CORRELATION OF POINT DEFECTS IN LITHIUM - RICH LAYERED CATHODE MATERIALS FOR LITHIUM - ION BATTERY APPLICATIONS By Christine N icole James A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of Chemical Engineering Doctor of Philosophy 201 9 ABSTRACT CORRELATION OF POINT DEFECTS IN LITHIUM - RICH LAYERED CATHODE MATERIALS FOR LITHIUM - ION BATTERY APPLICATIONS By Christine N icole James The limiting component of lithium - ion batteries continues to be the cathode componen t. Since the layered materials, such as LiCoO 2 , have ob served capacities of roughly half of their theoretical capacities, advances have been made in attempt s to improve their stability and thus capacity. One such attempt is adding Li 2 MnO 3 , thus creating Li 2 MnO 3 - LiMO 2 materials, where M is typically a transitio n metal ion or combination of transition metals. These Li 2 MnO 3 stabilized materials have been shown to be promising with >200mAh/g but still suffer from performance issues. The Li 2 MnO 3 component is observed to lose oxygen during the first charge cycle and thus creates Li 2 - X MnO 3 - . These oxygen vacancies are related to some of the cathode performance issues. However, t he amount of oxygen released and the role of the oxygen vacancies are still not very well understood. Therefore, this work takes an atomic level computational approach using density functional theory calculations to explore the impact of oxygen vacancies and the correlated effects on voltage, capacity, lithium diffusion, chemical strain, dopants and electrolyte decomposition. Despite t he extensive computational work in the literature on lithium transitio n metal oxide cathode materials , little work has been devoted t o the correlated effects of two vacancy types in these materials. Therefore, this work offers novel approaches to model bot h vacancy types and their impacts on each other. First, it was found that the oxygen vacancies can decrease the formation energy of lithium vacancies. Less hopping of lithium atoms is observed and the energy barrier for lithium hopping is increased w h en o xygen vacancies are present . T he cal culated diffusion coefficient decrease s by ~ 5 order of magnitude f r o m the perfect crystal structure. This suggests oxygen vacancies cause a n increased capacity but at the expense of decreased rate capability of these mat erials. The chemical strain associated with both non - dilute lithium vacancies and dilute vacancies w ere analyzed with an anisotropic model. I t was found that the oxygen vacancies and lithium vacancies are highly correlated causing the associated chemical expansion to not be a linear sum of the individual vacancy types. The predicted chemical strain due to a low energy V Li - V O - V Li dumbbell structure can be corr elated with the in situ experimentally measured stress. To investigate if the amount of oxygen vacancies can be controlled , the effects of Si and Al dop ants were also studied. The silicon was shown to decrease the oxygen vacancy formation energy in neighb oring octahedral to the silicon, thus suggested to activate the manganese and increase the capacity of the materials , consistent with experimental observations . Lastly, the impact of surface o xygen vacancies on ad sorption and decomposition of an electroly te component, ethylene carbonate (EC), on the Li 2 MnO 3 surface was investigated. A two proton removal reaction from EC to Li 2 MnO 3 (131) was discovered, suggesting some beneficial effect on the perfect Li 2 MnO 3 surface . However, an EC appears to be repelled near a surface oxygen vacancy. The released oxygen can react with the EC molecule and t rigger different decomposition reactions. O verall, the oxygen vacancies generated in the lithium - rich layered cathode materials are shown to have a very highly correlated impact on lithium, dopant and electrolyte - surface interactions which therefore can significantly impact battery performance and life . iv ACKNOWLEDGEMENTS I would like to thank my advisor, Professor Yue Q i, for all of her guidance and support during my time as a PhD student. She taught me a lot, guided me and encouraged me during my time at MSU. I also appreciate the guidance and support provided by Dr. Kevin Leung for mentoring me for a summer and helping me with my project. His expertise and guidance were invaluable, and he taught me a lot. My committee members, Professor Carl Lira, Professor Donald Morelli, Professor Jeff Sakamoto and Professor Phillip Duxbury were also immensely helpful with their feedb ack and advice. Working with Leah Nation, Professor Brian Sheldon and Dr. Yan Wu was also instrumental to this work and I thank them for their assistance. My group members were also helpful. I could not have completed this without the support of my friends and my family, thank you to all who were there for me to encourage and support me during this process. I especially would like to thank my parents, Michael James and Diana James, and all my friends for their unwavering support and care. This work was done at and with the help of the High Performance Computing Center (HPCC) at Michigan State University. I gratefully acknowledge the National Science Foundation for their support for my work through Grant No. DMR - 141085 0 and 1410946 . Additionally, t his dissertation includes material based upon work supported by the U.S. Dep a rtment of Energy, Office of Science, Office of Workforce Development for Teachers and Scientists, Office of Science Graduate Student Research (SCGSR) program. The SCGSR program is administered by the Oak Ridge lnstitute for Science and Education (ORISE) for the DOE. ORISE is managed by ORAU under contract number DE - 5CAOL4664 v TABLE OF CONTENTS LIST OF TABLES ................................ ................................ ................................ ........................ vii LIST OF FIGURES ................................ ................................ ................................ ..................... viii Chapter 1. Introduction ................................ ................................ ................................ ................... 1 1.1 Introduction to Lithium - Ion Batteries ................................ ................................ ................... 1 1.2 Motivation for Computational Analysis ................................ ................................ .............. 11 1.3 Li 2 MnO 3 Stabilized Layered Materials ................................ ................................ ............... 17 1.4 Overview of Dissertation ................................ ................................ ................................ .... 21 Chapter 2. Effect of Oxygen Vacancies on Lithium - Ion Battery Capacity ................................ .. 23 2.1 Computational Methods ................................ ................................ ................................ ...... 25 2.2 Incr eased Capacity with Oxygen Vacancies ................................ ................................ ....... 29 2.3 Conclusions ................................ ................................ ................................ ......................... 33 Chapter 3. Decreased Lithium Diffusion with Oxygen Vacancies ................................ ............... 34 3.1 Computational Methods ................................ ................................ ................................ ...... 35 3.2 Mole cular Dynamics Simulations ................................ ................................ ....................... 37 3.3 Estimation of Diffusion Coefficient ................................ ................................ .................... 40 3.4 Conclusions ................................ ................................ ................................ ......................... 45 Chapter 4. Correlated Chemical Expansion Due to Oxygen and Lithium Vacancies .................. 46 4.1 Method of Calculating Anisotropic Chemical Expansion ................................ ................... 49 4.2 DFT calculation of the Elastic Stiffness Tensor ................................ ................................ .. 51 4.3 Chemical Expansion of Non - Dilute Concentrations of Lithium Vacancies ....................... 54 4.4 Chemical Expansion due to Dilute Vacancies ................................ ................................ .... 56 4.5 Conclusions ................................ ................................ ................................ ......................... 68 Chapter 5. Controlling Oxygen Vacancy Concentration with Dopants ................................ ........ 69 5.1 Silicon Dopant ................................ ................................ ................................ ..................... 71 5.2 Aluminum Dopant ................................ ................................ ................................ ............... 76 5.3 Conclusions ................................ ................................ ................................ ......................... 78 Chapter 6. Interactions between Li2MnO3 Surface and Ethylene Carbonate .............................. 79 6.1 Computational Method ................................ ................................ ................................ ........ 80 6.2 Ethylene Carbonate Adsorbed on Li 2 MnO 3 Surface ................................ ........................... 81 6.3 Decomposition of Ethylene Carbonate on Surface ................................ ............................. 85 6.4 The Effect of Oxygen Vacancies on the EC Interaction with the Li 2 MnO 3 - (131) Surface ................................ ................................ ................................ ................................ ................... 87 6.5 Conclusions ................................ ................................ ................................ ......................... 92 Chapter 7. Conclusions and Proposed Work ................................ ................................ ................ 93 7.1 Conclusions ................................ ................................ ................................ ......................... 93 7.2 Proposed Future Work ................................ ................................ ................................ ........ 94 vi REFERENCES ................................ ................................ ................................ ............................. 95 vii LIST OF TABLES Table 1.1 Table of various anode and cathode materials used for lithium - ion batteries. Republished with permission of CRC Press, from [Lithium - ion batteries : advanced materials and technologies, Daiwon Choi, Wei Wang and Zhenguo Yang, 2011]; permission conveyed through Copyright Clearance Center, Inc. 5 ................................ ................................ ................................ ................... 6 Table 1.2 Calculated Li 2 MnO 3 lattice parameters compared to previously calculated parameters, by Koyama, et al. 18 and Okamoto, 19 and experimentally determined parameters by Strobel et al . 20 Table adapted from James, et al. 17 ................................ ................................ ................................ 18 Table 4.1 Reuss and Hill schemes, all are in GPa. ................................ ................................ ........................ 54 Table 4.2 A summary of the relaxed bond lengths and the percent difference between these bond lengths and the perfect bond lengths for systems with V O , V Li , V O - V Li and V Li - V O - V Li . ............ 58 Table 4.3 Calculated G matrices for V O , V Li , V O - V Li and V Li - V O - V Li . Portion of table reprinted with permission from Cambridge University Press from James, et al. 87 ................................ ...... 60 Table 4.4 Computed values of the chemical expansion coefficient tensor for V O , V Li , V O - V Li and V Li - V O - V Li . Portion of table reprinted with permission from Cambrid ge University Press from James, et al. 87 ................................ ................................ ................................ ................................ 61 Table 4.5 Estimated oxygen vacancy concentrations from capacity compared to estimation from strain. Table adapted from N ation, et al. 86 ................................ ................................ .................... 65 Table 5.1. DFT predicted crystallographic parameters in comparison with as - synthesized HE - NMC samples. 104 Volume was allowed to relax. Table adapt ed from Nation, et al. 104 and reprinted with permission from Cambridge University Press. ................................ ................................ ..... 73 Table 6.1 The surface energy values for the (101), (131) and (001) Li 2 Mn O 3 surfaces. ............. 82 Table 6.2 The total system energy, energy of formation of a V O for each oxygen site on the Li 2 MnO 3 (131) surface. Additionally, the number of Li and Mn neighbors, both in plane and in other pl anes, are listed. ................................ ................................ ................................ .................. 89 Table 6.3 Total energies for each configuration both while the C - O distance was constrained and when all the atoms were allowed to relax. ................................ ................................ .................... 91 Table 6.4 The difference between the energy of configuration 1 and the other configurations summarized for both while the C - O bond distance was fixed and when all atomi c positions were minimized. ................................ ................................ ................................ ................................ .... 91 viii LIST OF FIGURES Figure 1.1 The theoretical and practical energy densities of different battery technol ogies. Republished with permission of RSC Publishing, from Electrical energy storage for transportation - approaching the limits of, and going beyond, lithium - ion batteries, Thackeray, M. M.; Wolverton, C.; Isaacs, E. D., 5 (7) 2012; 1 permission conveyed through Copyright Clearance Center, Inc. .. 2 Figure 1.2 Sales (in cells) of lithium ion batteries. Reprinted by permission from RightsLink Permis sions Springer Nature Customer Service Centre GmbH: Springer Nature Journal of Solid State Elecrochemistry (Lithium ion, lithium metal, and alternative rechargeable battery technologies: the odyssey for high energy density, Placke, T.; Kloepsch, R.; Duhn en, S.; Winter, M), 2 COPYRIGHT 2017. ................................ ................................ ................................ ............... 2 Figure 1.3 Schematic of a lithium - ion battery showing the flow of electrons and lithium ions during the charge and discharge c ycle. Republished with permission of RSC Publishing, from Electrical energy storage for transportation - approaching the limits of, and going beyond, lithium - ion batteries, Thackeray, M. M.; Wolverton, C.; Isaacs, E. D., 5 (7) 2012; 1 permission conveyed th rough Copyright Clearance Center, Inc. ................................ ................................ ...................... 3 Figure 1.4 Batteries can be designed in different ways such as: (a) cylindrical, (b) coin, (c) prismatic or (d) the pouch c ell. Reprinted by permission from RightsLink Permissions Springer Nature Customer Service Centre GmbH: Springer Nature, Nature 3 (Issues and challenges facing rechargeable lithium batteries, Tarascon, J. M.; Armand, M.), COPYRIGHT 2001. .................... 4 Figure 1.5 Crystal structure of spinel materials of the form LiM 2 O 4 . Reprinted from Materials Science and Engineering: R: Reports, 73, Bo Xu, Danna Qian, Ziying Wang, Ying Shirley Me ng, Recent progress in cathode materials research for advanced lithium ion batteries, Pages 51 - 65, Copyright 2012, with permission from Elsevier. 6 Color scheme: lithium (red), M transition metal ions (blue). ................................ ................................ ................................ ................................ ...... 7 Figure 1.6 Crystal structure of LiMPO 4 , olivine, materials. Reprinted from Materials Science and Engineering: R: Reports, 73, Bo Xu, Danna Qian, Ziying Wang, Ying Shirley Meng, Recent progress in cathode materi als research for advanced lithium ion batteries, Pages 51 - 65, Copyright 2012, with permission from Elsevier. 6 Color scheme: lithium (red), phosphorous (yellow), M transition metal (blue). ................................ ................................ ................................ .................... 8 Figure 1.7 Crystal structure of layered materials of the form LiMO 2 . Reprinted from Materials Science and Engineering: R: Reports, 73, Bo Xu, Danna Qian, Ziying Wang, Ying Shirley Meng, Recent progress in cathode materials research for advanced lithium ion batteries, Pages 51 - 65, Copyright 2012, with permission from Elsevier. 6 Color scheme: lithium (red), M transition metal (blue). ................................ ................................ ................................ ................................ .............. 9 Figure 1.8 The progression of LiCoO 2 materials as Co was replaced. Shown with Li(yellow), Ni (green), Mn(blue) and Co (purple). Republished with permission of Electrochemical Society , from Review - Li - Rich Layered Oxide Cathodes for Next Generation Li - Ion Batteries: Chances and ix Challenges, Patrick Roziera and Jean Marie Tarascon, 162, 2015]; permission conveyed through Copyright Clearance Center, Inc. 8 ................................ ................................ ............................... 10 Figure 1.9 Different levels of modeling techniques for materials. Used with permission from Chinese Physics B. 9 ................................ ................................ ................................ ...................... 11 Figure 1.10 Comparison of two di fferent migration pathways for lithium in Li x TiS 2 . Reprinted figure with permission from [ Anton Van der Ven, John C. Thomas, Qingchuan Xu , Benjamin Swoboda and Dane Morgan, PHYSICAL REVIEW B , 78 , 104306 and 2008.] Copyright 2008 by the American Physical Society, https://doi.org/10.1103/PhysRevB.78.104306. 15 ....................... 13 Figure 1.11 The relative error of the calculated potential for lithium intercalation for several cathode materials and GGA, GGA+U and HSE06. Reprinted figure with permission from [ V. L. Chevrier, S. P. Ong, R. Armiento, M. K. Y. Chan, and G. Ceder , PHYSICAL REVIEW B , 82 , 075122, 2010.] 16 Copyright 2010 by the American Physical Society, https://doi.org/10.1103/PhysRevB.82.075122 . ................................ ................................ ............. 15 Figure 1.12 - ion battery electrode materials. Figure from Qi, et al. 14 and licensed under CC BY - NC - ND 4.0 . ................................ ................ 16 Figure 1.13 The crystal structures of LiMO 2 , such as LiCoO 2 , and Li 2 MnO 3 for comparison. .. 