隨著科技日新月異的發展，人們對於能源的需求日益增加，但同時石油短缺與二氧化碳排放等問題也逐漸浮現，成為全人類共同關注之議題。現今，除了發展太陽能、風力與地熱等可再生能源，電池儲能技術的發展也開始被重視，其中鋰離子電池具有能量密度高、重量輕、高電容與低環境污染等優點，為目前最符合綠色科技的儲能元件之一，同時為最具有發展潛力的電池系統之一。
在鋰離子電池中，電極材料的性質尤為重要，在考慮更高能量密度與更高電容的電極材料時，同時須考慮到安全性與循環壽命，其中鋰鈦氧負極材料於充放電反應時幾乎不會有體積變化，因此有著極佳的安全性，近年來，諸多學者致立於提升鋰鈦氧負極材料之性能，但並沒有針對表面有系統性的分析。
本研究透過密度泛函理論(Density functional theory)與第一原理計算(Ab initio calculation)材料計算，對鋰鈦氧負極材料的表面進行模擬，探討不同鋰原子含量之表面原子排列情形，以了解表面對16d位置鋰原子分佈之影響，並根據計算結果建構出最穩定的鋰鈦氧原子級表面模型。

The defect spinel Li4Ti5O12(LTO) is a promising anode material due to its negligible volume change, excellent cycling stability and safety. However, there are still many disadvantages such us poor electronic conductivity need to be improved. The research about atomistic structure of LTOs have been well-established but the systematic studies of LTO surface are required. In this work, ab initio calculations based on density functional theory (DFT) were performed to investigate the surface stability of LTO. A full supercell model of Li32Ti40O96 with exact stoichiometry is used to construct the surface model for the calculation. According to the calculated results, the most stable surface structure can be obtained. This model provides an in-depth understanding of LTO surface structure and can be a starting point for future studies to improve the properties of LTO.

[1] B. BP, "Energy outlook 2020 edition," ed: BP London, 2020.
[2] H. Mountford et al., "COP26: Key Outcomes From the UN Climate Talks in Glasgow," 2021.
[3] M. M. Rahman, A. O. Oni, E. Gemechu, and A. Kumar, "Assessment of energy storage technologies: A review," Energy Conversion and Management, vol. 223, p. 113295, 2020.
[4] M. Morris and S. Tosunoglu, "Comparison of rechargeable battery technologies," in ASME Early Career Technical Conference, Atlanta, Georgia, 2012, pp. 2-12.
[5] H. Budde-Meiwes et al., "A review of current automotive battery technology and future prospects," Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, vol. 227, no. 5, pp. 761-776, 2013.
[6] Y. Liang et al., "A review of rechargeable batteries for portable electronic devices," InfoMat, vol. 1, no. 1, pp. 6-32, 2019.
[7] F. Schipper and D. Aurbach, "A brief review: Past, present and future of lithium ion batteries," Russian Journal of Electrochemistry, vol. 52, no. 12, pp. 1095-1121, 2016.
[8] C. Liang, M. Gao, H. Pan, Y. Liu, and M. Yan, "Lithium alloys and metal oxides as high-capacity anode materials for lithium-ion batteries," Journal of alloys and compounds, vol. 575, pp. 246-256, 2013.
[9] W. A. v. S. B. Scrosati, Advances in lithium-ion batteries. Springer Science & Business Media, 2002.
[10] M. Yoshio, R. J. Brodd, and A. Kozawa, Lithium-ion batteries. Springer, 2009.
[11] X. Shen, H. Liu, X.-B. Cheng, C. Yan, and J.-Q. Huang, "Beyond lithium ion batteries: Higher energy density battery systems based on lithium metal anodes," Energy Storage Materials, vol. 12, pp. 161-175, 2018.
[12] S. Passerini and B. Scrosati, "Lithium and lithium-ion batteries: challenges and prospects," The Electrochemical Society Interface, vol. 25, no. 3, p. 85, 2016.
[13] M. Osiak, H. Geaney, E. Armstrong, and C. O'Dwyer, "Structuring materials for lithium-ion batteries: advancements in nanomaterial structure, composition, and defined assembly on cell performance," Journal of Materials Chemistry A, vol. 2, no. 25, pp. 9433-9460, 2014.
[14] N. Nitta, F. Wu, J. T. Lee, and G. Yushin, "Li-ion battery materials: present and future," Materials today, vol. 18, no. 5, pp. 252-264, 2015.
