簡易檢索 / 詳目顯示

回結果列表
研究生： 陸飛鳳
Lu, Feye-Feng
論文名稱： 以第一原理計算探討c-LLZO固態電解質中摻雜元素對鋰離子傳輸的影響
Revealing the Dopant Effect on the Transport of Li in the c-LLZO Solid Electrolyte via First-Principles Calculations
指導教授： 田弘康
Tian, Hong-Kang
學位類別： 碩士
Master
系所名稱： 工學院 - 化學工程學系
Department of Chemical Engineering
論文出版年： 2024
畢業學年度： 112
語文別： 英文
論文頁數： 113
中文關鍵詞： 固態電解質 、導離度 、摻雜 、質子化 、第一原理計算
外文關鍵詞： solid electrolyte, ionic conductivity, dopant, protonation, first-principles calculations
相關次數： 點閱：70  下載：0 
分享至:
查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報

    • 立方石榴石型Li7La3Zr2O12 （c-LLZO）具有高導離度 (~ 1 mS/cm)、寬電化學窗 (> 6 V vs. Li+/Li)等特性，為全固態鋰電池中極具潛力的固態電解質。鋰空缺濃度被視為影響導離度的關鍵，常透過摻雜高價態元素以取代結構中的鋰來引入鋰空缺。由此可見，同樣的鋰空缺濃度應具有相似程度的導離度。然而，鎵 (Ga)、鋁 (Al)、鐵 (Fe)等三價元素摻雜後即使具有相同濃度的鋰空缺，Ga 和 Fe 摻雜的導離度卻比 Al 摻雜高出一個數量級，表示仍有未知的關鍵因素。因此，本研究旨在探討Ga、Al、Fe等摻雜元素對c-LLZO的影響，摻雜後元素比控制在Li6.625A0.125La3Zr16O12 (A = Ga、Fe、Al)。我們運用密度泛函理論（DFT）來分析摻雜元素電子性質對鋰傳輸的影響。結果顯示，摻雜元素及其鄰近的氧原子電荷分佈影響了鋰的化學位能，Ga和Fe保留更多電子在其周圍，使相鄰氧原子所帶電荷較不偏負，減少了氧及鋰的作用力，使鋰的化學位能提高，降低鋰傳輸的活化能，因此增強了鋰的導離度；相反地，Al將電子推向鄰近的氧原子，增加了氧及鋰的作用力，穩定了鋰的化學位能並增加鋰傳輸的活化能，導致導離度降低。此外，Fe的摻雜在能隙中引入了額外的能態，表示Fe摻雜LLZO可能更易被還原，與實驗結果一致。另一方面，LLZO對於與空氣接觸的不穩定性也是一個不容忽視的問題，LLZO會與水發生鋰離子/質子交換反應，質子化後LLZO的導離度明顯降低了二到四個數量級，因此，了解背後影響的機制變得至關重要。透過第一原理分子動力學（AIMD）模擬，我們探討了質子化c-LLZO中鋰離子和質子傳輸的機制。儘管在鋰離子濃度相對較低的情況下（表示質子化程度較高），由於Li-O的鍵結相對於O-H的鍵結較不穩定，鋰離子的導離度仍然佔據主導地位。然而，隨著質子含量的增加，鋰離子擴散途徑變得較不連接，導致總導離度降低。我們的研究強調了c-LLZO中電荷分佈的重要性，以及其如何影響導離度，並為質子化c-LLZO的離子傳輸機制提供了有價值的見解，對於開發新型固態電解質有正面幫助。

    Cubic garnet-type Li7La3Zr2O12 (c-LLZO) exhibits high conductivity (~1 mS/cm) and a wide electrochemical window (> 6 V vs. Li+/Li), making it a promising solid electrolyte for all-solid-state lithium batteries. Lithium (Li) vacancy concentration has been considered a key factor influencing conductivity, often achieved by doping high-valent elements to replace Li ions in the structure. Despite anticipating similar ionic conductivities due to comparable Li vacancy concentrations, the doping of c-LLZO with trivalent elements, namely Ga, Al, and Fe, reveals a marked distinction. Specifically, Ga and Fe-doped LLZO demonstrate conductivity levels one order of magnitude higher than their Al-doped counterpart. This indicates the existence of unidentified factors influencing conductivity beyond Li vacancy concentration. Therefore, this study aims to investigate the impact of various dopants such as Ga, Al, and Fe on c-LLZO. Dopant concentrations were controlled at 0.125 with the formula of Li6.625A0.125La3Zr16O12 (A = Ga, Fe, Al). Density functional theory (DFT) was employed to analyze the influence of dopant electronic properties on Li transport. Results show that the charge distribution of dopant and adjacent oxygen (O) atoms affects the Li chemical potential. Ga and Fe retain more electrons around themselves, making the neighboring O atoms less negative, decreasing the restraining forces between O and Li, elevating the Li chemical potential, lowering the activation energy (Ea) for Li transport, and enhancing Li ionic conductivity. Conversely, Al pushes electrons toward nearby O atoms, increasing the interactions between O and Li, stabilizing the Li, raising the Ea for Li transport, and reducing ionic conductivity. Additionally, Fe doping introduces additional states in the bandgap, indicating that Fe-doped LLZO may be more susceptible to reduction, consistent with experimental results.