17 Figure 1.14 Pe rfect Li 2 MnO 3 unit cell projected along [100] direction, serving as the staring structure for vacancy generations. The Wyckoff positions are depicted. Figure from James, et al. 17 ................................ ................................ ................................ ................................ ....................... 18 Figure 1.15 The first and second charge/discharge cycles for a half cell using 0.3Li 2 MnO 3 0.5 Ni 0.5 O 2 . Reprinted from Electrochemistry Communications, 8 (9), Thackeray, M.; Kang, S. - H.; Johnson, C.; Vaughey, J.; Hackney, S., Comments on the structural complexity of lithium - rich Li 1+x M O 2 electrodes (M = Mn, Ni, Co) for lithium batteries, 1531 - 1538, 21 Copyright 2006 , with permission from Elsevier. ................................ ............................. 19 Figure 2.1 A schematic showing the figure sampling, first oxygen vacancies were introduced and then lithium vacancies were creat ed one at a time. Each row represents the sampled structures and the highlighted structure is the most energetically favorable. ................................ ...................... 28 Figure 2.2 The energy of formation of all the sampled V Li sites for systems with the varying V Li concentrations with (a) one V O or (c) two V O . The distribution of the lithium ions from the (b) V O and at an average distance from the (d) two V O . Figure from James, et al. 17 ............................... 30 Figure 2.3 Energetically most favorable configurations for the systems containing (a) one oxygen vacancy with the first two lithium vacancies and (b) two oxygen v acancies with the first four lithium vacancies. The dotted black lines encircle the V Li - V O - V Li energetically most favorable structures. ................................ ................................ ....................... 31 Figure 2.4 Calculated OCV curve for Li 2 - X MnO 3 - . Figure adapted from James, et al. 17 ........... 32 x Figure 3.1 Initial positions for MD simulations with (a) one V Li , (b) one V L i - V O in most energetically favorable positions, (c) one V Li - V O in not energetically minimized positions separate from each other and (d) V Li - V O - V Li in energetically most favorable positions. Figure reprinted from James, et al. 17 ................................ ................................ ................................ ........................ 36 Figure 3.2 AIMD results for system with a single V Li . The lithium ions which moved are shown in (a) with each color representing a different ions displacement from its original site over t ime. The displacement of the V Li with respect to its original position is shown in (b). Figure reprinted from James, et al. 17 ................................ ................................ ................................ ........................ 37 Figure 3.3 MD results from simulatio n with initial configuration shown in Figure 3.1 (b) with 1V O and 1V Li in their most favorable configurations in neighboring sites. The line shows the displacement of the one lithium ion which moved and its displacement over time. Figure from James, et al. 17 ................................ ................................ ................................ ................................ 38 Figure 3.4 Ionic movement during MD simulation with 1VO and 1VLi placed away from each other in the initial configuration, shown in Figure 3.1(c). The displac ement of all (a) lithium ions and (b) oxygen ions which moved significantly, beyond just vibrating around their equilibrium position, are shown. Figure from James, et al. 17 ................................ ................................ .......... 39 Figure 3.5 Lithium movement in system with two V Li and a single V O initially in most energetically favorable positions. Only the displacement of the lithium ions which hopped are shown. Figure from James, et al. 17 ................................ ................................ ................................ 40 Figure 3.6 Calculated energy barrier with no oxygen vacancies for (a) cross - layer hopping between the 4h and 2c positions, and (b) lithium - layer hopping between the 2c and 2b positions. The energy barrier was increased by the introduction of one oxygen vacancy in th e system for both the hopping between (c) the 4h and 2c positions and (d) the 2c and 2b positions. To show the barrier, the reference energy was set zero for the equilibrium structure with the lowest energy for the four cases separately. Adapted from Jame s, et al. 17 ................................ ................................ 41 Figure 4.1 The (a) energy of formation for various configurations was calculated and these configurations were used to analyze the (b) strain in the a xes and the (c) overall volume change. ................................ ................................ ................................ ................................ ....................... 55 Figure 4.2 Configurations for systems with (a) VO, (b) VLi - VO and (c) V¬Li - VO - VLi which are energetically most stable and were used for chemical expansion calculations. The bonds that are numbered in the schematic to the right of each configuration are the local bonds to the vacancies which were monitored and summarized in Table 4.2. ................................ ................................ .. 57 Figure 4.3 The calculated energy of formation of a vacancy or vacancy set plotted against the applied strain for (a) VO, (b) VLi, (c) VO - VLi and (d) VLi - VO - VLi. Figure (a) and (b) are adapted and reprinte d with permission from Cambridge University Press from James, et al. 87 ............... 59 Figure 4.4 The chemical expansion for the actual chemical expansion in Li 2 - X MnO 3 - (solid purple lines) is compared to the chemical expansion for the linear sum of V Li (red lines) and V O (blue lines) and shown by the purple dotted lines. The chemical expansion is shown in the (a) xx xi direction (b) yy direction and (c) zz direction. Adapt ed from James, et al. 87 and reprinted with permission from Cambridge University Press. ................................ ................................ ............. 62 Figure 4.5 The chemical expansion for the V Li - V O - V Li dumbbell is plotted i n the solid purple lines and compared to the dotted purple lines which represent the linear sum of the V O chemical expansion (blue lines) and twice the chemical expansion of the V Li (red lines). The chemical expansion is plotted for the (a) xx direction, ( b) yy direction and (c) zz direction. ..................... 63 Figure 4.6. (a) Experimental results of stress and voltage for a Li/ Li 1.2 Mn 0.55 Ni 0.125 Co 0.125 O 2 cell during the initial two cycles. (b) Comparison of oxygen vacancy concentration calculated from capacity and strain. Figure (a) reprinted from and figure (b) adapted from Nation, et al. 86 64 Figure 5.1 Charge and discharge curves for the first cycle of Li[Li 0.2 Mn 0.54 Ni 0.13 Co 0.13 ]O 2 (control) and Li[Li 0.2 Mn 0.49 Si 0.05 Ni 0.13 Co 0.13 ]O 2 (HENMC - Si 0,05 ). Figure adapted from Nation, et al. 104 and reprinted with permission from Cambridge University Press. ................................ ...................... 70 Figure 5.2 Simulation cells used for the Li 2 MnO 3 systems with an (a) aluminum dopant atom and (b) a silicon dopant atom. ................................ ................................ ................................ .............. 71 Figure 5.3 The (a) Mn - O bond lengths for the perfect crystal structure and (b) Si - O bond lengths for the structure with one silicon dopant. Volume was fixed. Figure adapted from Nation, et al. 104 and reprinted with permission from Cambridge University Press. ................................ ............... 72 Figure 5.4 Oxygen vacancy formation energy compared to distance from silicon dopant. Volume was fixed at all points. ................................ ................................ ................................ .................. 74 Figure 5.5 The supercell with a single silicon dopant and a V O in the most favorable position. Volume was fixed for these calculations. Figure adapted from Nation, et al. 104 and reprinted with permission from Cambridge University Press. ................................ ................................ ............. 74 Figure 5.6 Bond lengths of manganese/aluminum with their neighboring oxygen ions. Volume was fixed during calculation. Portion of figure with manganese was adapted from Nation, et al. 104 and reprinted with permission from Cambridge University Press. ................................ ............... 76 Figure 5.7 Calculated formation energy for V O as compared to their distance from the aluminum dopant ion. Volume was fixed during calculations. ................................ ................................ ...... 77 Figure 6.1 Plots of E Slab vs the number of layers (N) for the (a) (101) and (b) (131) Li 2 MnO 3 surfaces. ................................ ................................ ................................ ................................ ........ 83 Figure 6.2 Comparison of the similar structure of (a) Li 2 MnO 3 (131) and (b) LiCoO 2 (104) surfaces. Green atoms are lithium, red are oxygen, purple are manganese and blue are cobalt. .. 84 Figure 6.3 Fully atomically relaxed structures with EC (a) parallel to the surface, (b) horizontal on the surface and (c) vertically placed on the surface. White atoms are hydrogen, bronze are carbon, red are oxygen, green are lithium and purple are manganese. ................................ ......... 84 xii Figure 6.4 The decomposition of EC via breaking one of the C - O bonds in the ring on (a) Li 2 MnO 3 . A more zoomed in image of the EC is shown in (b). The (c) EC decomposition in a similar manner on LiMn 2 O 4 is shown for comparison, figure (c) was adapted with permission from Leung. 109 Copyright 2012 American Chemical Society. ................................ ................................ .............. 86 Figure 6.5 The intact EC are plotted along with the different possible decomposition configurations studied and their corresponding energies with respect to the EC adsorbed state. Color scheme: carbon (brown); oxygen (red); hydrogen (white); manganese (purple); lithium (green). ................................ ................................ ................................ ................................ .......... 86 Figure 6.6 An EC molecule on the (131) Li 2 MnO 3 surface containing a single V O on the top, surface, layer and the EC (a) tilted or (b) completely vertical. ................................ ..................... 90 Figure 6.7 Configurations of EC molecule plus an ext ra oxygen before and after the atomic positions were minimized using DFT. ................................ ................................ .......................... 91 1 Chapter 1. Introduction The work presented in this dissertation focuses on l ithium - rich material s used for cathod es for lithium - i on batteries. Thus, S ection 1.1 below will give an introduction into materials for lithium - i on batter ies. Section 1.2 discusses computational methods which have be en used to predict material propertie s for lithium - ion batteries. Then, Section 1.3 will discuss what was known in previous literature about the lithium - rich cathode materials and identify the key research problem to be investigated by this thesis . Lastly, an overview of the rest of the dissertat ion will be given in Section 1.4 . 1.1 Introduction to Li thium - Ion Batteries Rechargeable l ithium - ion batteries are increasingly used in a wide variety of applications which include: mobile electronics, space power systems, aircraft power sys tems, plug - in hybrid electric vehicles (PHEV)/all - electric vehicles (EV), and smart grids due to their high gravimetric and volumetric energy densities compared to other current battery technologie s, as shown below in Figure 1.1 . Thus, the sales of lithium - ion batteries has been increasing over time, as shown in Figure 1.2. The energy density of lithium - ion batteries is around 160 Whkg - 1 now and this is after it has been increasing by around 5Whkg - 1 each year during the past few . However, th is energy density is much lower than the needs for electric vehicles (500 - 700 Whkg - 1 ), as shown in Figure 1.1. In addition , simultane ous improvements in energy density, rate capability, lifetime and safety are required . Therefore, much research is still ne eded in the area of materials for rechargeable lithium - ion batteries. 2 Figure 1.1 The theoretical and practical energy densities of different battery technologies. Republished with permission of RSC Publishing, from Electrical energy storage for transport ation - approaching the limits of, and going beyond, lithium - ion batteries, Thackeray, M. M.; Wolverton, C.; Isaacs, E. D., 5 (7) 2012; 1 permission conveyed through Copyright Clearance Center, Inc. Figure 1.2 Sales (in cells) of lithium ion batteries. Reprinted by permission from R ightsLink Permissions Springer Nature Customer Service Centre GmbH: Springer Nature Journal of Solid State Elecrochemistry ( Lithium ion, lithium metal, and alternative rechargeable ba ttery technologies: the odyssey for high energy density , P lacke, T.; Kloepsch, R.; Duhnen, S.; Winter, M ) , 2 COPYRIGHT 2017. 3 Li thium - ion batteries contain three main components: cathode (the positive electrode) , anode (the negative electrode) and electrolyte. When a l i thium - ion batter y is operated the Li + ions are shuttled between the cathode and the anode through the electrolyte while electrons move through an external circuit during the discharge cycles in order to power a device. The Li + ions move from the cathode to the anode during charging and back to the cathode during discharging. Figure 1.3 shows a schematic of the lithium - ion battery along with the direction of electron flow during both the charging and discharging cycles. Figure 1.3 Schematic of a lithium - ion batter y showing the flow of electrons and lithium ions during the charge and discharge cycle. Republished with permission of RSC Publishing, from Electrical energy storage for transportation - approaching the limits of, and going beyond, lithium - ion batteries, Tha ckeray, M. M.; Wolverton, C.; Isaacs, E. D., 5 (7) 2012 ; 1 permission conveyed through Copyright Clearance Center, Inc. 4 The design in which the anode, cathode, electrolyte and other lithium - ion battery components , including the separator and current collectors, are assembled together varies in size and shape according to the application for which it is being used. These cells can be cylindrical, coin, prismatic or pouch, all of which are shown s chematically in Figure 1.4. Figure 1.4 Batteries can be designed in different ways such as: (a) cylindrical, (b) coin, (c) prismatic or (d) the pouch cell. Reprinted by permission from RightsLink Permissions Springer Nature Customer Service Centre GmbH : Springer Nature, Nature 3 (Issues and challenges facing rechargeable lithium batteries, Tarascon, J. M.; Armand, M.), COPYRIGHT 2001. The electrolytes for lithium - ion batteries are typically liquids which should be good conductors of lithium ions while being electronic insulators . These liquids are usually composed of a lithium salt, commonly LiPF 6 , dissolved in a mixture of organic solvents. The organic solvents are typically comprised of the high dielectric ingredients such as ethylene carbonate (EC), and low 5 viscosity ingredients, such as dimethyl carbonate (DMC), diethyl carbonate (DEC) and ethylmethyl carbonate (EMC), and other additives. Solid electrolytes for lithium - ion batteries is currently a n active area of research. 4 Replacing the liquid electrolyte with a solid would improve the battery in terms of safety. However, most of the current solid electrolytes have ionic conductivities which are significantly smaller than those of liquid electrolytes. Table 1.1 lists v arious positive electrode (cathode) and neg ative electrode (anode) materials , along with their electrochemical potential with respect to lithium - metal electrodes for lithium - ion batteries. The cell voltage of the lithium - ion battery refers to the difference in electrochemical potential between the positive and negative electrode materials. The energy of the battery is the capacity times the cell voltage. Two of the most common anode materials are graphite and silicon which are shown to have considerably high observed capacities and lower voltages . A significant concern with silicon is about 300%. Other anode materials include metal oxides and tin. The cathode material is the focus of this research because it is the limiting component in terms of battery capacity. Common cathode materials include layered materials (such as LiCoO 2 ), spinel materials (such as LiMn 2 O 4 ) and olivine materials (such as LiFePO 4 ). The cathode materials: LiCoO 2 (160 mAh/g), LiMn 2 O 4 (130 mAh/g) and LiFePO 4 (160 mAh/g) have much lower observed capacities than graphite (330 mAh/g). 5 From comp aring the capacity of anode and cathode materials listed in Table 1.1, it is apparent that the cathode material is the limiting component in terms of battery capacity. Therefore, the cathode material is the focus of the research presented here. 6 Table 1.1 Table of various anode and cathode materials used for lithium - ion batteries. Republished with permission of CRC Press , from [ Lithium - ion batteries : advanced materials and technologies , Daiwon Choi, Wei Wang and Zhenguo Yang, 2011 ] ; permission conveyed thr ough Copyright Clearance Center, Inc. 5 7 Three of the common and commercially used cathode materials have unique crystal structures of the forms: spinel (such as LiMn 2 O 4 ), olivine (such as LiFePO 4 ) and layered (such as LiCoO 2 ). The spinel materials are of the form LiM 2 O 4 and their crystal structure is illustrated below , Figure 1.5 . The most common spinel material is LiMn 2 O 4 , in which the oxide ions are at a close - packed face centered cubic arrangement with lithium cations occupying 1/8 of the available tetrahedral sites and the manganese cations occupying ½ of the octahe dral sites. This material has a low theoretical capacity and also has issues with cyclability as it does not maintain its capacity as it is continued to cycle. Figure 1. 5 Crystal structure of spinel materials of the form LiM 2 O 4 . Reprinted from Materials Science and Engineering: R: Reports, 73, Bo Xu, Danna Qian, Ziying Wang, Ying Shirley Meng, Recent progress in cathode materials research for advanced lithium ion batteries , Pages 51 - 65 , Copyright 2012 , with permission from Elsevier. 6 Color scheme: lithium (red), M transition metal ions (blue ) . Another common cathode material is LiFePO 4 which is an olivine material, structure shown in Figure 1. 