[15] A. Manthiram, "A reflection on lithium-ion battery cathode chemistry," Nature communications, vol. 11, no. 1, pp. 1-9, 2020.
[16] Y. Mekonnen, A. Sundararajan, and A. I. Sarwat, "A review of cathode and anode materials for lithium-ion batteries," in SoutheastCon 2016, 2016: IEEE, pp. 1-6.
[17] A. Manthiram, "An outlook on lithium ion battery technology," ACS central science, vol. 3, no. 10, pp. 1063-1069, 2017.
[18] Y. S. Meng and M. E. Arroyo-de Dompablo, "First principles computational materials design for energy storage materials in lithium ion batteries," Energy & Environmental Science, vol. 2, no. 6, pp. 589-609, 2009.
[19] J. Kalhoff, G. G. Eshetu, D. Bresser, and S. Passerini, "Safer electrolytes for lithium‐ion batteries: state of the art and perspectives," ChemSusChem, vol. 8, no. 13, pp. 2154-2175, 2015.
[20] J. Hassoun and B. Scrosati, "Advances in anode and electrolyte materials for the progress of lithium-ion and beyond lithium-ion batteries," Journal of The Electrochemical Society, vol. 162, no. 14, p. A2582, 2015.
[21] C. F. Francis, I. L. Kyratzis, and A. S. Best, "Lithium‐ion battery separators for ionic‐liquid electrolytes: a review," Advanced Materials, vol. 32, no. 18, p. 1904205, 2020.
[22] S. S. Zhang, "A review on the separators of liquid electrolyte Li-ion batteries," Journal of power sources, vol. 164, no. 1, pp. 351-364, 2007.
[23] J.-G. Zhang, W. Xu, and W. A. Henderson, Lithium metal anodes and rechargeable lithium metal batteries. Springer International Publishing Cham, 2017.
[24] X. Shen et al., "Advanced electrode materials in lithium batteries: Retrospect and prospect," Energy Material Advances, vol. 2021, 2021.
[25] J. Lu, Z. Chen, F. Pan, Y. Cui, and K. Amine, "High-performance anode materials for rechargeable lithium-ion batteries," Electrochemical Energy Reviews, vol. 1, no. 1, pp. 35-53, 2018.
[26] J. Park, Z.-L. Xu, and K. Kang, "Solvated ion intercalation in graphite: sodium and beyond," Frontiers in Chemistry, p. 432, 2020.
[27] H. Zhang, Y. Yang, D. Ren, L. Wang, and X. He, "Graphite as anode materials: Fundamental mechanism, recent progress and advances," Energy Storage Materials, vol. 36, pp. 147-170, 2021.
[28] W. Qi, J. G. Shapter, Q. Wu, T. Yin, G. Gao, and D. Cui, "Nanostructured anode materials for lithium-ion batteries: principle, recent progress and future perspectives," Journal of Materials Chemistry A, vol. 5, no. 37, pp. 19521-19540, 2017.
[29] J. Asenbauer, T. Eisenmann, M. Kuenzel, A. Kazzazi, Z. Chen, and D. Bresser, "The success story of graphite as a lithium-ion anode material–fundamentals, remaining challenges, and recent developments including silicon (oxide) composites," Sustainable Energy & Fuels, vol. 4, no. 11, pp. 5387-5416, 2020.
[30] V. Petkov, A. Timmons, J. Camardese, and Y. Ren, "Li insertion in ball-milled graphitic carbon studied by total x-ray diffraction," Journal of Physics: Condensed Matter, vol. 23, no. 43, p. 435003, 2011.
[31] H. Kim, G. Jeong, Y.-U. Kim, J.-H. Kim, C.-M. Park, and H.-J. Sohn, "Metallic anodes for next generation secondary batteries," Chemical Society Reviews, vol. 42, no. 23, pp. 9011-9034, 2013.
[32] P.-E. Lippens, M. Womes, P. Kubiak, J.-C. Jumas, and J. Olivier-Fourcade, "Electronic structure of the spinel Li4Ti5O12 studied by ab initio calculations and X-ray absorption spectroscopy," Solid state sciences, vol. 6, no. 2, pp. 161-166, 2004.
[33] C. Ouyang, Z. Zhong, and M. Lei, "Ab initio studies of structural and electronic properties of Li4Ti5O12 spinel," Electrochemistry Communications, vol. 9, no. 5, pp. 1107-1112, 2007.
