase (i.e., 𝜅𝑒𝑞 ) is determined by the equilibrium solution. One could allow this to vary as well, by adding one more additional solution parameter to Equation E.1.5. However, this additional complexity is superfluous given the uncertainty about the actual solution thermodynamics. The full formulation of the thermodynamic model discussed above can be applied to the experimental results as observed in Chapter 5. In this preliminary model, one can calculate the total change in the Gibb’s free energy in the two phases p and q, by summing the chemical component, Gchem, given by Equation E.1.5 and the stress component, G, given as (adapted from Bucci et al.1 ): For phase q, q Xq 2 q   qVmLi X Li 1 Li 1 G  (1  X )  [ q  q { }]dX  (1  X Li  q ) [ { }]dX Li (E.1.12) 0 (1  X Li ) 3(1  c) V2O5 0 (1  X Li ) Li q 2 Li q 2 3 V p  q where  q  M q [ op  ] 3Vm 𝑞 𝑞 Δ𝐺𝑡𝑜𝑡𝑎𝑙 ≅ Δ𝐺𝑐𝑕𝑒𝑚 + Δ𝐺𝜎𝑞 (E.1. 13) and for phase p, Δ𝐺𝜎𝑝 ≅ 0 (E.1.14) 𝑝 𝑝 Δ𝐺𝑡𝑜𝑡𝑎𝑙 ≅ Δ𝐺𝑐𝑕𝑒𝑚 + Δ𝐺𝜎𝑝 (E.1.15) 244 Equations E.1.13 and E.1.15 can be used to evaluate the Gtotal for phases p and q. For example, Figure E.1.1 plots the Gchem and Gtotal for phases p =  and q =  obtained using the above formulation for the case when 𝜀𝑜𝑝 = 0.008, = 800000 and 𝑉𝑚𝐿𝑖 = 3.5 mL/mole; note that the stress and strain values used here are randomly selected and are not the same as measured from the experiments. Also, our calculations were severely limited because of the lack of knowledge of the precise thermodynamic parameters for example, partial molar volume of Li and the oxide in each of the Li-rich V2O5 phases, modulus values of each of the phases, activity coefficient of Li in each of the phases, etc. Nevertheless, Figure E.1.1(b) clearly shows that stress in the system can shift the free energy curves thereby shifting the driving force for lithiation/delithiation and hence causing shifts in the position of the two phase equilibrium plateaus. 245 -0.06 -0.06 (a) G p =G p total chem -0.08 q -0.08 G ph chem -0.10 as G q -0.10 ep total common tangent to Gchem -0.12 -0.12 ph common tangent to Gtotal Gmix (MJ) as -0.14 eq -0.14 -0.16 -0.16 -0.18 p q -0.18 common tangent to Gchem to Gchem : -0.20 intercept = -0.22192 => 2.30004 V -0.20 p q common tangent to Gtotal to Gtotal : -0.22 -0.22 intercept = -0.22169 => 2.297 V -0.24 -0.24 0.4 0.5 0.6 0.7 0.8 0.9 1.0 XLi (b) G q -0.136 chem q G total common tangent to Gchem -0.138 common tangent to Gtotal Gmix (MJ) -0.140 phase q -0.142 stress induced shift in -0.144 shift in the Gq curve common tangent -0.146 0.65 0.66 0.67 0.68 0.69 0.70 XLi Figure.E.1.1. (a) Free energy curves for the two phases p =  and q = as calculated using the formulation described in the text, for the case when 𝜀𝑜𝑝 = 0.008, = 800000 and 𝑉𝑚𝐿𝑖 = 3.5 mL/mole. For clarity, an expanded view of the free energy curve for phase 𝑞 q showing the shift in the ∆𝐺𝑡𝑜𝑡𝑎𝑙 due to stress contributions is shown in (b). 246 Figure E.1.2 plots the equilibrium voltage position for the  phase equilibrium calculated using the above formulation against the initial stress state in the film. It can be seen that the  equilibrium voltage shifts to a lower value with an increase in the initial tensile stress state of the active material. Such calculations were done for different values of M, 𝑉𝑚𝐿𝑖 , , fp and fq and similar trend was observed. We would like to point out that all the above calculations were done for smaller values of 𝜀𝑜𝑝 as the code failed to converge for higher values. None the less, the trend observed is qualitatively consistent with what we observe experimentally i.e., the  equilibrium plateau for the film on Al (with relatively higher initial tensile stress state) forms at lower voltage compared to that for the film on Au (with lower initial tensile stress state). 2.3005 2.3000 Equillibrium voltage 2.2995 2.2990 2.2985 2.2980 Li 2.2975 Vm = 3.5 mL/mole 2.2970 0.000 0.002 0.004 0.006 0.008 p o Figure.E.1.2. equilibrium voltage plateau position plotted against the initial stress state in the film calculated using the formulation for the case when = 800000 and 𝑉𝑚𝐿𝑖 = 3.5 mL/mole. 247 E.2 References 1. G. Bucci, S. P. V. Nadimpalli, V. A. Sethuraman, A. F. Bower and P. R. Guduru, Journal of the Mechanics and Physics of Solids, 62, 276 (2014). 248