6 . The lithium and iron are in ½ of the available octahedral sites. The phosphorous ions occupy 1/8 of the tetrahedral sites. It has a hexagonal analog of the cubic spinel structure. It has several advantages such as being inexpensive and safe. However, this material has 8 a low theoretical capacity as compared to other materials, such as the layered materials and a relatively low voltage. Figure 1. 6 Crystal structure of LiMPO 4 , olivine, materials. Reprinted from Materials Science and Engineering: R: Reports, 73, Bo Xu, Danna Qian, Ziying Wang, Ying Shirley Meng, Recent progress in cathode materials research for advanced lithium ion batteries, Pages 51 - 65, Copyright 2012, with permission from Elsevier. 6 Color scheme: lithium (red), phosphorous (yellow), M transition metal (blue). The first widely used lithium - ion battery cathode material was LiCoO 2 . The structure of LiCoO 2 , and more broadly LiMO 2 , is referred to as layered. The structure of these layered materials are shown in Figure 1. 7 and contain discrete layers of lithium, oxygen and the transition metal(s). In the layered LiCoO 2 structure, the oxygen ions are in a close - packed face centered cubic arrangement with the lithium and cobalt cations occupying the octahedral sites in an alternating manner between the close packed planes of oxygen ions. However , there are several proble ms with LiCoO 2 , such as the high cost due to the cobalt and the instability upon cycling. This structural instability is largely why the observed capacity of LiCoO 2 is so low in comparison to the theoretical capacity . The structural instability of LiCoO 2 i s complicated and includes several different 9 phenomenon. One structural change is the dissolution of cobalt from the cathode into the electrolyte. This dissolution of cobalt allows for less lithium to be removed/replaced upon cycling. Additionally, there a re further reactions between the LiCoO 2 surface and the electrolyte which causes the formation of a surface layer. After more than half of the lithium is deintercalated the material undergoes a phase change which also limits the observed capacity to about half of the theoretical capacity. 7 Figure 1. 7 Crystal structure of layered materials of the form LiMO 2 . Reprinted from Materials Science and Engineering: R: Reports, 73, Bo Xu, Danna Qian, Ziying Wang, Ying Shirley Meng, Recent progress in cathode materials research for advanced lithium ion batteries, Pages 51 - 65, Copyright 2012, with permission from Elsevier. 6 Color scheme: lithium (red), M transition metal (blue). In an attempt to solve the structural stability problems associated with LiCoO 2 , other layered materials of the form LiMO 2 have been studied, where M is most commonly another transition metal or combination of transiti on metals. LiNiO 2 results have shown a slight improvement compared to LiCoO 2 as it is less expensive and has a slightly higher observed capacity. However, the capacity still remains very low. LiMnO 2 was studied also and was promising due to its high theore tical capacity. However, it showed a significant drop in capacity immediately when it was cycled. Another common layered material mixes Ni, Mn and Co in the 10 transition metal layer to form LiCo x Mn y Ni 1 - x - y O 2 . These materials have shown to be inexpensive and relatively stable. However, t heir capacity still remains low compared to typical anode materials. Therefore , the problem of finding a cost effective and stable cathode material still persists with the layered materials. This has led to the study of Li 2 MnO 3 stabilized (also known as lithium - rich ) cathode materials, which will be described in further detail in Section 1.3. This evolution of improving the layered cathode materials beyond LiCoO 2 is summarized in Figure 1. 8 . First, replacing or partially rep lacing the cobalt was attempted and now adding the Li 2 MnO 3 component to form Li[LiM]O 2 , another way of writing xLi 2 MnO 3 - (1 - x)LiMO 2 , materials is being investigated. Figure 1. 8 The progression of LiCoO 2 materials as Co was replaced. Shown with Li(yellow), Ni (green), Mn(blue) and Co (purple). Republished with permission of Electrochemical Society , from Review - Li - Rich Layered Oxide Cathodes for Next Generation Li - Ion Batteries: Chances and Challenges, Pat rick Roziera and Jean Marie Tarascon, 162, 2015]; permission conveyed through Copyright Clearance Center, Inc. 8 11 1.2 Motivation for Computational Analysis Computational studies can be used to explore phenomenon that are not observable in experiments and to also make predictions for further experi ments. There are many different computational methods which can be used to simulate varying length scales in lithium - ion batteries, as summarized by Shi et al. in Figure 1. 9 . 9 Figure 1. 9 Different levels of modeling techniques for materials. Used with permission from Chinese Physics B . 9 At the lowest length scale, quantum mechanics methods , such as density functiona l theory (DFT), can be used to calculate the electronic structure of the material and predict material properties such as reaction energy, elastic constants, structural stability and dynamics of simple 12 lattice defects. Atomistic level simulations that repr esent the system energy as a function of atomic positions, allow for slightly larger scale simulations and include molecular dynamics simulations which enable the structural evolution to be studied. Above these two levels, the governing equations will be t ailored to address specific material questions. For example, the microstructural simulations at the level of grains and grain boundaries can be described by continuum - level mechanics models with constitutive equations, so that the mechanical behavior (such as stress and strain) can be modeled. Or, the phase field model can be used to describe microstructural evolution based on governing thermodynamics equations, diffusion equations, and boundary evolution at the continuum level. Among these methods, quantum methods are the most accurate. It becomes more than a tool for explaining experiments but rather can be key to the prediction of material properties and ultimately structure and composition design. First - principles methods have been used extensively in th e literature to calculate properties of and simulate cathode materials for lithium - ion batteries. 10 One of these first - principles methods is DFT calculations which allows for an approximate solution to the time independent , Equation 1 .1, and allows for the prediction of the electron density in and energy of crystal structures , especially with plane wave DFT . (1 .1) DFT calculations can be used to identify defects, simulate defect hopping and predict the diffusion barrier. 11 DFT can also be used to predict open circuit voltage (OCV) 12, 13 and elastic properties of electrode materials. 14 Being able to calculate the diffusion barrier in electrode materials for lithium - ion batteries allows for the study of how the lithium moves in and out of the material and can be used in other 13 instances such as how the ionic movement can cause a p hase change in the material. The calculation of the diffusion barrier frequently uses the nudged elastic band (NEB) method alongside the DFT calculations. An example of the use of using the NEB method and DFT to calculate the energy barrier for lithium dif fusion is an Li x TiS 2 study by Van der Ven et al . comparing two different migration pathways, shown in Figure 1. 10 . 15 In this study, they found that lithium on the octahedral site prefers to go through the tetrahedral site when it moves to another octahedral site. Figure 1. 10 Comparison of two different migration pathways for lithium in Li x TiS 2 . Reprinted figure with permission from [ Anton Van der Ven, John C. Thomas, Qingchuan Xu , Benjamin Swoboda and Dane Morgan, PHYSICAL REVIEW B , 78 , 104306 and 2008 .] Copyright 2008 by the American Physical Society , https://doi.org/10.1103/PhysRevB.78.104306 . 15 Density functional theory (DFT) has long been used to predict the OCV of electrodes that store lithium via intercalation and alloying, through solid state reactions. The average OCV f or a typical lithium reaction with host material M , such as : 14 , (1.2) with reference to the lithium - metal a s 0V is defined as: , (1.3) Where is the Gibbs free energy of reaction (1.2), is the lithiation amount /amount of charge transferred and In typical solid state lithiation reactions, the PV term and the term in Equation 1.3 are often dropped, as they a re much smaller than at room temperature for solids. Therefore, with lithium - metal as the reference electrode (0V), the equation simplifies to . (1. 4) All of the energy terms in Equation 1.4 can be directly computed with DFT. The voltage for different battery materials is frequently calculated with DFT and some of the results are summarized in Figure 1. 11 by Chevrier et al. 16 As seen from Figure 1. 11 , a typical exchange correlation function used in DFT, such as the generalized gradient approximation ( GGA ) does not do well as far as calculat ing the intercalation potential due to the self - interaction of the d - electrons associated with the transition m etals. As seen in Figure 1.11, Chevrier et al. 16 compared conventional GGA, GGA +U, and the HSE06 hybrid functional approaches in terms of their accuracy by computing redox potentials , specifically looking at various cathode materials. In the GGA+U approach, U can be adjusted and is a parameter which accounts for on - site Coulomb and 15 exchange interactions , this is estimated with a Hartree - Fock approximation added t o the DFT Hamiltonian . Chevrier et al. 16 determined the most reliable results came from the hybrid functionals and avoided the necessity of finding the U parameter in the GGA +U method . However, d ue to the long computation time of the HSE06 hybrid functional approach, this work uses GGA+U fo r Li 2 MnO 3 with a careful selection of the U parameter for Mn. Figure 1. 11 The relative error of the calculated potential for lithium intercalation for several cathode materials and GGA, GGA+U and HSE06. Reprinted figure with permission from [ V. L. Chevrier, S. P. Ong, R. Armiento, M. K. Y. Chan, and G. Ceder , PHYSICAL REVIEW B , 82 , 075122, 2010 .] 16 Copyright 2010 by the American Physical Society , https://doi.org/10.1103/PhysRevB.82.075122 . 16 Figure 1. 12 s for several lithium - ion battery electrode materials. Figure from Qi , et al . 14 and license d under CC BY - NC - ND 4.0 . Elastic properties such as the el for electrode materials in lithium - ion batteries. An example of this is shown in Figure 1. 12 where - ion electrode materials. These properties have been input to continuum diffusion - induced - stress models. T he se key elastic properties , along with their dependence on lithium concentration, are not reported in th e literature, largely because many lithiated materials are air (oxygen, nitro gen, and moisture) sensitive, and obtaining them experimentally is difficult. Another first - principles technique which has been used in the study of lithium - ion battery cathode materials is ab - initio molecular dynamics (AIMD) which uses first - principles to calculate second law of motion. These methods are frequently used to simulate the lithium ion diffusion in cathode materials in lithium - ion batteries with just some lithium ions being removed (forming lithium 17 vacancies) . However, the material of interest in this study, Li 2 MnO 3 , contains both lithium vacancies (V Li ) and oxygen vacancies (V O ) upon cycling. Therefore, this work uses previous ly developed computational methods and i t s nove lty lies in developing new models in order to determine the correlated effects of the two vacancy types. 1.3 Li 2 MnO 3 Stabilized Layered Materials A material with a similar structure to the layered materials is Li 2 MnO 3 . The structure of layered materials, LiMO 2 where M is a single or combination of transition metals and possibly other dopants, and Li 2 MnO 3 are v ery similar, shown in Figure 1. 13 . Both LiMO 2 and Li 2 MnO 3 have oxygen, lithium and transition metal layers. The main difference is that Li 2 MnO 3 contains excess lithium as compared to LiMO 2 because there is also lithium in the transition metal layers. Figure 1. 13 The crystal structures of LiMO 2 , such as LiCoO 2 , and Li 2 MnO 3 for comparison. The unit cell of Li 2 MnO 3 , shown in Figure 1. 14 , shows that there are two distinct oxygen sites, Wyckoff positions 8j and 4i, and three distinct lithium sites, Wyckoff positions 2c, 4h and 2b. The lattice parameters used in this study are shown in Table 1.2 and compared to other calculated and experimentally measured literature values. 18 Figure 1. 14 Perfect Li 2 MnO 3 unit cell projected along [100] direction, serving as the staring structure for vacancy generations. The Wyckoff positions are depicted. Figure from James, et al. 17 Table 1.2 Ca lculated Li 2 MnO 3 lattice parameters compared to previously calculated parameters, by Koyama, et al. 18 and Okamoto, 19 and experimentally determined parameters by Strobel et al . 20 Table adapted from James, et al. 17 Lattice Parameters Calculated ( Å ) Experimental (Å) Current calculation Ko yama et al. Okamoto Strobel, et al. a 5.01 5.02 4.98 4.94 b 8.66 8.68 8.63 8.53 c 5.07 5.09 5.00 5.03 Since Li 2 MnO 3 has lithium in the lithium layer and in the transition metal layer, it has a higher theoretical capacity than layered materials. However, Li 2 MnO 3 is theoretically electrochemically inactive due to the high 4+ oxidation state of the manganese ion. The high manganese oxidation state inhibits the removal of lithium ions because the charge of losing lithium cannot be compensated by the oxidation of man ganese. In the layered materials the loss of lithium is accompanied by the oxidation of M from 3+ charge state to 4+. 19 Therefore, Li 2 MnO 3 was added to LiMO 2 materials for stabilization purposes and created materials of the form xLi 2 MnO 3 - (1 - x)LiMO 2 . Unexpect edly, these materials have very high capacities. As these materials are cycled it has been shown that there is an activation process during the first charging cycle which allows for higher capacity upon subsequent cycling. There are several possible mechan isms that could be occurring during the activation process which are outlined in Chapter 2. However, it is largely agreed that atleast part of the activation process which occurs above 4.4V includes the release of oxygen, creating oxygen vacancies within t he Li 2 MnO 3 material. This activation process is seen as the plateau around 4.5V in Figure 1. 15 which then accounts for the increase in capacity from the first to the second cycle, again in Figure 1. 15 . The release of oxygen forms Li 2 - X MnO 3 - , which is elec trochemically active and adds capacity to the material. Figure 1. 15 The first and second charge/discharge cycles for a half cell using 0.3Li 2 MnO 3 0.5 Ni 0.5 O 2 . Reprinted from Electrochemistry Communications, 8 (9), Thackeray, M.; Kang, S. - H.; Johnson, C.; Vaughey, J.; Hackney, S., Comments on the structural complexity of lithium - rich Li 1+x M O 2 electrodes (M = Mn, Ni, Co) for lithium batteries , 1531 - 1538, 21 Copyright 2006 , with permission from Elsevier . 20 First - principles calculations could greatly help in the understanding of what is happen ing in Li 2 - X MnO 3 - on the atomic level. However, few simulation studies had been done on Li 2 MnO 3 prior to this work with many more done in the past few years. 22 - 26 Additionally , prior to this work, no studies were done on the correlation of the oxygen and lithium vacancies. Most Li 2 MnO 3 computational work has been focused on the structural change and oxygen dimer formation due to lithium removal . Upon cycling, the Li 2 MnO 3 containing materials have been experimentally shown to undergo a phase transformation from a layered structure to a s pinel - like structure which is associated with the transition metal ions moving from the transition metal layer to the lithium layer. Thus many computational studies have focused on the energy barrier associated with the movement of manganese to the lithium layer in Li 2 MnO 3 . 22, 23 Additionally, researchers have looked at the possibility of the oxygen forming oxygen dimers instead of oxygen being released. 27 Lee and Persson 23 suggested that the migration barri er for oxygen was too large for the oxygen ions to move through the material and thus oxygen vacancies must be formed only on the surface, which Shin and Persson later explored. 25 Xiao et al . studied the diffusion of lithium - ions in the material without oxygen vacancies and at very high temperatures which seem to melt the crystal and therefore not truly c apture diffusion. 22 The refore, since it is still unclear where oxygen vacancies are formed and more than plausible that they are forming in the bulk of the lattice to contribute to the high capacity, there is a large area that still remains unexplored. The impact of oxygen vacan cies on capacity and rate capability are not understood and even the concentration of oxygen vacancies is unknown. 21 1 . 4 Overview of Dissertation Cathode materials have a low capacity compared to anode materials and therefore limit the overall capacity of b atteries. Materials which contain Li 2 MnO 3 have been shown to have high capacities , atleast in part , due to the introduction of oxygen vacancies within the first cycle. Computational techniques have long been used to study materials for lithium - ion batteries. However, the amount of and role of oxygen vacancies is still unclear and largely unexplored by c omputational methods. Therefore, this work simulates Li 2 - X MnO 3 - using first - principle computational methods. Specifically, it is found that the oxygen vacancies and the lithium vacancies formed upon cycling are correlated and this correlation is further studied. This work uses DFT calculations to calculate t he effect of oxygen vacancies on the rem oval of lithium and the capacity of the material, in Chapter 2. Then, the diffusion of lithium is studied with AIMD and the migration barrier is calc ulated with the NEB method to determine the impacts of V O on rate capability in Chapter 3 . A method of calculating the chemical expansion due to oxygen and lithium vacancies and how they are corr elated is discussed in Chapter 4 . Th e aim of Chapter 4 is to further understand the chemical expansion induced by oxygen vacancies so that in the future these calculations can be combined with experimental in situ stress measurements in order to discern the amount of oxygen vacancies created upon activation o f this material. Since Chapter 2 shows that the amount of oxygen vacancies influences the capacity and Chapter 3 shows the oxygen vacancies affect the rate capabiliti es of these materials, Chapter 5 looks at how dopant ions may influence the oxygen vacancy concen tration within these materials and the activation of the manganese ions. Chapter 6 concludes with an analysis of how an electrolyte component, ethylene carbonate (EC), interacts with the Li 2 MnO 3 surface with and without oxygen vacancies. Overall, these studies discuss the 22 impact of the oxygen vacancies in Li 2 MnO 3 and their coupled effects on capacity, Li diffusion, chemical strain, dopants, and electrolyte decomposition. 