[34] H. S. Majdi et al., "Nano and Battery Anode: A Review," Nanoscale Research Letters, vol. 16, no. 1, pp. 1-26, 2021.
[35] N. Takami, K. Hoshina, and H. Inagaki, "Lithium diffusion in Li4/3Ti5/3O4 particles during insertion and extraction," Journal of the Electrochemical Society, vol. 158, no. 6, p. A725, 2011.
[36] T. Yuan, Z. Tan, C. Ma, J. Yang, Z. F. Ma, and S. Zheng, "Challenges of spinel Li4Ti5O12 for lithium‐ion battery industrial applications," Advanced energy materials, vol. 7, no. 12, p. 1601625, 2017.
[37] Y. Tan and B. Xue, "Research progress on lithium titanate as anode material in lithium-ion battery," JOURNAL OF INORGANIC MATERIALS-BEIJING-, vol. 33, no. 5, pp. 475-482, 2018.
[38] P.-c. Tsai, W.-D. Hsu, and S.-k. Lin, "Atomistic structure and ab initio electrochemical properties of Li4Ti5O12 defect spinel for Li ion batteries," Journal of The Electrochemical Society, vol. 161, no. 3, p. A439, 2014.
[39] B. Zhao, R. Ran, M. Liu, and Z. Shao, "A comprehensive review of Li4Ti5O12-based electrodes for lithium-ion batteries: The latest advancements and future perspectives," Materials Science and Engineering: R: Reports, vol. 98, pp. 1-71, 2015.
[40] S. Goriparti, E. Miele, F. De Angelis, E. Di Fabrizio, R. P. Zaccaria, and C. Capiglia, "Review on recent progress of nanostructured anode materials for Li-ion batteries," Journal of power sources, vol. 257, pp. 421-443, 2014.
[41] A. Franco Gonzalez, N.-H. Yang, and R.-S. Liu, "Silicon anode design for lithium-ion batteries: Progress and perspectives," The Journal of Physical Chemistry C, vol. 121, no. 50, pp. 27775-27787, 2017.
[42] X. Zuo, J. Zhu, P. Müller-Buschbaum, and Y.-J. Cheng, "Silicon based lithium-ion battery anodes: A chronicle perspective review," Nano Energy, vol. 31, pp. 113-143, 2017.
[43] X. Chen, H. Li, Z. Yan, F. Cheng, and J. Chen, "Structure design and mechanism analysis of silicon anode for lithium-ion batteries," Science China Materials, vol. 62, no. 11, pp. 1515-1536, 2019.
[44] S. Scharner, W. Weppner, and P. Schmid‐Beurmann, "Evidence of Two‐Phase Formation upon Lithium Insertion into the Li1. 33Ti1. 67 O 4 Spinel," Journal of the Electrochemical Society, vol. 146, no. 3, p. 857, 1999.
[45] 藍三, "高性能鋰離子電池負極材料鈦酸鋰 (LTO) 之表面性質研究," 2020.
[46] K. Kataoka, Y. Takahashi, N. Kijima, H. Hayakawa, J. Akimoto, and K.-i. Ohshima, "A single-crystal study of the electrochemically Li-ion intercalated spinel-type Li4Ti5O12," Solid State Ionics, vol. 180, no. 6-8, pp. 631-635, 2009.
[47] K. Kataoka, Y. Takahashi, N. Kijima, J. Akimoto, and K.-i. Ohshima, "Single crystal growth and structure refinement of Li4Ti5O12," Journal of Physics and Chemistry of Solids, vol. 69, no. 5-6, pp. 1454-1456, 2008.
[48] D. Liu, C. Ouyang, J. Shu, J. Jiang, Z. Wang, and L. Chen, "Theoretical study of cation doping effect on the electronic conductivity of Li4Ti5O12," physica status solidi (b), vol. 243, no. 8, pp. 1835-1841, 2006.
[49] B. Ziebarth, M. Klinsmann, T. Eckl, and C. Elsässer, "Lithium diffusion in the spinel phase Li 4 Ti 5 O 12 and in the rocksalt phase Li 7 Ti 5 O 12 of lithium titanate from first principles," Physical Review B, vol. 89, no. 17, p. 174301, 2014.