    On another note, the instability of LLZO upon contact with air is a significant concern. LLZO undergoes Li+/H+ exchange reactions with water, resulting in a drastic reduction in ionic conductivity by two to four orders of magnitude. Thus, understanding the underlying mechanisms becomes crucial. Through ab initio molecular dynamics (AIMD) simulations, we explore the mechanisms of Li and proton transport in protonated c-LLZO. Despite low Li concentrations (high protonation level), the ionic conductivity of Li ions dominates the total ionic conductivity because of the less stable bonding of Li-O compared to O-H. However, as the proton content increases, the Li diffusion pathway appears less connected, reducing total ionic conductivity. Our study emphasizes the importance of local charge distribution in c-LLZO, influencing ionic conductivity, and provides valuable insights into the behavior of Li and protons in c-LLZO when protonated. This understanding is vital for developing high-performance solid electrolytes.

    TABLE of CONTENTS 摘要 i ABSTRACT ii ACKNOWLEDGEMENTS iv TABLE of CONTENTS v LIST of TABLES viii LIST of FIGURES ix 1. INTRODUCTION 1 1.1 Background and Motivation 1 2. LITERATURE REVIEW 5 2.1 The Working Principles of Li-ion Batteries 5 2.2 Solid-State Electrolytes 7 2.2.1 Garnet-Type Solid Electrolyte 9 2.2.2 Two Structural Types for LLZO: Cubic and Tetragonal 11 2.2.3 Challenging for LLZO 14 2.2.4 Li-site dopants 20 3. BACKGROUND COMPUTATIONAL THEORIES 26 3.1 Introduction to Schrödinger Equation 26 3.2 Hartree-Fock Approximation 28 3.3 Density Functional Theory 29 3.4 Kohn-Sham Equations 30 3.5 Exchange-Correlation Functionals 31 3.5.1 The Local Density Approximation (LDA) 31 3.5.2 The Generalized Gradient Approximation (GGA) 32 3.5.3 Self-interaction error and DFT+U 32 3.6 Plane Wave Functions and Brillouin Zone Sampling 34 3.7 Introduction to Molecular Dynamics (MD) 35 3.7.1 Principles of Molecular Dynamics 35 3.7.2 Integrating the Equations of Motion 36 3.7.3 The Velocity Verlet Algorithm 37 3.7.4 Statistical Ensembles 37 3.7.5 Ab initio Molecular Dynamics 39 3.8 The Vienna Ab initio Simulation Package (VASP) Code 40 3.8.1 VASP Input Files 40 3.8.2 VASP Output Files 43 3.9 Computational Setting Details 44 3.9.1 Initial Structure Construction 44 3.9.2 Structure Optimization 46 3.9.3 Ab initio Molecular Dynamics Calculations 49 3.10 Analysis Methods 49 3.10.1 Vacancy Formation Energy 49 3.10.2 Density of States 50 3.10.3 Bader Charge Analysis 51 3.10.4 MSD, Diffusivity, and Ionic Conductivity Obtained from AIMD Calculations 52 4. RESULTS and DISCUSSION 54 4.1 Unraveling the Root Causes of Diverse Dopant Effects on Ionic Conductivity 54 4.1.1 Comparison of Energy between Random Li Distribution and Li Distribution Following the Rule 54 4.1.2 Dopant Location: Investigating the Preferred Sites in LLZO Structures 55 4.1.3 Determining the Optimal U Value for Fe in Fe-Doped LLZO 57 4.1.4 Impact of Dopants on Density of States in c-LLZO 60 4.1.5 Impact of Dopants on Net Charges of O Atoms and Local Charge Distribution in c-LLZO 62 4.1.6 Influence of Different Types of Dopants on Li Chemical Potential in c-LLZO 65 4.1.7 Conclusion 67 4.2 Evaluating the Influence of Protons on Al-doped LLZO 68 4.2.1 Enhancing Accuracy in Protonated Al-doped LLZO Simulations Using PBE with Van der Waals Corrections Functional 68 4.2.2 Different Site Preferences for Li and Protons 70 4.2.3 Exploring the Impact of Protons on the Electronic Properties of LLZO 71 4.2.4 Investigations on the Changes in Activation Energy, Diffusivity, and Ionic Conductivity Following Protonation of LLZO 73 4.2.5 Conclusion 78 5. CONCLUSIONS and FUTURE WORKS 79 5.1 Conclusions 79 5.2 Future Works 80 REFERENCES 82 APPENDIX A. ADDITIONAL INFORMATION 96

    1. Goodenough, J. B. & Singh, P. Review—Solid Electrolytes in Rechargeable Electrochemical Cells. J Electrochem Soc 162, A2387–A2392 (2015).