23 Chapter 2. Effect of Oxygen Vacan cies on Li thium - Ion Battery Capacity This chapter is adapted from James, et al. 17 The layered lithium - rich transition metal oxides of x Li 2 MnO 3 - (1 - x )Li(Ni,Co,Mn)O 2 have gained muc h attention due to their large reversible capacity (>200 mAh/g) 28 compared to other common cathode materials for lithium - ion batteries (LIBs) 6, 29 - 31 , such as LiCoO 2 ( ~160 mAh/g), LiFePO 4 ( ~160 mAh/g) and LiMn 2 O 4 ( ~130 mAh/g). 7 This Li 2 MnO 3 V 28 , which is necessary to access the Li in the Li 2 MnO 3 phase. 32 - 34 While this material is promising, it suffers from problems such as structural instability, hysteresis, voltage decay 35 - 37 , low rate capability 38 , and poor life. These problems have prevented its practical applications. Althou gh there are still some arguments on whether x Li 2 MnO 3 - (1 - x )Li(Ni,Co,Mn)O 2 is mixed as a solid solution or segregated in separate domains 28, 39 , it is unarguably important to understand how the Li in the Li 2 MnO 3 component contributes to the observed high capacity. The Li 2 MnO 3 phase was initially thought to be electrochemically inactive due to the high oxidation st ate (4+) of the manganese cation, thus inhibiting access to the lithium cations. However, the Li 2 MnO 3 component alone 20, 40 - 48 and Li 2 MO 3 layered compounds 49 , where M is a combination of Mn and other transition metals or other transition metals, have been proven as high capacity cathodes as well. In them, an activation process is also necessary. Several mechanisms have been suggested for the process of activating the Li 2 MnO 3 component, such as oxidation of the O 2 - to O - ions 50, 51 , the loss of oxygen 28, 42, 47, 51 , the exchange of Li ions for H ions from the electrolyte 42 , and possibly the oxidation of Mn 4+ 40 . Several studies 24 have modeled the lithium removal process in Li 2 MnO 3 to mimic the activation process of Li 2 - x MnO 3 . 18, 19, 22, 23, 52 . These studies detailed the sequence of lithium being removed from either lithium layer or transition metal layer, and proved that it is energetically favorable to release O 2 after a large amount of lithium being removed (such as x >1 23 ). Thus, the oxygen loss contribution to the increase in capacity is still one of the most important and commonly accepted mechanisms, no matter whether the oxygen is lost from the bulk or the surface of the cathode. Lee and Persson 23 suggested that the oxygen diffusion barrier is too large for oxygen to be removed from the bulk and therefore it is removed from the surface. Oxygen vacancies can also be formed during material synthesis, as suggested by experiments 53 and modeling 54 . Regardless, it is likely that oxygen vacancies facilitate the high capacity, such that the cathode material should be written as Li 2 - x MnO 3 - during electrochemical cycling, where denotes the oxygen nonstoichiometry. To improve the subsequent durability and performance of this material after the activation process, we must understand how oxygen vacancies in Li 2 MnO 3 - impact the delithiation p rocess, structural change, and the rate performance of the Li 2 - x MnO 3 - phase. As discussed above, oxygen vacancies (although the actual amount may be unknown) n the durability and performance of Li 2 MnO 3 - . Therefore, it is critical to understand the effect of oxygen non - stoichiometry ( ) on the structural change and diffusion in Li 2 - x MnO 3 - and related compounds. Although the simultaneous removal of lithium and oxygen as Li 2 O has been widely used to estimate , Meng et al. took this estimation further and compared it to a Rietveld refinement of the structure after cycling and suggested that was significantly less than the amount required to give the observed extra capacity, assuming oxygen vacancies were formed as Li 2 O. 55 . Experimentally, the investigatio ns of oxygen non - stoichiometry in these materials have been 25 limited by the lack of in - situ measurements of the non - stoichiometry as a function of the state of charge (i.e., lithium content). Computationally, on the other hand, it is quite easy to control t he oxygen non - stoichiometry, , and study of the effect of oxygen non - stoichiometry, , on lithium vacancy formation and lithium diffusion, providing the insight on the capacity and rate performance of this material. Therefore, this study presented here is focused on using DFT calculations to analyze the effects of oxygen vacancies on the formation of lithium vacancies and the eff ects of oxygen vacancies on the delithiation process of Li 2 - x MnO 3 - in section . The open circuit voltage (OCV) is also calculated and used to explore how oxygen vacancies (V O ) changes the subsequent capacity, voltage, and diffusion in Li 2 - x MnO 3 - and relat ed compounds. 2.1 Computational Methods The Vienna Ab initio Simulation Package (VASP) 56 - 59 was used to perform plane wave density functional theory (DF T) calculations. Potentials constructed with the full potential projector augmented wave (PAW) method 60, 61 were used for the elemental cons tituents. The exchange - correlation part of the density functional was treated with the generalized gradient approximation (GGA) as parameterized by Perdew, Burke and Ernzerhof 62, 63 with a Hubbard U correction (so called GGA+U method). The U parameter was chosen to be 4.84eV for Mn, a similar value to literature. 18, 19, 22 Valence electron configurations for the elemental co nstituents were as follows: Li - 1s 2 2s 1 , Mn - 4s 2 3d 5 , and O - 2s 2 2p 4 . In all calculations, the electronic degrees of freedom were converged to 10 6 eV. During ionic position optimization, the Hellmann Feynman force components on each atom were relaxed to 0.02 e VÅ - 1 . 26 Prior to the vacancy calculations, the structure (lattice parameters and ionic positions) of the conventional cell of Li 2 MnO 3 (C2/m) were optimized. For this purpose, a plane - wave basis cutoff energy of 550 eV and a k - points mesh of 3x3x3 for Brillo uin zone sampling were found to be adequate to give an energy convergence of 0.2 meV/atom for the primitive cell. The minimized lattice parameters are listed in Table 1 .2 and compared with literature values determined by calculation and experiments. Our ca lculated lattice parameters are only less than 2% different from the experimental values, likely to be due to the under binding of GGA , validating the parameters used in DFT calculations. All reported vacancy calculations were performed on the 2x1x2 supercells ( 96 atoms for perfect Li 2 MnO 3 ). The first V O was determined by calculating the energy of two systems with either a V O at the 8j or 4i position (unique Wyckoff positions for O) and comparing the system energies. It was found that the first V O on the 8j site was more energetically favorable by 0.36 eV . However, this was unexpected at a first glance, since the bond length between the 8j oxygen ion and Mn was shorter than the bond length between the 4i oxygen ion and Mn. Therefore, we estimated the e lectrostatic energy ( E electrostatic ) of both positions of oxygen using their nearest neighboring four Li and two Mn ions, their respective charges ( , , ) and the distance between the oxygen and the neighboring atom ( r ). (2 .1 ) Thus, the oxygen ion at the 4i position had a more attractive electrostatic energy than the oxygen ion at the 8j position by 0.05 eV or 0.17 eV, when the classical or Bader point charges was used, respectively. Thus, it will be more energetically favorable to remove the oxygen at the 8 j position. This observation is consistent with previous calculations done by Okamoto et al., 27 although they showed that V O at the 8j position is energetically more favorable than the 4i position by 0.4 eV. The predicted V O formation energy (on 8j site) is 2.1 eV. For the system with two V O , or =0.1250, the most energetically favorable position for the second V O was in an 8j position 3.1 Å from the first V O . The energy of formation of the second vacancy was 0.05 eV smaller than the energy of formation of th e first oxygen vacancy, and thus 0.05 eV smaller than the energy required to remove a second oxygen atom far from the initial V O . From the system with no V O , a lithium atom from each unique Wyckoff position ( 4h, 2b , and 2c shown in Figure 1) was removed. A DFT calculation was performed to relax the atomic positions and the system energies were compared. For the system without V O the V Li were formed in the 4h position, consistent with Okamoto. 19 The V Li at the 4h position was more favorable than the V Li at the 2b position by 0.18 eV and 0.05 eV more favorable than the V Li a t the 2c position. Due to the small energy difference between these positions, it is likely that Li can sample all of these positions at room temperature. To determine where lithium would be removed during cycling one or two oxygen atoms were removed from the perfect structure to form oxygen vacancy (Vo) containing structures as = 0.0625 and 0.125 in Li 2 MnO 3 - , respectively. A continuous lithium vacancy (V Li ) generation simulation was designed to mimic the delithiation process at different oxygen vacancy concentrations. To be more general, we note the simulation structure as Li 2 - x MnO 3 - , where the lithium vacancy concentration x increases, as x = 0, 0.0625, 0.1250, 0.1875 and 0.2500, while the oxygen vacancy concentrati on varies, as = 0, 0.0625 and 0.1250. At a given value, the continuous delithiation simulation was performed by generating various new configurations with one more Li vacancy added to the minimized structure for the previous x value, until a 28 configur ation with minimized energy is found. This process repeats itself to increase x values. The process of creating structures is described schematically in Figure 2.1. Figure 2.1 A schematic showing the figure sampling, first oxygen vacancies were introdu ced and then lithium vacancies were created one at a time. Each row represents the sampled structures and the highlighted structure is the most energetically favorable. Although, there are many possible configurations at a given x and combination, a gen eral trend between Li vacancy formation energy and its distance from the oxygen vacancy was discovered. This relationship allows us to identify quickly the configurations with the lowest energy, instead of sampling all possible vacancy arrangements. In fac t, calculations on a smaller 2x1x1 supercell allowed sampling all possible lithium positions at each concentration, suggesting 29 the same trend. More specific details of the sampling and the minimized configurations are discussed in Section 2.2 . T he configur ations with the lowest energies at each x and in Li 2 - x MnO 3 - was taken as the minimized structure for further analysis and the energies were used to compute the formation energy. Assuming one more Li is removed from to form , or in other words, the Li extraction from the structure with x 1 amount of lithium initially leads to the final structure with x 2 amount of lithium removed, the V Li formation energy was calculated as : . ( 2.2 ) The systems with oxygen and lithium vacancies in the most energetically favorable sites were used to calculate open circuit voltage (OCV) and to run calculations to analyze the Li diffusion. OCV was calculated, as shown in Equation 2.3, from the current en ergy of the system ( ), the energy of the system with one less Li vacancy ( ), the energy of the Li ion which was removed within pure Li metal ( ) and the charge of an electron ( ). (2.3) 2. 2 Increased Capacity with Oxygen Vacancies To study the effect that oxygen vacancies had on the capacity of Li 2 MnO 3 containing materials, oxygen vacancies were first added to the lattice an d then Li vacancies were created one at a time each from the previously found most energetically favorable configuration. 30 Figure 2.2 The energy of formation of all the sampled V Li sites for systems with the varying V Li concentrations with (a) one V O or (c) two V O . The distribution of the lithium ions from the (b) V O and at an average distance from the (d) two V O . Figure from James, et al. 17 F igure 2.2 shows the energy of formations of each sampled V Li position for each X and concentration set which was sampled. In addition, the distribution of how far the lithium ions are from the oxygen vacancies is given as reference. It was predicted from calculations on a smaller cell that the lithium positions nearest the V O were less stable and therefore the nearest lithium sites to the V O were sampled along with an additional site further away as a reference and check. From 31 Figure 2.2, it was found tha t the trend of increasing vacancy formation energy at farther distances from the V O site was also true in this larger system size. In Figure 2.2 it is apparent that, for the most part, the energy of formation of V Li increases as you move farther away from the V O and then plateaus. Figure 2.3 Energetically most favorable configurations for the systems containing (a) one oxygen vacancy with the first two lithium vacancies and (b) two oxygen vacancies with the first four lithium vacancies. The dotted black lines encircle the V Li - V O - V Li energetically most favorable structures. The most energetically favorable configurations for Li 2 - X MnO 3 - for the system with 1V O and 2V Li h 2V O and 4V Li shown in Figure 2. 3 . The most energetically favorable configurations showed that the initial V Li added to the systems form V Li - V O - V Li tes. This was seen in Figure 2.3( a ) for the firs t two most energetically favorable V Li positions when a single V O was initially in the system. This was also seen for the system with two V O initially in the system where the first 4 V Li O , Figure 2.3 (b) . 32 The OCV was calculated using Equation 2.3 for X=0.0625,0.125,0.1875,0.25 at V O concentrations of =0,0.0625,0.125. Each OCV value was calculated for the lowest energy configuration found for each X and combination. These values are plotted in Figure 2.4 . Figure 2.4 Calculated OCV curve for Li 2 - X MnO 3 - . Figure adapted from James, et al. 17 Since 4.2V is a typical cutoff voltage for Li thium - ion batteries, the amount of capacity obtained below this voltage in Figure 2.4 would be the additional capacity added to this material when the Li 2 MnO 3 material loses oxygen during the activation process. Looking at the available capacity at 4.2V or lower shows that with no V O the material does appear to be electrochemically inactiv e. However, a significant amount of capacity is added to the material once V O are formed. 33 2.3 Conclusions The oxygen vacancies were shown to have a strong effect on where lithium vacancies form and their energy of formation. Thus, oxygen vacancies increase the capacity of the lithium - ion batteries. Interestingly, the first two lithium vacancies associated with each oxygen vacancy were found to form in neighboring positions to the oxygen vacancies, such that dumbbells were formed of V Li - V O - V Li . 34 Chapter 3 . Decreased Lithium Diffusion with Oxygen Vacancies This chapter is adapted from James, et al. 17 Chapter 2 illustrated how the oxygen vacancies impact the formation of lithium vacancies in and thus the capacity of the Li 2 MnO 3 component of lithium - rich cathode materials. However, the impact of oxygen vacancies on the diffusion of lithium is an area that remains largely unexplored in the literature. It has been demonstrated that oxygen vacancies can change the transition metal diffusion. It is well estab lished that degradation of the lithium - rich layered x Li 2 MnO 3 - (1 - x )Li(Ni,Co,Mn)O 2 phase is related to the transformation from layered to spinel 39, 64 - 67 which starts from Mn diffusion from the transition metal layer to the Li layer 68 . Computational studies have shown that the oxygen vacancies decrease the energy barrier for the transition metal migration . 69, 70 Because the spinel phase has lower energy and capacity than the layered phase, this is likely to be the fundamental reason for the voltage decay and hysteresis observed in this material. While various methods 6, 28 are purs u ed to prevent the phase transformation and maintain a layered structure, another technical challenge, its low intrinsic rate performance , 38 is still unsolved. It is not clear if oxygen vacancies will alter lithium diffusion as well. Practically, x Li 2 MnO 3 - (1 - x )Li(Ni,Co,Mn)O 2 also has the disadvantage of low intrinsic rate performance . 38 Without the proper kinetics, the high voltage and high capacity region cannot be accessed in practical applications. For example x Li 2 MnO 3 - (1 - x )Li(Ni,Co,Mn)O 2 exhibits very high resistance at low state of charge (SOC) , 71 where the resistance increases rapidly and lowers the usable energy obtained with normal charge - discharge conditions in practical applications. This dramatic resistance increase occurs at lower SOC, when the Li 2 - x MnO 3 - participates in delithiation/lithiation. Galvanostatic intermittent titration technique with electrochemical 35 impe dance spectroscopy measurements 71 and direct observation on the reaction kinetics for each element 38 clearly suggested that the underlying high resistance is caused by the Li 2 - x MnO 3 - phase after the activation process. With the existing experimental evidences, it is still not possible to determine whether slow electron or slow Li ion transport is respon sible for the high resistance. However, the computed band gap for Li 2 MnO 3 is 2.1 eV 22 (comparable to LiCoO 2 2.7 eV), thus the high resistance is more likely to be caused by slower l i thium - ion diffusion. Xiao et al. studied Li diffusion within Li 2 MnO 3 using ab - initio molecular dynamics (AIMD) simulations, without considering any vacancies and at 3000 K, a temperature appeared to melt the lattice. 22 However, the oxygen and lithium vacancies may be strongly correlated, making a computational study of the kinetics of the Li 2 - x MnO 3 - component of great interest. Shi et al. have discovered that Li diffusion is strongly correlated with neighboring oxygen ions in Li 2 CO 3 72, 73 , more specifically, lower oxygen coo rdination around the moving Li ions leads to higher diffusion energy barrier. This suggest that losing oxygen in Li 2 - x MnO 3 - may hinder Li diffusion and thus it is important to study Li diffusion kinetics with and without oxygen vacancies. 