[50] T.-F. Yi, Y. Xie, Y.-R. Zhu, R.-S. Zhu, and H. Shen, "Structural and thermodynamic stability of Li4Ti5O12 anode material for lithium-ion battery," Journal of Power Sources, vol. 222, pp. 448-454, 2013.
[51] Q. Zhang, M. G. Verde, J. K. Seo, X. Li, and Y. S. Meng, "Structural and electrochemical properties of Gd-doped Li4Ti5O12 as anode material with improved rate capability for lithium-ion batteries," Journal of Power Sources, vol. 280, pp. 355-362, 2015.
[52] S. Tanaka, M. Kitta, T. Tamura, T. Akita, Y. Maeda, and M. Kohyama, "First-principles calculations of OK ELNES/XANES of lithium titanate," Journal of Physics D: Applied Physics, vol. 45, no. 49, p. 494004, 2012.
[53] Z. Zhi-Yong, N. Zheng-Xin, D. Yan-Lan, O. Chu-Ying, S. Si-Qi, and L. Min-Sheng, "Ab initio studies on n-type and p-type Li4Ti5O12," Chinese Physics B, vol. 18, no. 6, p. 2492, 2009.
[54] V. r. Weber et al., "Computational study of lithium titanate as a possible cathode material for solid-state lithium–sulfur batteries," The Journal of Physical Chemistry C, vol. 119, no. 18, pp. 9681-9691, 2015.
[55] S. Zahn, J. Janek, and D. Mollenhauer, "A simple ansatz to predict the structure of Li4Ti5O12," Journal of The Electrochemical Society, vol. 164, no. 2, p. A221, 2016.
[56] S. Ganapathy, A. Vasileiadis, J. R. Heringa, and M. Wagemaker, "The Fine Line between a Two‐Phase and Solid‐Solution Phase Transformation and Highly Mobile Phase Interfaces in Spinel Li4+ xTi5O12," Advanced energy materials, vol. 7, no. 9, p. 1601781, 2017.
[57] P. Tasker, "The stability of ionic crystal surfaces," Journal of Physics C: Solid State Physics, vol. 12, no. 22, p. 4977, 1979.
[58] S. Parker, P. Oliver, N. De Leeuw, J. Titiloye, and G. Watson, "Atomistic simulation of mineral surfaces: studies of surface stability and growth," Phase Transitions, vol. 61, no. 1-4, pp. 83-107, 1997.
[59] C. AJ Fisher, M. Saiful Islam, and H. Moriwake, "Atomic level investigations of lithium ion battery cathode materials," Journal of the Physical Society of Japan, vol. 79, no. Suppl. A, pp. 59-64, 2010.
[60] Y. Shin and K. A. Persson, "Surface morphology and surface stability against oxygen loss of the lithium-excess Li2MnO3 cathode material as a function of lithium concentration," ACS applied materials & interfaces, vol. 8, no. 38, pp. 25595-25602, 2016.
[61] M. Kitta, T. Akita, Y. Maeda, and M. Kohyama, "Preparation of a spinel Li4Ti5O12 (1 1 1) surface from a rutile TiO2 single crystal," Applied surface science, vol. 258, no. 7, pp. 3147-3151, 2012.
[62] M. Kitta et al., "Atomistic structure of a spinel Li4Ti5O12 (111) surface elucidated by scanning tunneling microscopy and medium energy ion scattering spectrometry," Surface science, vol. 619, pp. 5-9, 2014.
[63] T. Minato and T. Abe, "Surface and interface sciences of Li-ion batteries:-research progress in electrode–electrolyte interface," Progress in Surface Science, vol. 92, no. 4, pp. 240-280, 2017.
[64] X. Lu et al., "New insight into the atomic-scale bulk and surface structure evolution of Li4Ti5O12 anode," Journal of the American Chemical Society, vol. 137, no. 4, pp. 1581-1586, 2015.
[65] Y. Gao, Z. Wang, and L. Chen, "Stability of spinel Li4Ti5O12 in air," Journal of Power Sources, vol. 245, pp. 684-690, 2014.
[66] M. Wagemaker, W. Borghols, U. Lafont, E. Kelder, and F. Mulder, "Size Effects in Li4+ xTi5O12 Spinel," in ECS Meeting Abstracts, 2009, no. 7: IOP Publishing, p. 405.
[67] S. Ganapathy and M. Wagemaker, "Nanosize storage properties in spinel Li4Ti5O12 explained by anisotropic surface lithium insertion," ACS nano, vol. 6, no. 10, pp. 8702-8712, 2012.