    2. Bachman, J. C. et al. Inorganic Solid-State Electrolytes for Lithium Batteries: Mechanisms and Properties Governing Ion Conduction. Chem Rev 116, 140–162 (2016).
    3. Manthiram, A., Yu, X. & Wang, S. Lithium battery chemistries enabled by solid-state electrolytes. Nature Reviews Materials 2017 2:4 2, 1–16 (2017).
    4. Tarascon, J. M. & Armand, M. Issues and challenges facing rechargeable lithium batteries. Nature 2001 414:6861 414, 359–367 (2001).
    5. Sun, C., Liu, J., Gong, Y., Wilkinson, D. P. & Zhang, J. Recent advances in all-solid-state rechargeable lithium batteries. Nano Energy 33, 363–386 (2017).
    6. Fan, L., Wei, S., Li, S., Li, Q. & Lu, Y. Recent Progress of the Solid-State Electrolytes for High-Energy Metal-Based Batteries. Adv Energy Mater 8, 1702657 (2018).
    7. Kerman, K., Luntz, A., Viswanathan, V., Chiang, Y.-M. & Chen, Z. Review—Practical Challenges Hindering the Development of Solid State Li Ion Batteries. J Electrochem Soc 164, A1731–A1744 (2017).
    8. Wu, J. F., Pang, W. K., Peterson, V. K., Wei, L. & Guo, X. Garnet-Type Fast Li-Ion Conductors with High Ionic Conductivities for All-Solid-State Batteries. ACS Appl Mater Interfaces 9, 12461–12468 (2017).
    9. Murugan, R. et al. Fast Lithium Ion Conduction in Garnet-Type Li7La3Zr2O12. Angewandte Chemie International Edition 46, 7778–7781 (2007).
    10. Ramakumar, S., Deviannapoorani, C., Dhivya, L., Shankar, L. S. & Murugan, R. Lithium garnets: Synthesis, structure, Li+ conductivity, Li+ dynamics and applications. Prog Mater Sci 88, 325–411 (2017).
    11. Thangadurai, V., Kaack, H. & Weppner, W. J. F. Novel Fast Lithium Ion Conduction in Garnet-Type Li5La3M2O12 (M = Nb, Ta). Journal of the American Ceramic Society 86, 437–440 (2003).
    12. Thangadurai, V. & Weppner, W. Li6ALa2Nb2O12 (A=Ca, Sr, Ba): A New Class of Fast Lithium Ion Conductors with Garnet-Like Structure. Journal of the American Ceramic Society 88, 411–418 (2005).
    13. Zhang, Y. et al. Field assisted sintering of dense Al-substituted cubic phase Li7La3Zr2O12 solid electrolytes. JPS 268, 960–964 (2014).
    14. Wolfenstine, J., Ratchford, J., Rangasamy, E., Sakamoto, J. & Allen, J. L. Synthesis and high Li-ion conductivity of Ga-stabilized cubic Li7La3Zr2O12. Mater Chem Phys 134, 571–575 (2012).
    15. Rettenwander, D., Geiger, C. A. & Amthauer, G. Synthesis and crystal chemistry of the fast Li-ion conductor Li 7La3Zr2O12 doped with Fe. Inorg Chem 52, 8005–8009 (2013).
    16. Rangasamy, E., Wolfenstine, J. & Sakamoto, J. The role of Al and Li concentration on the formation of cubic garnet solid electrolyte of nominal composition Li7La3Zr2O12. Solid State Ion 206, 28–32 (2012).