3.1 Computatio nal Methods Diffusion was studied by using ab - initio m olecular dynamics (AIMD) simulations , implemented in VASP , which uses first principles to calculate the forces between ions. The AIMD simulations were performed on cells of approximately 96 atoms at 1500 K using the Nosé 74 thermostat. To investigate the impact of oxygen vacancy on the diffusion of Li, ab inito molecular dynamics (AIMD) implemented i n VASP were used. Systems of Li 2 - x MnO 3 - were analyzed with several different starting configurations for x = 0.0625, 0.1250 and = 0, 0.0625, shown in Figure 36 3.1. The starting configurations included a lattice just a single V Li and configurations with both V Li and V O near each other and far apart to examine the correlation between the vacancy types. Figure 3.1 Initial positions for MD simulations with (a) one V Li , (b) one V Li - V O in most energetically favorable positions, (c) o ne V Li - V O in not energetically minimized positions separate from each other and (d) V Li - V O - V Li in energetically most favorable positions. Figure reprinted from James, et al. 17 Di ffusion was studied by tracking the displacement of the lithium and oxygen atoms from their initial positions. Additionally, the climbing image nudged elastic band (cNEB) method implemented in VASP was used to calculate energy barriers (E A ) for lithium d iffusion. 75, 76 The lower bound of the diffusion coefficient was also esti mated using the E A for lithium hopping near a V O site using the equation for the diffusion coefficient assuming random walk: (3.1) The temperature, T, was assumed to be 300K and the vibrational frequency, , was estimated as 10 13 Hz . The hop distance, a, was varied to correspond to each hop. The values of E A were estimated using the climbing image nudged elastic band method (cNEB) 37 3.2 Molecular Dynamics Simulations Molecular dynamics simulations were run to determine the effects of oxygen vacancies on the diffusion of lithium ions. For comparison the first simulation cell only contained a single lithium vacancy . Figure 3.1(a) . The motion of all lithium ions which mov ed further than vibrations around their site were tracked and their displacement is plotted in Figure 3.2 (a). Additionally, the movement of the vacancy was estimated based on the movement of the lithium ions and plotted in Figure 3.2 (b). From Figure 3.2 it was shown that there was a significant amount of lithium movement. Figure 3.2 AIMD results for system with a single V Li . The lithium ions which moved are shown in (a) with each color representing a different ions displacement from its original site over time. The displacement of the V Li with respect to its original position is shown in (b). Figure reprinted from James, et al. 17 38 The next simulation contained one V Li and one V O in the configuration which was determined most optimal, as discussed in chapter 2 and shown in Figure 3.1 (b). Only one lit hium ion was shown to move farther than just vibrating around its original site. This ion moved to the site which originally contained the V Li but only for a few picoseconds before moving back to its original position, Figure 3.3. Therefore, it appears tha t the V Li and V O appear to prefer to remain near each other in their most favorable position and that the barrier for oxygen or lithium ions to move into these sites must be high. Figure 3.3 MD results from simulation with initial configuration shown in Figure 3.1 (b) with 1V O and 1V Li in their most favorable configurations in neighboring sites. The line shows the displacement of the one lithium ion which moved and its displacement over time. Figure from James, et al. 17 To further explore the interaction between the V Li and V O and to test the favorability of the configuration where they are in their most energetically favorable position ano ther simulation was run with the V Li and V O initially placed far away from each other, Figure 3.1 (c). In this simulation, movement of both lithium ions an d oxygen ions were observed. The movement of two oxygen 39 ions was seen, Figure 3.4 (b), and they moved such that the V O moved across layers towards the V Li . Additionally, significant movement of several lithium ions, Figure 3.4 (a), was observed as the V Li moved to the favorable neighboring site of the oxygen ion. This unexpectedly large amount of movement of the ions showed that the configuration with V Li and V O in neighboring positions is very favorable. Figure 3.4 Ionic movement during MD simulation with 1VO and 1VLi placed away from each other in the initial configuration, shown in Figure 3.1(c). The displacement of all (a) lithium ions and (b) oxygen ions which moved significantly, beyond just vibrating around their equilibrium position, are shown. Figure from James, et al. 17 For the simulation with V Li - V O - V Li in the most stable configuration, Figure 3.1(d), a lot of lithium displacement was observed, Figure 3.5. The V Li position in the lithium layer stayed vacant for the 40 majority of the simulation. Only one lithium atom moved into this site and it was only for very short periods, shown by the blue line in Figure 3.5. Figure 3.5 Lithium movement in system with two V Li and a single V O initially in most energetically favorable positions. Only the displacement of the lithium ions which hopped are shown. Figure fr om James, et al. 17 While the system with one V O and one V Li appears very stable it was concluded that when the second V Li was added the system is much less likely to stay in the most energetically favorable V Li - V O - V Li configuration. One of the V Li in the V Li - V O - V Li seems significantly less stron gly bonded and free to move. Therefore , it seems that while two V Li may be able to be removed for every V O , it appears that only one of the V Li can be replaced and thus add to the capacity of this material. 3 .3 Estimation of Diffusion Coefficient Although multiple hopping events can be observed at 1500K with 50ps AIMD, this times cale is still too short to compute the diffusion coefficient with the mean displacement method. Therefore, we performed cNEB calculations to quantitatively compare the Li vacancy hopping barrier with and without oxygen vacancies. According to the sequences of Li to be removed from the st ructure 41 with one Vo , two diffusion paths were computed: Li and vacancy hopping between Wyckoff positions ( 4h , 2c ), within the Li layer, and ( 2c , 2b ), between the Li layer and the transition metal layer. These cNEB calculatio ns were performed with and without a single V O , Figure 3.6 . Figure 3.6 Calculated energy barrier with no oxygen vacancies for (a) cross - layer hopping between the 4h and 2c positions, and (b) lithium - layer hopping between the 2c and 2b positions. The ene rgy barrier was increased by the introduction of one oxygen vacancy in the system for both the hopping between (c) the 4h and 2c positions and (d) the 2c and 2b positions. To show the barrier, the reference energy was set zero for the equilibrium structur e with the lowest energy for the four cases separately. Adapted from James, et al. 17 The energy barrier for V Li hopping between the 4h and 2c positions within the lithium layer was higher than the barrier along the hopping pathway between the 2c and 2b positions through results. 22 Additi onally, the energy barriers increased significantly due to the nearby V O . For V Li 42 hopping between the 4h and 2c positions, the forward energy barrier increased from 0.78 eV to 1.01 eV and the reverse hopping energy barrier increased from 0.83 eV to 1.20 eV . For V Li hopping between the 2c and 2b positions, the forward energy barrier increased from 0.55 eV to 0.91 eV and the reverse hopping energy barrier increased from 0.69 eV to 0.98 eV. To make comparisons with experimental measurements, the diffusion coef ficient was estimated using Equation 3.1 . The value of in Equation 3.1 was estimated as 10 13 Hz, as commonly used in the literature. 77 - 82 As a comparison to the AI MD results, the number of hops expected in the 50 ps simulated time period was estimated by using the hopping frequency, . The MD results for the system with one Li vacancy and no oxygen vacancy ( x =0.0625 and =0) was used as a comparison for simplicity. Based on the E A of Li hopping within the Li layer, because the AIMD simulation showed lithium diffusion on the lithium layer only, it was calculated that ~ 1 lithium atom should hop within 50 ps at the simulated 150 0 K. This is consistent with the 4 lithium atoms hops observed in the AIMD simulation. This also supports the choice of vibrational frequency =10 13 Hz for diffusion coefficient calculations. It is also estimated that it would require about 1100 ps for a h op to be observed at 1000 K and would be computationally too expensive for AIMD. Thus 1500 K was an appropriate temperature in terms of being high enough to see diffusion in a reasonable computation time and low enough to prevent the structure from melting or being significantly distorted. was then calculated for both Li ion migrations ( 4h 2c and 2c 2b ) according to Eq. (3). The value of was estimated to be 2.9 Å. The average value of E A was chosen as an average of the forward and reverse hopping barrier between the 4h and 2c positions , about 0.81 eV with no V O and about 1.1 eV for the system with one V O . At T =300K, the calculated is 2.5x10 - 16 cm 2 s - 1 for the system with no V O and 2.2x1 0 - 21 cm 2 s - 1 with V O, five orders of magnitude smaller. 43 For the 2c 2b hopping, the average E A values were again used, about 0.62 eV for the system without V O and about 0.95 for the system with one V O , and the value of a was estimated as 2.9Å. The value of at T =300K was calculated to be 3.3x10 - 13 cm 2 s - 1 without V O and 1.01x10 - 18 cm 2 s - 1 with V O present, five orders of magnitude lower. Note we only used the diffusion barrier near the V O to estimate the for the system with Vo, if the V Li hopping occurs far away from the V O , the effect of Vo will be reduced. Thus, this estimation represents the lower bound of in a V O containing structure. The estimated for the system without oxygen vacancies is smaller compared to the estimated value of 4.78x10 - 11 cm 2 s - 1 determined for uncycled Li 2 MnO 3 from muon - spin rotation and relaxation expe riments 83, 84 but closer to 10 - 14 ~10 - 18 cm 2 s - 1 obtained for 0.5Li 2 MnO 3 - 0.5LiMn 0.42 Ni 0.42 Co 0.16 O 2 at higher activation voltage (in the activated Li 2 MnO 3 phase). 71 Using to interpret the computational results correspond s to a lower bound value, since it assumes oxygen vacancies impact all of the atomic jumps. While this permitted the approximate comparisons above, it is important to note that simple random walk statistics are not valid here (i.e. if the oxygen vacancies have the predicted effect on diffusion). Specifically, the oxygen vacancies should lead to correlation effects. In general, , where the correlation factor, , describes deviations from random walk behavior 85 . E ven a standard substitutional diffusion of a tracer atom based on random vacancy motion leads to 0.56 for the two dimensional hexagonal lattice considered below 85 :, because of correlations between the motion of the tracer and a neighboring vacancy. When is this large it is often neglected, however, in Li 2 - x MnO 3 - , the predicted changes in both the formation energ y and the mobility of Li vacancies will potentially lead to much larger correlation effects. A full analysis of these effects in different crystallographic directions is beyond the scope of this paper. However, to demonstrate the implications of oxygen 44 vac ancies on Li diffusion, it is instructive to consider Li diffusion in the Li layers as a relatively simple example (i.e. a 2D problem). A simplified treatment can be obtained by defining only sites that are fully surrounded by occupied oxygen positions (A sites) and those that are adjacent to an oxygen vacancy (B sites). The Li diffusion coefficient in this plane can then be described as 85 : (3.2) (3.3) (3.4) where n is the total number of atomic jumps taken in time , t , is the mole fraction of Li vacancies, and is the fraction of the Li sites that are adja cent to oxygen vacancies. In Equation 3.3 , the frequencies refer to jumps between a Li atom in site (A or B), to a vacant site (A or B). The thermodynamic quantity , is based on the free energies of forming Li vacancies around fully occupied oxygen sites ( ) and adjacent to a vacant oxygen site ( ). A factor is retained here to describe additional correlation effects that extend beyond the assumptions that lead to Equation 3.3 . Two limiting cases of Eq uation 3. 2 are worth noting. In fully stoichiometric material, the limiting diffusion coefficient at is . With higher , large (compared to the other ), and the assumption that neighboring oxygen vacancies are not likely (i.e. such that the term is negligible), Equations 3.2 and 3.3 can be used to obt ain the following approximation for : 45 (3.5) This result provides a relatively simple demonstration of the expected impact of oxygen nonstoichiometry, , on the Li diffusivity. Note here that / is the same ratio obtained by comparing values with and without oxygen vacancies, where the computational results predicted values of 10 - 5 or smaller. The remaining part of the right hand side of Eq. 3.5 is the ratio of Li vacancies on A and B sites. The DFT results in section 3.2 indicate that . Thus with values of several percent, the ratio is expected to be on the order 10. While this increases the value of , the approximation in Eq. 3.5 still indicates that oxygen vacancies are expected to produce large decreases in the Li diffusivity. A more detailed kin etic Monte Carlo simulation could be used to further explore the Li diffusion as a function of x and value in Li 2 - x MnO 3 - . 3.4 Conclusions The molecular dynamics simulations and the calculation of the energy barrier of hopping both show that the diffusion of the lithium is clearly hindered by oxygen vacancies. Thus, while Chapter 2 showed the advantages of the oxygen vacancies in that they increase the capacity of the battery, there appears to be a limit to the amount of oxygen vacan cies which should be added so that the rate capability is not greatly hindered. Chapter 5 will discuss adding dopants to Li 2 MnO 3 and their impact on the quantity of oxygen vacancies. 46 Chapter 4 . Correlated Chemical Expansion Due to Oxygen and Lithium Vacan cies The work in this chapter was adapted from Nation, et al. 86 and adapted and reproduced from James, et al. 87 with permission from Cambridge University Press. Chemical expansion ( ) is the change in dimensions of a material due to compositional changes . For an isotropic system , chemical expansion is a scalar compu ted using the initial lattice length ( ) and the lattice length with the defects in the crystal ( ) : (4 .1) Chemical expansion takes place in various electrochemical devices and impacts the durability of these devices. Most electrode materials used in lithium - ion batteries undergo volume changes which are associated with the changing lithium concentrations withi n the host electrode materials during the charging and discharging . Graphite, the most common anode material for lithium - ion batteries, undergoes an increase in volume by as much as 10% when the material is lithiated and lithium ions intercalate between th e carbon sheets. 88 For the common cathode materials: LiCoO 2 , LiMn 2 O 4 and LiFePO 4 the volume typically changes by - 2%, - 7.3% and - 6.5% to their fully delithiat ed states, respectively. 89 The volume expansion of these ceramic electrode materials beyond their elastic limitations and combined with the lithium diffusion - induced stresses can cause mechanical degradation and fracture. As a result, the battery can lose capacity and suffer from power fade. 47 However, the chemical strain can be taken advantage of in order to characterize the concentration of point defects in various materials. 90, 91 Typically, t he amo unt of expansion per defects is known as the chemical expansion coefficient ( ) and is calculated from and the amount of v or such: ( 4 .2) Furthermore, the elastic model, Equation 4.3, can be used to compute strain in a material from the stress response ( ) measured using the multi - beam optical stress sensor (MOSS) method and the . The MOSS method measures the stress in a thin film geometry (achieved by coating a thick substrate, with known properties, with a thin electrode film). 92, 93 ( 4 . 3 ) While it is widely agreed that oxygen is lost from Li 2 MnO 3 during the cycling of the material, the quant ity of oxygen lost is unknown. A main reason the amount of oxygen lost is unknown i s that it cannot be easily measured experimentally. One potential way to experimentally determine the oxygen loss quantity is to deconvolute the MOSS measured change in stress ( ca used by both lithium and oxygen during the charge and discharge cycles: . (4 .4 ) The values of x and are the lithium vacancy (V Li ) and oxygen vacancy (V O ) concentrations, respectively; is the original volume per formula unit and is the effective modulus . T he volume chan ge associated with oxygen vacancies ( ) is defined as : 48 (4 .5 ) and the volume change associated with lithium vacancies ( ): (4 . 6 ) Then, accurately determining and via DFT calculations while measuring allows for the number of oxygen vacancies formed to be solved for. However, in the case of Li 2 - X MnO 3 - the V O and V Li exhibit correlated effects and therefore the volume change associated with each cannot just be analyzed separately. Another challenge is how to calculate the chemical strain accurately using the DFT calculations. Equations 4.1 and 4 .3 are for the case of an isotropic system and therefore we must modify our approach slightly for Li 2 - X MnO 3 - as both the elastic constants and the c hemical expansion in Li 2 - X MnO 3 - a are anisotropic due to the layered crystal structure with low symmetry. In fact, anisotropic ch emical expansion is even needed for cubic structures, such as CeO 2 94 because the point defect is chemically anisotropic and causes anisotropic local deformation. However, anisotropic calculations are less common and our method will be described below. Overall , this chapter looks at the chemical expansion of V O and V Li individually as well as a 1:1 and a 1:2 ratio of V O and V Li . 49 4 . 1 Method of Calculating Anisotropic Chemical Expansion This work looks at two methods of computing two types chemical expansion. The first method is straightforward and involves relaxing the volume of the sing l e crystal of the electrode material with the vacancies introduced and calculating the lattice and volume change as compared to the perfect lattice volume. The lattice parameter tensor ( ) of the structure which contains a large amount of V Li can be modeled by the following equatio n, where the initial lattice parameters are the matrix and the chemical expansion matrix is : (4 . 7 ) From Equation 3.6 and from the finding by relaxing the lattice parameters once the V Li were added the values of can be solved for: (4 . 