[68] F. Wang, L. Wu, C. Ma, D. Su, Y. Zhu, and J. Graetz, "Excess lithium storage and charge compensation in nanoscale Li4+ xTi5O12," Nanotechnology, vol. 24, no. 42, p. 424006, 2013.
[69] B. J. Morgan, J. Carrasco, and G. Teobaldi, "Variation in surface energy and reduction drive of a metal oxide lithium-ion anode with stoichiometry: a DFT study of lithium titanate spinel surfaces," Journal of Materials Chemistry A, vol. 4, no. 43, pp. 17180-17192, 2016.
[70] X. Lu et al., "Lithium storage in Li4Ti5O12 spinel: the full static picture from electron microscopy," Advanced Materials, vol. 24, no. 24, pp. 3233-3238, 2012.
[71] Y.-B. He et al., "Gassing in Li4Ti5O12-based batteries and its remedy," Scientific reports, vol. 2, no. 1, pp. 1-9, 2012.
[72] R. Wen, J. Yue, Z. Ma, W. Chen, X. Jiang, and A. Yu, "Synthesis of Li4Ti5O12 nanostructural anode materials with high charge–discharge capability," Chinese Science Bulletin, vol. 59, no. 18, pp. 2162-2174, 2014.
[73] D. Sholl and J. A. Steckel, Density functional theory: a practical introduction. John Wiley & Sons, 2011.
[74] G. Kresse and J. Furthmüller, "Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set," Computational materials science, vol. 6, no. 1, pp. 15-50, 1996.
[75] G. Kresse and J. Furthmüller, "Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set," Physical review B, vol. 54, no. 16, p. 11169, 1996.
[76] K. Momma and F. Izumi, "VESTA: a three-dimensional visualization system for electronic and structural analysis," Journal of Applied crystallography, vol. 41, no. 3, pp. 653-658, 2008.
[77] E. Schrödinger, "An undulatory theory of the mechanics of atoms and molecules," Physical review, vol. 28, no. 6, p. 1049, 1926.
[78] P. Hohenberg and W. Kohn, "Inhomogeneous electron gas," Physical review, vol. 136, no. 3B, p. B864, 1964.
[79] W. Kohn and L. J. Sham, "Self-consistent equations including exchange and correlation effects," Physical review, vol. 140, no. 4A, p. A1133, 1965.
[80] J. P. Perdew and W. Yue, "Accurate and simple density functional for the electronic exchange energy: Generalized gradient approximation," Physical review B, vol. 33, no. 12, p. 8800, 1986.
[81] M. Fuchs, "Exchange-correlation energy: From LDA to GGA and beyond," ed: Faradayweg.
[82] K. Schwarz, "Computation of materials properties at the atomic scale," Selected Topics in Application of Quantum Mechanics, p. 275, 2015.
[83] P. Schwerdtfeger, "The pseudopotential approximation in electronic structure theory," ChemPhysChem, vol. 12, no. 17, pp. 3143-3155, 2011.
[84] P. E. Blöchl, "Projector augmented-wave method," Physical review B, vol. 50, no. 24, p. 17953, 1994.
[85] G. Kresse and D. Joubert, "From ultrasoft pseudopotentials to the projector augmented-wave method," Physical review b, vol. 59, no. 3, p. 1758, 1999.
[86] E. G. Leggesse, K.-H. Tsau, Y.-T. Liu, S. Nachimuthu, and J.-C. Jiang, "Adsorption and Decomposition of Ethylene Carbonate on LiMn2O4 Cathode Surface," Electrochimica Acta, vol. 210, pp. 61-70, 2016.
[87] V. Weber et al., "Computational study of lithium titanate as a possible cathode material for solid-state lithium–sulfur batteries," The Journal of Physical Chemistry C, vol. 119, no. 18, pp. 9681-9691, 2015.
[88] S. Tanaka, M. Kitta, T. Tamura, Y. Maeda, T. Akita, and M. Kohyama, "Atomic and electronic structures of Li4Ti5O12/Li7Ti5O12 (001) interfaces by first-principles calculations," Journal of Materials Science, vol. 49, no. 11, pp. 4032-4037, 2014.
[89] S. Fu et al., "Ultrathin [110]‐Confined Li4Ti5O12 Nanoflakes for High Rate Lithium Storage," Advanced Energy Materials, vol. 11, no. 22, p. 2003270, 2021.