    17. Meier, K., Laino, T. & Curioni, A. Solid-state electrolytes: Revealing the mechanisms of Li-Ion conduction in tetragonal and cubic LLZO by first-principles calculations. Journal of Physical Chemistry C 118, 6668–6679 (2014).
    18. Luo, Y. et al. Effect of dual doping on the structure and performance of garnet-type Li7La3Zr2O12 ceramic electrolytes for solid-state lithium-ion batteries. Ceram Int 45, 17874–17883 (2019).
    19. Xiang, X. et al. Crystal structure of cubic Li7-3xGaxLa3Zr2O12 with space group of I-43d. Ceram Int 48, 9371–9377 (2022).
    20. Liu, X. et al. Elucidating the mobility of H + and Li + ions in (Li 6.25−x H x Al 0.25 )La 3 Zr 2 O 12 via correlative neutron and electron spectroscopy. Energy Environ Sci 12, 945–951 (2019).
    21. Scrosati, B. & Garche, J. Lithium batteries: Status, prospects and future. J Power Sources 195, 2419–2430 (2010).
    22. Xu, K. Nonaqueous liquid electrolytes for lithium-based rechargeable batteries. Chem Rev 104, 4303–4417 (2004).
    23. Arora, P. & Zhang, Z. Battery separators. Chem Rev 104, 4419–4462 (2004).
    24. Reddy, M. V., Subba Rao, G. V. & Chowdari, B. V. R. Metal oxides and oxysalts as anode materials for Li ion batteries. Chem Rev 113, 5364–5457 (2013).
    25. Whittingham, M. S. Lithium batteries and cathode materials. Chem Rev 104, 4271–4301 (2004).
    26. Golubkov, A. W. et al. Thermal-runaway experiments on consumer Li-ion batteries with metal-oxide and olivin-type cathodes. RSC Adv 4, 3633–3642 (2013).
    27. Bruce, P. G., Freunberger, S. A., Hardwick, L. J. & Tarascon, J. M. LigO2 and LigS batteries with high energy storage. Nat Mater 11, 19–29 (2012).
    28. Zhang, Z. et al. New horizons for inorganic solid state ion conductors. Cite this: Energy Environ. Sci 11, 1945 (2018).
    29. Hikima, K., Totani, M., Obokata, S., Muto, H. & Matsuda, A. Mechanical Properties of Sulfide-Type Solid Electrolytes Analyzed by Indentation Methods. Cite This: ACS Appl. Energy Mater 2022, (2349).
    30. Rodger, A. R., Kuwano, J. & West, A. R. Li+ ion conducting γ solid solutions in the systems Li4XO4-Li3YO4: X=Si, Ge, Ti; Y=P, As, V; Li4XO4-LiZO2: Z=Al, Ga, Cr and Li4GeO4-Li2CaGeO4. Solid State Ion 15, 185–198 (1985).
    31. Stramare, S., Thangadurai, V. & Weppner, W. Lithium Lanthanum Titanates: A Review. Chemistry of Materials 15, 3974–3990 (2003).
    32. Thangadurai, V., Narayanan, S. & Pinzaru, D. Garnet-type solid-state fast Li ion conductors for Li batteries: critical review. Chem Soc Rev 43, 4714–4727 (2014).
    33. Kanno, R., Hata, T., Kawamoto, Y. & Irie, M. Synthesis of a new lithium ionic conductor, thio-LISICON-lithium germanium sulfide system. Solid State Ion 130, 97–104 (2000).
    34. Kamaya, N. et al. A lithium superionic conductor. Nature Materials 2011 10:9 10, 682–686 (2011).
    35. Muramatsu, H., Hayashi, A., Ohtomo, T., Hama, S. & Tatsumisago, M. Structural change of Li2S–P2S5 sulfide solid electrolytes in the atmosphere. Solid State Ion 182, 116–119 (2011).
    36. Arbi, K., Mandal, S., Rojo, J. M. & Sanz, J. Dependence of ionic conductivity on composition of fast ionic conductors Li1+xTi2-xAlx(PO4)3, 0 ≤ x ≤ 0.7. A parallel NMR and electric impedance study. Chemistry of Materials 14, 1091–1097 (2002).
    37. Hartmann, P. et al. Degradation of NASICON-Type Materials in Contact with Lithium Metal: Formation of Mixed Conducting Interphases (MCI) on Solid Electrolytes. Journal of Physical Chemistry C 117, 21064–21074 (2013).