8 ) Th e first method was to model the chemical expansion due to the V Li that were not directly correlated with the dilute V O and added to the high capacity of these materials. This method however was not used for the systems which contained oxygen vacancies since the ox ygen vacancies are present in dilute concentrations and therefore their effect would not be accurately captured by this method. The results of this met hod are presented in Section 4.3 . The second method for calculating the chemical expansion coefficient te nsor for dilute vacancies involved a derivation beginning with the total energy ( ) balance which accounts for the long ( ) and short range ( ) interactions of the vacancies: (4 . 9 ) 50 This method is f ollowing the definition of Gilla n 95 and is similar to that used by Er et al. for CeO 2 - . 96 However, the model of Er et al. is for isotropic systems and therefore is modified in this work so that it shows the anisotropy of the chemical expansion. The ma in difference between this work and the derivation by Er et al. is that here the chemical expansion is solved for as a matrix ( ) instead of as sing le averaged value. In Equation 4 . 9 , represented the local changes directly around the vacancy s ites and was calculated using the unit cell volume and the elastic dipole tensor ( ): (4 . 10 ) The values of were calculated from the equation for the energy of formation for a vacancy ( ) : (4 .1 1 ) From tak ing the derivative of Equation 4 .11 with respect to chemical expansion the values of are found to be: (4 .1 2 ) The long range energy interactions were found from the following equation where is the elastic stiffness tensor: (4 .1 3 ) 51 Returning to the total energy balance in Equation 4. 9 , the next step towards deriving the chemical expansion coefficient is to take the derivative of the entire equation with respect to and set it to zero at equilibrium: (4.14) Then, solving equation 4.14 yields the chemical expansion tensor equation which allows the computation of chemical expansion in all directions for an anisotropic material , in GPa : (4 .15) The chemical expansion coefficient is the chemical ex pansion per concentration of defects and can also be solved for as a matrix: (4.16) Equation 4.16 was again solved for V O , V Li , V O - V Li and V Li - V O - V Li and the values are shown in Table 4. 4 which will be presented in S ection 4. 4 . For this chapter all structural relaxations were again done in VASP in the same manner as is outlined in Section 2.1 4. 2 DFT calculation of the Elastic Stiffness Tensor The values of can be computed from the following linear relationship between stress and strain: (4.1 7 ) 52 The values of the elasticity tensor, , were c alculated by taking the first derivatives of the VASP computed stresses instead of taking the second derivatives with respect to strain of the total energ ies , according to the Le Page and Saxe et al. 97, 98 least squares method, as implemented in MedeA. All of C tensor values were c alculated at the same time instead of as independent sums. All computations were done with DFT at 0K, since there is likely to be very minimal temperature - related differences in the C tensor values . For this work, the component values of are solved for Li 2 MnO 3 both manually and directly using the software package MedeA. A strain of ± 0.2% was used to calculate the values of . For all other calcula tions strain s of ± 1% and ± 2% was used. The computed least squares residual was used to assess accuracy and was found to be The values calculated via MedeA for Li 2 MnO 3 are below , in GPa : The LiCoO 2 values were calculated by Qi et al. , in GPa : 14 There are logical similarities and differences between and . The fact that Li 2 MnO 3 has lower C ij values in the xx and yy directions than LiCoO 2 is likely due to the added lithium within the transition metal layer . Whereas the only slightly lower C ij value in the zz 53 direction also makes sense because the structure of Li 2 MnO 3 and LiCoO 2 are very similar in the z direction. This paragraph is adapted and reprinted from Qi , et al. 14 which is license d under CC BY - NC - ND 4.0. Deposited electrode thin film s are typically polycrysta lline and are also often modeled as isotropic elastic materials ; therefore, the averaged bulk ( B ), shear ( G E ) moduli ) can be calculated by inputting the experimental or theoretical C ij into . 99 All of these models use the assumption of a polycrystalline structure . The Voigt scheme assumes there is a uniform strain on each grain and therefore i s an upper bound on elastic. The Reuss scheme , on the other hand is a lower bound because it uses the assumption of a constant state of stress in the crystallites or grains , which therefore preserves equilibrium . Taking an average of the Voigt and Reuss va lues is t he Hill scheme . 100 The averaged bulk modulus ( B ) and shear modulus ( G ) were computed first and are listed in Table 4.1. For an isotropic system, the following equations are used to calculate ( E) ): 99 (4.18 ) ( 4.19 ) 54 Table 4.1 Reuss and Hill schemes, all are in GPa. Voigt Reuss Hill Bulk Modulus , B 111 109 110 Shear Modulus , G 96 94 95 Young's Modulus , E 224 219 221 4 . 3 Chemical Expansion of Non - Dilute Concentrations of Lithium Vacancies For the non - dilute concentrations of lithium vacancies, which contribute to the high capacities of the Li 2 MnO 3 containing materials, a more direct approach was taken. A few structures were generated at several Li vacancy concentrations, and each has several conjurations containing lithium vacancies at random and their atomic positions and cell volume were relaxed. The system that had the lowest V Li formation energy was used for each lithium vacancy concentration. The systems which were analyzed and the associated V Li formation energies are shown in Figure 4. 1 (a). 55 Figure 4. 1 The (a) energy of formation for various configurations was calculated and these configurations were used to analyze the (b) strain in the axes and the (c) overall volume change. The red line in Figure 4. 1 (a) connects the lowest energy structures which were evaluated. One of the structures at X=0.875 is significantly, 45 meV/formula unit, lower in energy than the second lowest energy structure at this concentration. This lowest energy structure at X=0.875 is so low in energy because a lithium ion migrate d to a tetrahedral site from the octahedral site. This could be showing the system undergoing a structural change and the movement of lithium ions from octahedral sites to tetrahedral sites would be interesting to further study. However, for this work only the systems with all lithium ions still in the octahedral sites were considered. 56 The lowest energy configurations determined by Xiao et al . are also shown in Figure 4. 1 for comparison. The lowest energy configurations determined by this study were used to analyze the anisotropic chemical expansion by looking at the chemical expansion in all three lattice pa rameters, as shown in Figure 4.1 (b). However, the chemical expansion in the three directions did not show linear trends which could be modeled. There fore, the overall volume change was studied, F igure 4.1 (c). The volume change shows a clearer trend of chemical expansion up to a current concentration (about X=0.875), followed by contraction of the lattice. These results could potentially be combined wi th experimental stress measurements in order to determine the amount of vacancies in the system. The general trend of the c - lattice parameter first increasing before decreasing as the lithium concentration decreases was also observed in LiCoO 2 by Van der V en et al. 101 4 . 4 Chemical Expansion due to Dilute Vacancies In order to explore the chemical expansion due to the dilute oxygen vacancies and oxygen - lithium vacancy pairs, the systems with V O , V O - V Li and V Li - V O - V Li were explored. These point - defect structures will create large short - range/local lattice distortion, which is then balanced by the long range elastic deformation, as shown in Equation 4. 9 . The chemical expansion and the local bond length changes were calculated for the energetically most stable configurations with a single V O or single set of V O and V Li . These configurations are shown in Figure 4.2 along with the bonds we analyzed and numbered for clarity. In order to analyze the short range effects of the vacancies, the bonds which are numerically labeled in Figure 4.2 were measured and summarized in Table 4. 2 . 57 Figure 4.2 Configurations for systems with (a) VO, (b) VLi - VO and (c) V¬Li - VO - VLi which are energetically most stable and were used for chem ical expansion calculations. The bonds that are numbered in the schematic to the right of each configuration are the local bonds to the vacancies which were monitored and summarized in Table 4.2. 58 Table 4 . 2 A summary of the relaxed bond lengths and the percent difference between these bond lengths and the perfect bond lengths for systems with V O , V Li , V O - V Li and V Li - V O - V Li . Figure 4.2 and Table 4. 2 collectively show that a fter the addition o f the first V O the directly connected bonds increased quite significantly in length. On the other hand, the bonds between the lithium ions and the other oxygen ions they were connected to either increased a smaller amount or decreased in length. When the first V Li was a dded in order to create the V O - V Li pair, all of the neighboring oxygen ions to the V Li moved away from the V Li . When the second V Li was added in order to form the V Li - V O - V Li dumbbell structure the same trend was seen. The oxygen ions near the V Li moved awa y from the V Li . This increase in the lengths between the first nearest neighbor ions and the site where the vacancies are created is expected and likely due to the loss of the shielding effect when the vacancy is first formed. Another interesting observati on is that with the 59 V Li - V O - V Li set of vacancies the first nearest neighbor lithium ions which remain in the system have moved closer to the V O while the nearest two manganese ions are further away from the V O than they were initially. Figure 4.3 The calculated energy of formation of a vacancy or vacancy set plotted against the applied strain for (a) VO, (b) VLi, (c) VO - VLi and (d) VLi - VO - VLi. Figure (a) and (b) are adapted and reprinted with permission from Cambridge University Press from James, e t al. 87 60 The long range chemical strain was calculated following the procedure listed in Section 4.2. First, the elastic dipole tensor, G values, were obtained by fitting the formation energy to the applied strain along each deformation direction. Thus E quation 4.11 was solved for by plotting the against and finding the slope, shown in figure 4.2. These G values are summarized in Table 4. 3 . Table 4. 3 Calculated G matrices for V O , V Li , V O - V Li and V Li - V O - V Li . Portion of table reprinted with permission from Cambridge University Press from James, et al. 87 [eV] [eV] [eV] [eV] Using Equation 4 .15 the chemical expansion in each direction was calculated for V O , V Li , V O - V Li and V Li - V O - V Li . The chemical expansion for the V O and V Li alone at dilute concentrations were compared to the chemical expansion observed with the V O - V Li pair, Figure 4 .3, and the V Li - V O - V Li set , Figure 4 .4 . The chemical expansion was calculated for a single defect or defect set and then extrapolated to other di lute concentrations , plotted in Figure 4. 4 and Figure 4 . 5 , using the chemical exp ansion coefficients which are calculated and shown in Table 4 . 4 . 61 Table 4 . 4 Computed values of the chemical expansion coefficient tensor for V O , V Li , V O - V Li and V Li - V O - V Li . P ortion of table reprinted with permission from Cambridge University Press from James, et al. 87 The chemical expansion wa s compared for the three directions which were largest in magnitude, xx, yy and zz. The chemical expansion for the various vacancy types were compared to determine if the chemical expansion of multiple vacancies was equal to the linear sum of the chemical expansion of the individual vacancy types. Figure 4 . 4 shows the chemical expansion for only V O and only V Li and how they compare to Li 2 - X MnO 3 - X both in the actual system and if the chemical expansion of V Li and V O is summed together. It is clearly shown th at the chemical expansion seen for Li 2 - X MnO 3 - X is not equal to a linear sum of the chemical expansion due to V O and V Li . Therefore showing that the V O and V Li interact and have correlated effects. 62 F igure 4 . 4 The chemical expansion for the actual chemical expansion in Li 2 - X MnO 3 - (solid purple lines) is compared to the chemical expansion for the linear sum of V Li (red lines) and V O (blue lines) and shown by the purple dotted lines. The chemical expansion is shown in the (a) xx direction (b) yy dire ction and (c) zz direction. Adapted from James, et al. 87 and reprinted with permission from Cambridge University Press. 63 Figure 4 . 5 The chemical expansion for the V Li - V O - V Li dumbbell is plotted in the solid purple lines and compared to the dotted purple lines which represent the linear sum of the V O chemical expansion (blue lines) and twice the chemical expansion of the V Li (red lines). The chemical expansion is plotted for t he (a) xx direction, (b) yy direction and (c) zz direction. 64 The chemical expansion of V O and V Li in a 1:2 ratio was studied in a similar way to the vacancies in a 1:1: ratio. The chemical expansion due to V O only, V Li only and Li 2 - 2X MnO 3 - X are plotted in Figure 4. 5 along with the linear sum of V O and V Li in a 1:2 ratio. It was again shown that the actual chemical expansion is significantly different than the linear sum of the chemical expansion due to the individual vacancies separately. Figures 4 .4 an d 4 .5 also both show that the chemical expansion in the xx and yy directions are significantly greater in magnitude than the chemical expansion in the zz direction. The DFT prediction shows that oxygen vacancy generation causes volume expansion in the electr ode materials, this will induce a compressive stress in the electrode thin film, since the substrate constrains the in - plane expansion of the active electrode material during electrochemical cycling. The refore, the DFT predic ted chemical strain contribution due to the creation of oxygen vacancies in Li 2 MnO 3 was compared to MOSS measured stress and experimental strain values associated with the irreversible first delithiation expansion in the lithium - rich samples. Fig ure 4 .6 . (a) Experi mental results of stress and voltage for a Li/ Li 1.2 Mn 0.55 Ni 0.125 Co 0.125 O 2 cell during the initial two cycles . (b) Comparison of oxygen vacancy concentration calculated from capacity and strain. Figure (a) reprinted from and figure (b) adapted from Nation, et al. 86 65 Table 4. 5 Estimated oxygen vacancy concentrations from capacity compared to estimation from strain. Table adapted from Nation, et al. 86 Sample capacity max Strain 1 0.30 0.15 2 0.43 0.30 3 0.46 0.51 4 0.44 0.09 5 0.11 0.08 Fig 4.6(a) shows a typical measured stresses (with respect to the initial stress state of the pristine film), correspond to lithiation and delithiation induced structural and chemical changes. The voltage profiles (blue curves) and average in - plane stress (orange curves) response of the first two cy cles in a rewriting Li 1.2 Mn 0.55 Ni 0.125 Co 0.125 O 2 film. The stress response during electrochemical cycling is mostly reversible beginning in the second cycle, where delithiation induces a tensile stress (volume contraction), and lithiation involves a compre ssive stress (volume expansion). The stress response during the first delithiation is initially tensile but reverses around 4 V and becomes compressive, which is attributed to oxygen vacancy generation. More discussions related to the exp e r iments can be fo und in Nation et al . 86 Traditionally, a vacancy concentration is estima ted using the first charge capacity during To estimate the number of oxygen vacancies created during the first charge, it was assumed that 60% of the material was Li 2 MnO 3 by rewriting Li 1.2 Mn 0.55 Ni 0.125 Co 0.125 O 2 as 0.6 Li 2 MnO 3 - 0.4 LiMn .375 Ni .3125 Co .3125 O 2 . This is not a comment as to whether this material is a solid solution or a two - phase system, but rather an approximate exploration of a potential explanation for the compressive drop behavior. This breakdown made it 66 possibl e to estimate the lithium vacancy concentrations that were created in the Li 2 MnO 3 phase using the measured capacity as (4.20) Where is the first charge capacity of Li 1.2 Mn 0.55 Ni 0.125 Co 0.125 O 2 , is the theoretical capacity of LiMn .375 Ni .3125 Co .3125 O 2 and is the theoretical capacity of Li 2 MnO 3 . It is assumed that during the activation process, oxygen and lithium are removed in a 1:2 ratio. This gives an upper limit value on the oxygen non - stoichiometry, since it assumes that all of the lithium removed along the plateau is accompanied by oxygen loss. Thus, it is defined as (4.21) in Fig 4.6(b). We the n compared the strain - based estimated ox ygen vacancy concentration with estimated using the first charge capacity To estimate the oxygen vacancy concentration using DFT predicted chemical strain, the strain associated with the measured stress is first estimated. The elastic constants are assumed to be isotropic and independent of lithium content, with a biaxial modulu s of 135 GPa based on DFT predictions in Section 4.3 and experimentally derived values 102 of oxide cathodes . With this rudimentary analysis and elastic deformation relationships ( ) , the average measured irreversible stress during the first delit hiation cycled corresponds to an expansion strain of 0.1%. A vacancy concentration estimated using the compressive strain during the activation process can also be compared to the capacity based estimation described above. The chemical expansion coefficie nt tensor provides a strain per amount of oxygen non - stoichiometry, . Using 67 the strain per and the strain from experimental observations, the oxygen vacancy concentration can be inferred by Equation (4.2). An average strain - predicted vacancy concentration is estimated using the trace of the chemica l expansion coefficient tensor of the Li - O - Li vacancy dumbbell structure, assuming Li:O ration is 1:2. These are indicated by the solid diamond symbols in Figure 4.6(b). An upper bound for the strain prediction of the oxygen vacancy concentration is also calculated using the minimum normal chemical expansion coefficient. There are indicated by the solid square symbols in Figure 4.6(b). Assuming that dilute approximations are valid and that the compre ssive drop effect is entirely due to oxygen removal, a measured strain of 0.13% corresponds to an average oxygen 2 - x MnO 3 - using the trace of the chemical expansion coefficient .29 using the minimum normal chemical expansion coefficient. Based on the analysis described above (i.e., using the capacity to calculate the oxygen vacancy levels), comparisons with the estimates of oxygen vacancies based on the measured stress were carr ied out for five samples. These results are tabulated in Table 4 . 5 and plotted in Fig. 4.6(b) . Most of the strain - derived values are below this equal trend line, which is consistent with idea that the values estimated from the capacity, which assume all Li removal is accompanied by oxygen loss, provide an upper bound on oxygen loss. This seems to be consistent with other estimations of significantly less than the amount required to give the observed extra capacity, assuming oxygen vacancies were formed as Li 2 O. 55 There are several possible explanations for the observation that the capacity - derived oxygen vacancy estimate usually overestimates the vacancies using the strain estimation method. As already noted, it is possible that the actual o xygen loss is less than the 68 assumed 1:2 ratio here, or more Li are lost in addition to the V Li V O V Li dumbbell structure generation. The additional Li loss will likely cause the volume to decrease, countering the compression due to oxygen loss. Also, e dge relaxations along the crack faces in these films tend to decrease the stresses. Other possible factors include oxygen parti cipation in the redox reactions , 103 the impact of non - dilute vacancies (i.e., correlation effect s), or a lower elastic modulus in the delithiated state, as the modulus of a layered compound can be four times higher in the lithiated state than when fully delithiated . 14 Furthermore, oxygen mobility is low, 23 but measurements on thin films are likely more sensitive to oxygen loss than measurements in particles. In spite of the possible discrepan cies that are cited above, the DFT predicted chemical strains can account for the observed stress, and on average accounts for 65% and 13% of the stress using the max and trace chemical expansion coefficients, respectively. These findings support the hypot hesis that oxygen loss during the first charge cycle leads to significant irreversible compressive stress during the first charge cycle. 4 .5 Conclusions The chemical expansion was analyzed for both large amounts of lithium removal and dilute vacancy concentrations. The analysis for the large quantities of lithium removal showed that the volume of the material first increased and then decreased with the extraction of lithium. The chemical expansion associated with the dilute oxygen and lithium vacancies was shown to be highly correlated as opposed to a linear sum of the individual vacancies. 69 Chapter 5 . Controlling Oxygen Vacancy Concentration with Dopants This Chapter is adapted and reprinted from Nation, et al. 1 04 with permission from Cambridge University Press. Chapters 2 - 4 showed that V O and V Li are much correlated. Chapter 2 showed that V O can increase the capacity of the cathode material by activating the manganese ions. The V O were also shown, in Chapter 3, to have a negative impact on battery performance by decreasing the diffusion coefficient of the lithium ions. It appears that there might be an ideal amount of oxygen vacancies that increase the capacity without significantly hindering diffusion. This c hapter focuses on the addition of dopant ions in the material and specifically how they affect the formation of V O . Through the collaborations with experimentalists, several redox active dopants, such as Si, Sn and Al, have been tried. Interestingly, only Si has shown improved discharge capacity. Figure 5.1 shows experimentally that the high - energy NMC (HENMC) , referred to here as lithium - rich, materials exhibit a higher discharge capacity when doped with silicon. The charge curve also exhibited a slight s hift (higher capacity at the same voltage) with Si doping. Since silicon is not a redox active element, it seems that it should not affect the capacity of Li 2 MnO 3 when added in dilute concentrations. Therefore, section 5.2 first explores the effect of the silicon dopant both locally and on its effect on the energy of formation of lithium ions. Silicon is likely to subsite t he manganese, since Si form s a Li 2 MO 3 phase 105 that is structurally compatible with the layered oxide. Additionally, Si (4 + ) has the same valence state as manganese, and therefore should not change the valence of the other ions in the pristine material. Si has been successful incorporated into LiNi x Mn y Co (1 - x - y) O 2 and was shown to increase the capacity and decrease electroc hemical impedance . 106 70 Figure 5.1 Charge and discharge curves for the first cycle of Li[Li 0.2 Mn 0.54 Ni 0.13 Co 0.13 ]O 2 (control) and Li[Li 0.2 Mn 0.49 Si 0.05 Ni 0.13 Co 0.13 ]O 2 (HENMC - Si 0,05 ) . Figure adapted from Nation, et al. 104 and reprinted with permission from Cambridge University Press. Aluminum was also studied as a dopant ion for comparison with Si. In experiments, the ionic size is often used as a guideline for dopant selection. In the layered compounds, the ionic size of Li is about 0.76 Å, much larger than the tra nsition metal ions, Co 3+ =0.545 Å, Mn 3+ (high spin) =0.65 Å, Mn 4 + (high spin) = 0.53 Å. Since the ionic size for Al 3+ =0.535 Å is larger than Si 4+ = 0.40 Å, it may be more compatible with the transition metal layer. Section 5.2 shows how it affects the material differently because it has a different oxidation state (3 + ) than the manganese it replaces. Both aluminum and silicon were added in dilute concentrations, replacing one of the 48 manganese ions in the 96 atom Li 2 MnO 3 cells. With one Si or Al substitution of Mn, the concentration is Li 2 Mn 0.94 Si 0.06 O 3 and Li 2 Mn 0.94 Al 0.06 O 3. The aluminum or silicon ions were added at the octahedral site of the manganese ion they replaced, as shown in Figure 5.2. In a perfect Li 2 MnO 3 lattice , the Mn is in the center of an oxygen - octahedral site. However, Si generally prefers 71 tetrahedral coordination (e.g., in SiO 2 and Li 4 SiO 4 ), therefore its energy at a tetrahed ral site is also computed. This tetrahedral site substitution quickly relaxed back to the octahedral site upon ionic relaxtion , which confirms that the octahedral Mn - site substitution is preferred. All structures went through ionic relaxation with either fixed volume or fully relaxed volume using VASP using the same parameters as outlined in section 2.1. The v alence electron conf igurations for the additional elemental constituents were as follows : Si - 3 s 2 3 p 2 , Al - 3 s 2 3p 1 . For structures with fully relaxed volume, a ll cell parameters were fully relaxed to keep the stress below 100MPa . Figure 5.2 Simulation cells used for the Li 2 MnO 3 systems with an (a) aluminum dopant atom and (b) a silicon dopant atom. 5 .1 Silicon Dopant The fully relaxed structures of Li 2 MnO 3 with and without silicon dopant at the manganese octahedral site were compared. Figure 5.3 shows the relaxed octahedral structures , with fixed volume, and the bond lengths with the neighboring oxygen ions for the manganese in the perfect system and the silicon with only a single manganese replaced with silicon. By comparing bond lengths it is clear that the silicon brings the neighboring oxygen ions closer. This is consistent with the smaller Si 4+ ionic radii than Mn 4+. 72 Figure 5.3 The (a) Mn - O bond lengths for the perfect crystal structure and (b) Si - O bond lengths for the structure with one silicon dopant. Volume was fixed. Figure adapted from Nation, et al. 104 and reprinted with permission from Cambridge University Press. Table 5. 1 compares the lattice parameters change when the volume was fully relaxed and contained Si dopants with experiments. Experim entally, a control sample with Li 1.2 Mn 0.54 - x Ni 0.13 Co 0.13 O 2 stoichiometry , and Si doped samples with two concentrations, Li[Li 0.2 Mn 0.52 Si 0.02 Ni 0.13 Co 0.13 ]O 2 (HENMC - Si 0.02 ) and Li[Li 0.2 Mn 0.49 Si 0.05 Ni 0.13 Co 0.13 ]O 2 (HENMC - Si 0.05 ), were synthesized. The lattice parameters of these structures were determined using X - ray powder diffraction measurements while all X - ray patterns were matched to the - NaFeO 2 type layered structure ( space group). More experimental details can be found in the work by Natio n et al. 104 The Li 2 MnO 3 crystal structure C2/m has a different symmetry with - NaFeO 2 type layered structure. To facilitate comparison with experiments, the lattice parameters of the 2x1x2 super cell of Li 2 MnO 3 were converted to the - NaFeO 2 structure . (5.1) (5.2) T he increased Experimental data shows that the a and c parameters increase by ~0.05% - 0.15% as the Si doping level increases and the c/a ratio also increases with the doping level . This effect on lattice parameters was also observed in Si - doped LiNi x Mn y Co 1 - x - y O 2 . 106 However , the DFT 73 predicted lattice par ameters show that the lattices reduces the increasing Si doping. This seems to contradict lattice parameters observed with Si doping. However, Si incorporation can also impact lithium and oxygen vacancy generation, due to defect coupling. Table 5. 1. DFT predicted crystallographic parameters in comparison with as - synthesized HE - NMC samples. 104 Volume was allowed to relax. Table adapted from Nation, et al. 104 and reprinted with permission from Cambridge University Press. Sample a (Å) c (Å) c/a Vol (Å 3 ) / f.u. of LiMO 2 Experiment Control 2.8502 14.2234 4.9903 33.3552 HENMC - Si 0.02 2.8515 14.2313 4.9908 33.4042 HENMC - Si 0.05 2.8524 14.2448 4.9940 33.4570 DFT calculations Li 2 MnO 3 2.8840 14.3509 4.9760 34.5237 Li 2 Mn 0.94 Si 0.06 O 3 2.8765 14.3423 4.9860 34.3232 Li 2 Mn 0.94 Si 0.06 O 2.94 2.8865 14.3402 4.9680 34.5587 Oxygen vacancies are widely believed to play a role in HE - NMC activation. Thus, the impact of Si doping on all possible oxygen vacancy sites was evaluated. The energy of formation of all possible oxygen vacancies in the system was calculated at a fixed vol ume and the formation energy is plotted as the oxygen vacancy distance to the Si dopant, as shown in Figure 5.4. 74 Figure 5.4 Oxygen vacancy formation energy compared to distance from silicon dopant. Volume was fixed at all points. Figure 5.5 The supercell with a single silicon dopant and a V O in the most favorable position. Volume was fixed for these calculations. Figure adapted from Nation, et al. 1 04 and reprinted with permission from Cambridge University Press. Figure 5.4 shows that the energy of formation for V O was decreased by 0.05eV with a silicon dopant ion as compared to the perfect system, 2.09eV to 2.04eV. Additionally, the energy of fo rmation of V O However, there was a small decrease in formation energy for V O around 6 Å from the silicon ion. 75 The location of the oxygen ion with the lowest energy of formation a t a fixed volume is shown schematically in Figure 5.5. The most favorable oxygen vacancy position (the lowest formation energy) was located within the octahedral of a lithium which shared a corner with the silicon octahedral. The oxygen vacancy is in anoth er transition metal layer, connecting to the Si via Si - O - Li - O bonding. This could be a reason why the silicon ions cause the Li 2 MnO 3 to have a higher capacity even though the silicon is not redox active. The V O formed away from the silicon might activate neighboring manganese ions allowing lithium to be removed. In this environment, the oxygen vacancy formation energy is sensitive to t he dopant and the strain in the lattice. For example, with a constant volume approach, the oxygen vacancy formation energy is reduced from 2.09eV to 2.04eV (i.e., by 0.05 eV due to Si doping). Without the Si dopant , just expanding the volume by 1%, the vac ancy formation energy is reduced from 2.09 to 2.03 eV, as shown in Figure 4. 3 for G calculation , due to the volume expansion induced by oxygen vacancy generation. Si dopants may slightly increase the oxygen vacancy concentration as it lowers the oxygen v acancy formation energy, To further investigate this the system with a silicon dopant and the most favorable V O was volumetrically relaxed and shown to expand by 0.84 Å 3 . With the volume of the cells relaxed the energy of formation of V O was 2.03 eV for th e perfect system and 2.06 eV for the system with the silicon dopant. T his resulting super cell with one Si dopant and one oxygen vacancy ( Li 2 Mn 0.94 Si 0.06 O 3 - 0.06 ) h as a larger volume than the perfect Li 2 MnO 3 , as shown in Table 5. 1 . Based on this result, increased oxygen vacancy concentrations in the Si - doped HE - NMC is a likely cause of the increased lattice parameter observed in the experiments. 76 Oxygen vacancies will also reduce the lithium vacancy formation energy. This should then increa se the Li storage capacity at a given cutoff voltage , which provides a possible explanation for the observed impact of Si doping on HE - NMC capacity. In Fig ure 5. 1, the shift in the charge curve means to obtain the amount of charge capacity, the Si - doped samples require less activation energy, as the length of the activation plateau is 13 mAh/g shorter; in the following discharge cycle, the Si - doped samples show ~10% increased capacity. Note these i nitial DFT calculations do not address the impact of Si doping on the other degradation mechanisms such as transition metal diffusion into the Li - layer, phase transformation, and electrolyte degradation. Additional experiments and modeling are needed to investigate these possibilities. 5 .2 Aluminum Dopant The addition of an aluminum ion at a manganese octahedral site was also calculated for comparison and the change in the bond lengths with the neighboring oxygen ions in the oxygen octahedral were calculated at fixed volume and compared to those with manganese in the perfect cell, Figure 5.6. Figure 5.6 Bond lengths of manganese/aluminum with their neighboring oxygen ions. Volume was fixed during calculation. Portion of figure with manganese was adapted from Nation, et al. 104 and reprinted with permission fr om Cambridge University Press. 77 As seen in figure 5.6, the bond lengths did not change significantly but became more even , when the volume was fixed . This is also consistent with the similar ionic size of Al 3+ =0.535 Å with Mn 4 + (high spin) = 0.53 Å. Figure 5.7 Calculated formation energy for V O as compared to their distance from the aluminum dopant ion. Volume was fixed during calculations. T he impact of Al doping on all possible oxygen vacancy sites was evaluated. As shown in Figure 5.7, the V O formation energy was significantly decreased (from 2 .09 eV to 0.89 eV) for the oxygen ions directly neighboring the aluminum dopant. This is very different from what is in Si dopant. This is mainly because the charge on Al is 3+ . Therefore the neighboring oxygen gets one electron less than that from Mn 4+ , thus becomes less stable that that in the bulk of Li 2 MnO 3 . This can be represented by the following defect reaction: (5.3) 78 It shows substituting Mn 4+ with Al 3+ will increase the oxygen vacancy concentration. Therefore, due to the change in the charge of aluminum as compared to manganese, the formation energy of V O changed significantly. However, it is expected that this oxygen vacancy generation will not affect the capacity of the Li 2 MnO 3 . In Si doped Li2MnO3, the V O formed away from the silicon is in a Mn - O octahedral. So oxygen vacancy generation will likely activate the neighboring manganese ions (changing it from Mn 4+ to Mn 3+ ), whi ch in turn allowing the lithium to be removed. However, in Al doped structure, the oxygen loss is next to the Al and it is compensated by the difference in oxidation state of aluminum compared to manganese. So this oxygen vacancy loss will not cause any va lence change on Mn and therefore will not activate the material to deliver more Li capacity. This h as been observed by experiments. 1 04 5 .3 Conclusions In Chapters 2 and 3 it was shown that the oxygen vacancies could increase the capacity of Li 2 MnO 3 and also decrease the rate capability. This chapter showed that adding dopant ions can change the energy of formation of the oxygen vacancies and thus potentially help to tune the amount of oxygen vacancies in the system. Silicon, specifically, was shown to decrease the energy of formation of an oxygen vacancy in a neighboring octahedral of the silicon dopant which could potentially ac tivate a manganese ion. 79 Chapter 6 . Interactions b etween Li2MnO3 Surface and Ethylene Carbonate The previous chapters have illustrated how oxygen vacancies impact some key performance criteria of lithium - ion batteries and how oxygen vacancy concentratio ns may be altered by dopants. The oxygen vacancies can be generated inside of particle 107 and surfaces 23 . Specifically, Lee et al. argued V O can only be created on the surface of Li 2 MnO 3 because of the large energy barrier O ion to hopping. 23 Nevertheless, oxygen vacancy should be easier to form on the surface than in the bulk. Recently, Jung et al. suggest ed that the oxygen release may accelerate the degradation of the electrolyte. 108 Therefore, this chapter focus on the interaction of electrolyte with the Li 2 MnO 3 surface with and without the oxygen vacancies on the surface. Another often observed degradation mechanism in Mn containing cathode materials is the disproportionation of Mn 3+ into Mn 4+ /Mn 2+ and the dissolution of Mn 2+ from the oxide surface. Many papers reported that ppm levels of dissolved Mn ions diffuse to the anode surface, deposit on the solid electrolyt e interface (SEI) on the anode, cause degradation of the passivating SEI layer and result in capacity loss. Previous Mn dissolution studies are largely focused on spinel LiMn 2 O 4 . Computational studies have been done on this material to illustrate the disso lution process in order to help the design of electrolyte additives and coatings. This problem has been computationally studied in the spinel cathode material Li 2 MnO 4 109 , 110, 111 Side reactions at the surface of the LiMn 2 O 4 /electrolyte interface have been observed that degrade the electrode surface and ethylene carbonate (EC) (a key component in common electrolytes) when the voltage is high. M aterials containing Li 2 MnO 3 are frequently cycled to ~4.4V or higher on the first cycle and thus it is of interest to study the interactions between EC and the Li 2 MnO 3 surfa ce. 80 Jung et al. investigated the reaction between oxygen and EC in the context of LiMO 2 materials and proposed that two O 2 molecules reacted with EC to form 2 CO 2 , CO and H 2 O. 108 However, the reaction between EC and the Li 2 MnO 3 surface, with and without V O remains largely unexplored. Additionally, there is little research done on the Li 2 MnO 3 surface itself. Shin et al. calculated the Wulff structure and studied many surfaces, proposing that the (001), (110) and (100) facets are dominate. 