    38. Knauth, P. Inorganic solid Li ion conductors: An overview. Solid State Ion 180, 911–916 (2009).
    39. Bohnke, O. The fast lithium-ion conducting oxides Li3xLa2/3 − xTiO3 from fundamentals to application. Solid State Ion 179, 9–15 (2008).
    40. Li, C. et al. NaSICON: A promising solid electrolyte for solid‐state sodium batteries. Interdisciplinary Materials 1, 396–416 (2022).
    41. Zhu, Y., He, X. & Mo, Y. Origin of Outstanding Stability in the Lithium Solid Electrolyte Materials: Insights from Thermodynamic Analyses Based on First-Principles Calculations. ACS Appl Mater Interfaces 7, 23685–23693 (2015).
    42. Thangadurai, V., Narayanan, S. & Pinzaru, D. Garnet-type solid-state fast Li ion conductors for Li batteries: critical review. This journal is Cite this: Chem. Soc. Rev 4714, 4714 (2014).
    43. Cussen, E. J., O’Callaghan, M. P., Powell, A. S., Titman, J. J. & Chen, G. Z. Switching on fast lithium ion conductivity in garnets: The structure and transport properties of Li3+xNd3Te2-xSb xO12. Chemistry of Materials 20, 2360–2369 (2008).
    44. O’Callaghan, M. P., Lynham, D. R., Cussen, E. J. & Chen, G. Z. Structure and ionic-transport properties of lithium-containing garnets Li3Ln3Te2O12 (Ln = Y, Pr, Nd, Sm-Lu). Chemistry of Materials 18, 4681–4689 (2006).
    45. Thangadurai, V. & Weppner, W. Li6ALa2Ta2O12 (A = Sr, Ba): Novel Garnet-Like Oxides for Fast Lithium Ion Conduction. Adv Funct Mater 15, 107–112 (2005).
    46. Raju, M. M., Altayran, F., Johnson, M., Wang, D. & Zhang, Q. Crystal Structure and Preparation of Li7La3Zr2O12 (LLZO) Solid-State Electrolyte and Doping Impacts on the Conductivity: An Overview. Electrochem 2021, Vol. 2, Pages 390-414 2, 390–414 (2021).
    47. Xie, H., Alonso, J. A., Li, Y., Fernández-Díaz, M. T. & Goodenough, J. B. Lithium Distribution in Aluminum-Free Cubic Li 7 La 3 Zr 2 O 12. Chemistry of Materials 23, 3587–3589 (2011).
    48. O’Callaghan, M. P. & Cussen, E. J. Lithium dimer formation in the Li-conducting garnets Li5+xBaxLa3−xTa2O12 (0 < x ≤ 1.6). Chemical Communications 2048–2050 (2007).
    49. Awaka, J., Kijima, N., Hayakawa, H. & Akimoto, J. Synthesis and structure analysis of tetragonal Li7La3Zr2O12 with the garnet-related type structure. J Solid State Chem 182, 2046–2052 (2009).
    50. Guo, S., Sun, Y. & Cao, A. Garnet-type Solid-state Electrolyte Li7La3Zr2O12: Crystal Structure, Element Doping and Interface Strategies for Solid-state Lithium Batteries. Chemical Research in Chinese Universities 2020 36:3 36, 329–342 (2020).
    51. Awaka, J. et al. Crystal structure of fast lithium-ion-conducting cubic Li7La3Zr2O12. Chem Lett 40, 60–62 (2011).
    52. Stability of Li, E. et al. Electrochemical Stability of Li10GeP2S12 and Li7La3Zr2O12 Solid Electrolytes. Adv Energy Mater 6, 1501590 (2016).
    53. Yang, L. et al. Interrelated interfacial issues between a Li7La3Zr2O12-based garnet electrolyte and Li anode in the solid-state lithium battery: a review. J Mater Chem A Mater 9, 5952–5979 (2021).
    54. Pervez, S. A. et al. Overcoming the Interfacial Limitations Imposed by the Solid–Solid Interface in Solid-State Batteries Using Ionic Liquid-Based Interlayers. Small 16, 2000279 (2020).
    55. Liu, J. et al. Review of the Developments and Difficulties in Inorganic Solid-State Electrolytes. Materials 2023, Vol. 16, Page 2510 16, 2510 (2023).
    56. Müller, M. et al. Reducing Impedance at a Li-Metal Anode/Garnet-Type Electrolyte Interface Implementing Chemically Resolvable in Layers. ACS Appl Mater Interfaces 14, 14739–14752 (2022).