25 However, that study did not look at the (131) surface and the (131) surface appears to be the most similar to the stable (104) LiCoO 2 surface. The work presented here, therefore, creates and analyzes the (131) Li 2 MnO 3 s urface and investigates the interaction between the surface and EC, both with and without the presence of V O . 6.1 Computational Method The calculations were done using a Li 2 MnO 3 slab in VASP . Most computational details are the same as listed in Section 2.1. The v alence electron configurations for the additional elemental constituents were as follows : C - 2s 2 2p 2 , H - 1s 1 . Slab model were constructed to compute surface energies. The slab models contained a vacuum space that was >15 Å thick above the Li 2 MnO 3 surface. A k - points mesh of 3x3x1 was used for all the slab models. The surface energy for two stoichiometric surfaces, namely (131) , and (101) and one non - stoichiometric (001) surface were calculated via the slab models. For stoi chiometric surfaces, t he surface energy ( ) was computed using its relation to the slab energy ( ), the number of layers ( ), the bulk energy per layer ( ) and the surface area of the slab ( ): (6.1) 81 In order to sol ve for from Equation 6.1, the was plotted against and the y - intercept of the linear fit of this plot was divided by 2A. After determining the surface orientation with the lowest surface energy, possible vacancy generation site was determ ined by computing the surface oxygen vacancy formation energy on all possible site. Then the adoption energy of EC molecule on the surface were computed via w here , and are the total energy of the optimized slab with the molecule (EC) adsorbed on the Li 2 MnO 3 surface, the clean Li 2 MnO 3 surface and the single molecule (EC). Various EC adsorption configurations were tested in order to identify the lowest energy configuration. Here a more negative adsorption energy indicates a stronger adsorption. 6.2 Ethylene Carbonate Adsorbed on Li 2 MnO 3 Surface First, the surface energy fo r Li 2 MnO 3 (001), (131) and (101) orientations were computed and compared. Each layer in the (131) and (101) slabs contain s stoichiometric lithium, manganese and oxygen as in the bulk Li 2 MnO 3 . The (001) surface is lithium - terminated and nonstoichiometric. I t is also important to note that one of the most favorable surface of the layered LiCoO 2 is (104) . 112 As Li 2 MnO 3 is usually added to the layered materials , it is likely that Li 2 MnO 3 surface will take the most comparable s tructure with the (104) LiCoO 2 surface. Due to the different 82 symmetry of LiCoO 2 and Li 2 MnO 3 , (131) Li 2 MnO 3 surface is the most compatible structure of the (104) LiCoO 2 surface. Following Equation 6.1, Figure 6. 1 plots the the as a function of the number of layers for the two stoichiometric surface models, (131) and (101) . The resulting values of are shown in Table 6.1. Table 6.1 The surface energy values for the (101), (131) and (001) Li 2 MnO 3 surfaces. Surface ( J/m 2 ) (101) 1.72 (131) 0.88 (001) 0.94 The surface energies of lithium - terminated (100) slab structures was determined according to: , (6.3 ) where A is the surface area, E is the total energy of the slab, formula is the integer number of stoichiometric formula units in the slab, is the energy of one formula unit of corresponding bulk structure, Li is the number of excel Li in the slab and Li is the chemical potential of Li ( - 1.9 eV/atom). The value for the (001) surface however was not solved for using several different num bers of layers, due to computational complexity only a slab with 5 layers was computed and used to calculate directly. 83 Figure 6.1 Plots of E Slab vs the number of layers (N) for the (a) (101) and (b) (131) Li 2 MnO 3 surfaces. The Li 2 MnO 3 (131) surface was chosen for the following surface studies because it was the lowest energy surface analyzed plus two additional reasons. First, it is most similar to the most stable LiCoO 2 surface, (104). Additionally, it contains lithium, manganese and oxygen ions which is helpful in determining how EC will adsorb. Figure 6. 2 shows both the Li 2 MnO 3 (131) and LiCoO 2 (104) surfaces. It is clear that the Li 2 MnO 3 (131) surface is the Li 2 MnO 3 surface most similar to the LiCoO 2 (104) surface. The transition metal and lithium layers of these materials are evident in both the Li 2 MnO 3 (131) surface and LiCoO 2 (104) surface. Also, the each of the transition metal ions have four nearest oxygen neighbors within the same layer, one oxy gen nearest neighbor below and one oxygen nearest neighbor above in both surfaces. 84 Figure 6. 2 Comparison of the similar structure of (a) Li 2 MnO 3 (131) and (b) LiCoO 2 (104) surfaces. Green atoms are lithium, red are oxygen, purple are manganese and blue a re cobalt. Figure 6. 3 Fully atomically relaxed structures with EC (a) parallel to the surface, (b) horizontal on the surface and (c) vertically placed on the surface. White atoms are hydrogen, bronze are carbon, red are oxygen, green are lithium and purple are manganese. To determine how the EC molecule would interact with the Li 2 MnO 3 (131) surface, three possible EC adsorption configurations were fully relaxed and their energies were compared. The fir st configuration of EC is referred to here as parallel to the surface, as shown in Figure 6. 3 (a). The second configuration is referred to as horizontal here because EC is not flat on the surface but on its side, as shown in Figure 6. 3 (b). Lastly, a verti cal configuration of EC was also analyzed, as shown in Figure 6. 3 (c). For each of the three EC configurations shown in Figure 6. 3 , the adsorption energy was calculated using Equation 6.2. The adsorption energies were - 0.66 eV, - 85 0.30 eV and - 0.12 eV for th e parallel EC, horizontal EC and vertical EC, respectively. This suggests that the EC molecule prefers to interact with the surface as the configuration with the EC most flat on the surface was the energetically most stable one. Typically when the adsorpti on energy is less than - 0.4eV (or - 40kJ/mol), the adsorption is considered a chemical adsorption. Therefore the parallel adopted configuration (Figure 6. 3 (a)) will be further investigated for different EC decomposition pathways. 6 .3 Decomposition of Ethyl ene Carbonate on Surface Two different EC decompositions were looked at which were found to be favorable on LiMn 2 O 4 (Leung). 109 The first was the breaking of one of the C - O bonds within the EC molecule , Figure 6.3 (a) and (b) . For this configuration the bond between the ketone c arbon and an oxygen with the ring was broken , similar to what was done by Leung, Figure 6. 4 (c) . 109 The broken molecule was placed such that the oxy gen in the broken bond was placed near a surface manganese ion and the carbon from the broken bond was near a surface oxygen ion. This configurat ion was 0 .10 eV higher in energy than the parallel adsorption configuration meaning it is not as energetically f avorable but still a possible decomposition configuration. 86 Figure 6. 4 The decomposition of EC via breaking one of the C - O bonds in the ring on (a) Li 2 MnO 3 . A more zoomed in image of the EC is shown in (b). The (c) EC decomposition in a similar manner on LiMn 2 O 4 is shown for comparison, figure (c) was adapted with permission from Leung. 109 Copyright 2012 American Chemical Society. Another decomposition of the EC which was studied was the loss of a single hydrogen to the Li 2 MnO 3 (131) surface. However, as the DFT atomic minimization was performed the syst em relaxed to a state where two hydrogen atoms left EC and were on the surface. The system with a single hydrogen on the surface is 0.95 eV higher in energy than the intact EC adsorbed parallel to the surface. The system with two hydrogen on the surface fo rming two OH bonds, however, is 1.20eV lower in energy that the system with the intact EC adsorbed. The systems with the possible decompositions of EC are summarized in Figure 6. 5 and compared to the intact EC configuration. Figure 6. 5 The intact EC are plotted along with the different possible decomposition configurations studied a nd their corresponding energies with respect to the EC adsorbed state. Color scheme : carbon (brown); oxygen (red); hydrogen (white); manganese (purple); lithium (green) . 87 The chemically adsorbed EC seems to be energetically favorable to loss two H atoms to the O on the Li 2 MnO 3 (131) surface. It suggested a new EC decomposition reaction as: (EC) 2 H - absorbed on Li 2 MnO 3 (131) surface as OH + ( VC ) The resulted produc t is a v inylene carbonate , ( VC ) , that is physically adsorbed on the Li 2 MnO 3 (131) surface indicated by the large distance of over 3 Å to the surface. This reaction was considered as a proton abstraction reaction by Borodin et al. 113 . They found that it was favorable for two protons to be removed at once for the EC/NMO[100] system and also they found a favorable reaction for the loss of a single proton on DMC/NMO[100], EC/NMO[111], and EC/NMO[111], where NMO refers to delithiated spinel - structured LiNi 0.5 Mn 1 . 5 O 4 cathode materials. Based on the energetics shown in Figure 6. 5 , the one proton abstraction reaction seems to be an energy barrier of 0.95eV for the two proton abstraction reaction. The physical adsorption of VC also means it will return to the electrolyte easily. VC is known to be a common electrolyte additive that is beneficial to SEI stability . 114 Therefore this decomposition mechanism may be beneficial as well. 6.4 The Effect of Oxygen Vacancies on the EC Interaction with the Li 2 MnO 3 - (131) Surface In order to further study the imp act of the oxygen vacancies, the location and impact of surface oxygen vacancies were explored on Li 2 MnO 3 - (131) surface . There were found to be 12 possible oxygen sites on the surface and amongst them were three categories in as far as nearest neighbors, this is summarized below in Table 6.2 along with the system energies and V O formation 88 energies. One of these categories had three in - plane lithium neighbors, one in plane manganese neighbor and one lithium neighbor below it. Another set of oxygen sites ha d two lithium in plane neighbors, two manganese in plane neighbors and one lithium neighbor below. The last category had 3 lithium in plane neighbors, 1 manganese in plane neighbor and one manganese neighbor below it. Within these categories were other ass umed configurational differences because there were surface V O with the same configuration of lithium and manganese neighbors but different formation energies. The V O which was determined most favorable had a formation energy of 0.85eV, 3 lithium in - plane neighbors, one manganese in plane neighbor and a single lithium neighbor below it. Note this formation energy is much lower than that in the bulk ( 2.09eV), therefore it confirms that the oxygen vacancy formation will likely start from the Li 2 MnO 3 (131) surface. 89 Table 6.2 The total system energy, energy of formation of a V O for each oxygen site on the Li 2 MnO 3 (131) surface. Additionally, the number of Li and Mn neighbors, both in plane and in other planes, are listed. Energy (eV) E f (eV) Li in Plane Mn in Plane Li below Mn below - 710.90 0.85 3 1 1 - 710.55 1.20 3 1 1 - 710.90 0.85 3 1 1 - 710.55 1.20 3 1 1 - 710.19 1.56 2 2 1 - 710.18 1.57 2 2 1 - 710.19 1.56 2 2 1 - 710.18 1.57 2 2 1 - 710.02 1.72 3 1 1 - 709.87 1.88 3 1 1 - 710.02 1.73 3 1 1 - 709.87 1.88 3 1 1 The adsorption of EC on the surface with the most favorable V O present was investigated. The EC was added both tilted and completely vertical with the ketone oxygen in the V O site. After full structure relaxation, the EC in the completely vertical position is more favorable by 0.02eV. Additionally, both molecules ap peared to move so the EC oxygen was not in the V O site on the Li 2 MnO 3 (131) surface. This suggests that the EC molecule does not interact as much with the surface near a V O . Therefore it can be considered that EC will prefer to be absorbed at the oxygen fr ee Li 2 MnO 3 (131) surface, as discussed in Section 6.3. However, will the oxygen release have an impact on electrolyte decomposition? 90 Figure 6. 6 An EC molecule on the (131) Li 2 MnO 3 surface containing a single V O on the top, surface, layer and the EC (a) tilted or (b) completely vertical. Therefore, t he interactions and possible reaction pathways between an oxygen atom released from the surface with the EC molecule were also investigated. The EC molecule and the oxygen atom were placed together in a 20Åx20Åx20Å cube. First all atomic positions except the extra oxygen atom and one of the carbon atoms it was closest to in the EC ring were relaxed. Then all the atoms in the EC plus the extra oxygen atom were relaxed. The initial and relaxed configuration s are shown below in Figure 6. 7 . The total energies of the systems shown in Figure 6. 7 are summarized in Table 6. 3 and the difference between the energy of configuration 1 and each configuration is summarized in Table 6. 4 . 91 Figure 6. 7 Configurations of EC molecule plus an extra oxygen before and after the atomic positions were minimized using DFT. Table 6. 3 Total energies fo r each configuration both while the C - O distance was constrained and when all the atoms were allowed to relax. Total Energy (eV) 1 2 3 4 5 Fixed C - O position - 63.55 - 63.77 - 66.12 - 63.64 - 67.88 All Atoms Relaxed - 63.72 - 63.80 - 68.55 - 67.80 - 67.94 Table 6. 4 The difference between the energy of configuration 1 and the other configurations summarized for both while the C - O bond distance was fixed and when all atomic positions were minimized. Difference in Energy from Configuration 1 (eV) 1 2 3 4 5 Fixed C - O position 0.00 - 0.22 - 2.57 - 0.09 - 4.33 All Atoms Relaxed 0.00 - 0.09 - 4.84 - 4.08 - 4.22 92 From Table 6. 4 it appears that the completely relaxed structure of EC and the oxygen where the oxygen bonds with the EC ring between a hydrogen and carbon atom is the most favorable structure. The OH group on the EC molecule may not be stable, so continuous reaction wi th O atoms will lead to further decomposition of EC to CO 2 , CO and H 2 O, as suggested by Jung et al. 108 Further calculations are needed to clarify this. 6.5 Conclusions Li 2 MnO 3 (131) is the most stable surface for Li 2 MnO 3. The (131) Li 2 MnO 3 contains lithium, manganese and oxygen on the surface. This is the surface which is most similar to the stable (104) LiCoO 2 as the lithium and transition metals have four in plane oxygen neighbors with one oxygen neighbor in the layer below and one oxygen neighbor in the layer above. EC chemically adsorbed on the Li 2 MnO 3 (131) surface. An EC to VC reaction after two proton abstraction reaction from EC is found on Li 2 MnO 3 (131) surface. We believe this reaction is beneficial to the life of the lithium - ion b attery, as VC tends to form more stable SEI. However, the oxygen vacancy on the surface did not promote EC adsorption. Therefore it will not facilitate this EC deprotonation reaction. At the same time, due to the oxygen loss, the Mn will be subject to Mn dissolution more easily and triggers more SEI related degradation mechanisms that are beyond the scope of this thesis. 93 Chapter 7. Conclusions and Proposed Work 7 .1 Conclusions Li 2 MnO 3 stabilized materials, or lithium - rich materials, have the potential t o be high capacity materials for lithium - ion batteries. These materials are activated during the first charging cycle, at least in part, with the release of oxygen. However, prior to this work, little was known about the impact of the created oxygen vacanc ies in the Li 2 MnO 3 component. This work found that there is a clear correlation between oxygen vacancies and lithium vacancies. The formation of oxygen vacancies causes the neighboring lithium sites to be unfavorable. This impacts the performance of the battery in two ways. First, it c auses a lower formation energy for lithium vacancies near the oxygen sites which increases the capacity of the material. Additionally, the migration barrier for lithium to hop into the sites near the oxygen vacancies increase, causing the battery to have a lower rate capability. The chemical expansion corresponding to the creation of oxygen vacancies and lithium vacancies was also explored. The oxygen vacancies and lithium vacancies were observed to also be correlated in terms of chemical expansion. The c hemical expansion associated with multiple vacancies was not a linear sum of the individual vacancy types which shows that the two vacancy types have a correlated impact. Oxygen vacancies were also found to be affected by dopants. In particular, silicon w as shown to decrease the energy of formation for oxygen vacancies in neighboring octahedral to the silicon dopants. This is important because it shows that the amount of oxygen vacancies might be tun able. Additionally, the oxygen vacancies that are now mor e favorable to form could act i vate manganese ions and add capacity to the material. 94 Lastly, the interactions between the Li 2 MnO 3 (131) surface and an electrolyte component, ethylene carbonate (EC), were explored. The Li2 M nO3 was shown to be similar to sta ble LiCoO 2 (104) surface in that the transition metals in both surfaces had four planar oxygen neighbors. An energetically favorable decomposition reaction of the loss of two hydrogen atoms from the EC to the Li 2 MnO 3 surface was found forming vinylene carb onate (VC). Additionally, interaction between EC an oxygen ions, which could potentially be lost from the surface was explored. The oxygen vacancies clearly impact electrochemical properties and decomposition of the electrolyte. Additionally, dopant ions h ave an impact on the formation of oxygen vacancies. 7 .2 Proposed Future Work The role of oxygen vacancies can still be more deeply explored in Li 2 - X MnO 3 - . Further combined experimental and theoretical studies to determine the amount of oxygen vacancie s in experimental Li 2 MnO 3 containing electrodes would be of interest. In particular, an unanswered question is if there is an optimal amount of oxygen vacancies that would increase electrochemical proper ties, such as capacity, of the material without signi fica nt negative impact of other electrochemical properties, such as rate capability . The amount of oxygen vacancies might be tunable via the addition of dopants to Li 2 MnO 3 and should be further investigated by looking at dopants beyond silicon and aluminu m. Lastly, more research could be done on the Li 2 MnO 3 surface to see how the EC which is interacting with an oxygen ion lost from the surface may decompose on the surfac 95 R EFERENCES 96 REFERENCES 1. Thackeray, M. M.; Wolverton, C.; Isaacs, E. D., Electrical energy storage for transportation - approaching the limits of, and going beyond, lithium - ion batteries. Energy & Environmental Science 2012, 5 (7), 7854 - 7863. 2. 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