    57. Jiang, W. et al. Improvement of the Interface between the Lithium Anode and a Garnet-Type Solid Electrolyte of Lithium Batteries Using an Aluminum-Nitride Layer. Nanomaterials 12, 2023 (2022).
    58. Shen, F. et al. A Simple and Highly Efficient Method toward High-Density Garnet-Type LLZTO Solid-State Electrolyte. ACS Appl Mater Interfaces 12, 30313–30319 (2020).
    59. Botros, M. et al. Microstrain and electrochemical performance of garnet solid electrolyte integrated in a hybrid battery cell. RSC Adv 9, 31102–31114 (2019).
    60. Grissa, R., Seidl, L., Dachraoui, W., Sauter, U. & Battaglia, C. Li7La3Zr2O12Protonation as a Means to Generate Porous/Dense/Porous-Structured Electrolytes for All-Solid-State Lithium-Metal Batteries. ACS Appl Mater Interfaces 14, 46001–46009 (2022).
    61. Liu, M. et al. Garnet Li7La3Zr2O12-Based Solid-State Lithium Batteries Achieved by In Situ Thermally Polymerized Gel Polymer Electrolyte. ACS Appl Mater Interfaces 14, 43116–43126 (2022).
    62. He, X. et al. Cu-Doped Alloy Layer Guiding Uniform Li Deposition on a Li-LLZO Interface under High Current Density. ACS Appl Mater Interfaces 13, 42212–42219 (2021).
    63. Sharafi, A. et al. Surface Chemistry Mechanism of Ultra-Low Interfacial Resistance in the Solid-State Electrolyte Li 7 La 3 Zr 2 O 12. Chemistry of Materials 29, 7961–7968 (2017).
    64. Xia, W. et al. Reaction mechanisms of lithium garnet pellets in ambient air: The effect of humidity and CO2. Journal of the American Ceramic Society 100, 2832–2839 (2017).
    65. Ye, R., Ihrig, M., Imanishi, N., Finsterbusch, M. & Figgemeier, E. A Review on Li + /H + Exchange in Garnet Solid Electrolytes: From Instability against Humidity to Sustainable Processing in Water. ChemSusChem 14, 4397–4407 (2021).
    66. Yow, Z. F., Oh, Y. L., Gu, W., Rao, R. P. & Adams, S. Effect of Li+/H+ exchange in water treated Ta-doped Li7La3Zr2O12. Solid State Ion 292, 122–129 (2016).
    67. Yang, H. & Wu, N. Ionic conductivity and ion transport mechanisms of solid-state lithium-ion battery electrolytes: A review. Energy Sci Eng 10, 1643–1671 (2022).
    68. Zhang, Y. et al. Synergistic regulation of garnet-type Ta-doped Li7La3Zr2O12 solid electrolyte by Li+ concentration and Li+ transport channel size. Electrochim Acta 296, 823–829 (2019).
    69. Rettenwander, D., Geiger, C. A. & Amthauer, G. Synthesis and crystal chemistry of the fast Li-ion conductor Li 7La3Zr2O12 doped with Fe. Inorg Chem 52, 8005–8009 (2013).
    70. Geiger, C. A. et al. Crystal chemistry and stability of ‘Li7La3Zr2O12’ garnet: a fast lithium-ion conductor. Inorg Chem 50, 1089–1097 (2011).
    71. Jin, Y. & McGinn, P. J. Al-doped Li7La3Zr2O12 synthesized by a polymerized complex method. J Power Sources 196, 8683–8687 (2011).
    72. Zhao, P. et al. Self-consolidation mechanism and its application in the preparation of Al-doped cubic Li7La3Zr2O12. Mater Des 139, 65–71 (2018).
    73. García Daza, F. A., Bonilla, M. R., Llordés, A., Carrasco, J. & Akhmatskaya, E. Structural and Electrochemical Consequences of Al and Ga Cosubstitution in Li 7 La 3 Zr 2 O 12 Solid Electrolytes. Chem. Mater 28, (2016).
    74. Wu, J.-F. et al. Gallium-Doped Li 7 La 3 Zr 2 O 12 Garnet-Type Electrolytes with High Lithium-Ion Conductivity. ACS Appl Mater Interfaces 9, 1542–1552 (2017).
    75. Wagner, R. et al. Crystal Structure of Garnet-Related Li-Ion Conductor Li7-3xGaxLa3Zr2O12: Fast Li-Ion Conduction Caused by a Different Cubic Modification? Chemistry of Materials 28, 1861–1871 (2016).
    76. Wagner, R. et al. Crystal Structure of Garnet-Related Li-Ion Conductor Li7-3xGaxLa3Zr2O12: Fast Li-Ion Conduction Caused by a Different Cubic Modification? Chemistry of Materials 28, 1861–1871 (2016).
    77. Wagner, R. et al. Fast Li-Ion-Conducting Garnet-Related Li 7–3 x Fe x La 3 Zr 2 O 12 with Uncommon I 4̅3 d Structure. Chemistry of Materials 28, 5943–5951 (2016).
    78. Rettenwander, D. et al. Interface Instability of Fe-Stabilized Li 7 La 3 Zr 2 O 12 versus Li Metal. The Journal of Physical Chemistry C 122, 3780–3785 (2018).
    79. Schrödinger, E. An Undulatory Theory of the Mechanics of Atoms and Molecules. Physical Review 28, 1049 (1926).
    80. Born, M. & Oppenheimer, R. Zur Quantentheorie der Molekeln. Ann Phys 389, 457–484 (1927).
    81. Slater, J. C. The Theory of Complex Spectra. Physical Review 34, 1293 (1929).
    82. Slater, J. C. A Simplification of the Hartree-Fock Method. Physical Review 81, 385 (1951).
    83. Artree, D. R. H. & Artree (, W. H. Self-consistent field, with exchange, for beryllium. Proc R Soc Lond A Math Phys Sci 150, 9–33 (1935).
    84. Brillouin, L. Les champs" self-consistents" de Hartree et de Fock. (No Title) (1934).
    85. Hohenberg, P. & Kohn, W. Inhomogeneous electron gas. Physical Review 136, B864 (1964).
    86. Kohn, W. & Sham, L. J. Self-consistent equations including exchange and correlation effects. Physical Review 140, A1133 (1965).
    87. Vosko, S. H., Wilk, L. & Nusair, M. Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis. Can J Phys 58, 1200–1211 (1980).
    88. Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys Rev Lett 77, 3865 (1996).
    89. Dudarev, S. L., Botton, G. A., Savrasov, S. Y., Humphreys, C. J. & Sutton, A. P. Electron-energy-loss spectra and the structural stability of nickel oxide: An LSDA+U study. Phys Rev B 57, 1505 (1998).
    90. Tuckerman, M. E. Statistical mechanics: theory and molecular simulation. (Oxford university press, 2023).
    91. Marx, D. & Hutter, J. Ab initio molecular dynamics: Basic theory and advanced methods. Ab Initio Molecular Dynamics: Basic Theory and Advanced Methods 978, 1–567 (2009).
    92. Verlet, L. Computer ‘Experiments’ on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules. Physical Review 159, 98 (1967).
    93. Swope, W. C., Andersen, H. C., Berens, P. H. & Wilson, K. R. A computer simulation method for the calculation of equilibrium constants for the formation of physical clusters of molecules: Application to small water clusters. J Chem Phys 76, 637–649 (1982).
    94. Hoover, W. G. Canonical dynamics: Equilibrium phase-space distributions. Phys Rev A (Coll Park) 31, 1695 (1985).
    95. Shuichi, N. Constant Temperature Molecular Dynamics Methods. Progress of Theoretical Physics Supplement 103, 1–46 (1991).
    96. Nosé, S. A unified formulation of the constant temperature molecular dynamics methods. J Chem Phys 81, 511–519 (1984).
    97. Dill, K. & Bromberg, S. Molecular driving forces: statistical thermodynamics in biology, chemistry, physics, and nanoscience. (Garland Science, 2010).
    98. Martin, R. M. Electronic structure: basic theory and practical methods. (Cambridge university press, 2020).
    99. Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys Rev B 59, 1758 (1999).
    100. Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys Rev B 59, 1758 (1999).
    101. Installing VASP.6.X.X - VASP Wiki. https://www.vasp.at/wiki/index.php/Installing_VASP.6.X.X.
    102. The VASP Manual - VASP Wiki. https://www.vasp.at/wiki/index.php/The_VASP_Manual.
    103. O’Callaghan, M. P. & Cussen, E. J. Lithium dimer formation in the Li-conducting garnets Li 5+xBaxLa3-xTa2O12 (0 < x ≤ 1.6). Chemical Communications 2048–2050 (2007).
    104. Xu, M. et al. Mechanisms of Li+ transport in garnet-type cubic Li3+xLa3M2O12 (M = Te, Nb, Zr). Phys Rev B 85, 052301 (2012).
    105. Thompson, T. et al. Electrochemical Window of the Li-Ion Solid Electrolyte Li7La3Zr2O12. ACS Energy Lett 2, 462–468 (2017).
    106. Tian, H. K., Liu, Z., Ji, Y., Chen, L. Q. & Qi, Y. Interfacial Electronic Properties Dictate Li Dendrite Growth in Solid Electrolytes. Chemistry of Materials 31, 7351–7359 (2019).
    107. Cococcioni, M. & De Gironcoli, S. Linear response approach to the calculation of the effective interaction parameters in the LDA+U method. Phys Rev B Condens Matter Mater Phys 71, 035105 (2005).
    108. Dederichs, P. H., Bl̈gel, S., Zeller, R. & Akai, H. Ground States of Constrained Systems: Application to Cerium Impurities. Phys Rev Lett 53, 2512 (1984).
    109. Anisimov, V. I. & Gunnarsson, O. Density-functional calculation of effective Coulomb interactions in metals. Phys Rev B 43, 7570 (1991).
    110. Linscott, E. B., Cole, D. J., Payne, M. C. & O’Regan, D. D. The role of spin in the calculation of Hubbard $U$ and Hund’s $J$ parameters from first principles. Phys Rev B 98, (2018).
    111. Klimeš, J., Bowler, D. R. & Michaelides, A. Chemical accuracy for the van der Waals density functional. Journal of Physics: Condensed Matter 22, 022201 (2009).
    112. Wang, V., Xu, N., Liu, J. C., Tang, G. & Geng, W. T. VASPKIT: A user-friendly interface facilitating high-throughput computing and analysis using VASP code. Comput Phys Commun 267, (2021).
    113. He, X., Zhu, Y., Epstein, A. & Mo, Y. Statistical variances of diffusional properties from ab initio molecular dynamics simulations. npj Computational Materials 2018 4:1 4, 1–9 (2018).
    114. Tian, H. K. et al. Electron and Ion Transfer across Interfaces of the NASICON-Type LATP Solid Electrolyte with Electrodes in All-Solid-State Batteries: A Density Functional Theory Study via an Explicit Interface Model. ACS Appl Mater Interfaces 12, 54752–54762 (2020).
    115. Haruyama, J., Sodeyama, K., Han, L., Takada, K. & Tateyama, Y. Space-charge layer effect at interface between oxide cathode and sulfide electrolyte in all-solid-state lithium-ion battery. Chemistry of Materials 26, 4248–4255 (2014).
    116. Bader, R. F. W. & Bader, R. F. Atoms in Molecules: A Quantum Theory. (Clarendon Press, 1990).
    117. Bader, R. F. W. Atoms in Molecules. Acc Chem Res 18, 9–15 (1985).
    118. Henkelman, G., Arnaldsson, A. & Jónsson, H. A fast and robust algorithm for Bader decomposition of charge density. Comput Mater Sci 36, 354–360 (2006).
    119. Sanville, E., Kenny, S. D., Smith, R. & Henkelman, G. Improved grid-based algorithm for Bader charge allocation. J Comput Chem 28, 899–908 (2007).
    120. Du, Q. et al. A grid-based Bader analysis algorithm without lattice bias. Journal of Physics: Condensed Matter 21, 084204 (2009).
    121. Djenadic, R. et al. Nebulized spray pyrolysis of Al-doped Li7La3Zr 2O12 solid electrolyte for battery applications. Solid State Ion 263, 49–56 (2014).
    122. Santosh, K. C., Longo, R. C., Xiong, K. & Cho, K. Point defects in garnet-type solid electrolyte (c-Li7La3Zr2O12) for Li-ion batteries. Solid State Ion 261, 100–105 (2014).
    123. Xu, M. et al. Mechanisms of Li + transport in garnet-type cubic Li 3+xLa 3M 2O 12 (M = Te, Nb, Zr). Phys Rev B Condens Matter Mater Phys 85, 052301 (2012).
    124. Wang, D. et al. Toward Understanding the Lithium Transport Mechanism in Garnet-type Solid Electrolytes: Li+ Ion Exchanges and Their Mobility at Octahedral/Tetrahedral Sites. Chemistry of Materials 27, 6650–6659 (2015).
    125. Chen, F., Xu, L., Li, J., Yang, Y. & Shen, Q. Effect of bottleneck size on lithium migration in lithium garnets Li7La3Zr2O12 (LLZO). Ionics (Kiel) 26, 3193–3198 (2020).

    下載圖示
    2026-01-23公開
    QR CODE