由於鈦酸鋰材料在鋰離子嵌入及脫嵌時所產生的體積變化極小，因此此種「零應變」材料以及石墨炭是目前最為受到廣泛應用的兩種鋰離子電池負極材料。然而在過往的研究中，大多針對鋰離子在其中的擴散行為進行探討，鮮少有關於充放電時所共存的兩種相：??4??5?12以及??7??5?12，所發生的相分離現象之相關研究。再加上兩種相的導電性因為鈦離子的混和價態而產生的巨大差異，令了解兩相間的相邊界之移動行為成為相當重要的課題。由於相邊界之尺度介於奈米(nm)至微米(μm)之間，因此可藉由傳統的經驗勢能來描述原子間作用力的分子動力學模擬便是一項用於觀察此現象的利器。
由於在兩種相間的轉變所伴隨的鈦離子價數變化，我們在既有的固定電荷分子動力學模擬基礎上額外使用了局部電荷平衡法(Qeq)。透過將文獻上所提供的參數進行調整，包括以結構穩定性以及彈性常數為目標值對離子電負度進行修正，成功得到了能精確描述兩種純相的一組Qeq參數。將此組參數應用於兩相分離之模擬，能得到接近預設值之兩相比例，並且從團簇分析也可以觀察到同相間之聚集，不過無法觀察到明顯的相分離現象。兩相間之附著能透過經驗勢能及第一原理計算所得之值皆為正值，顯現此組Qeq參數具有相當之參考性。透過第一原理過渡態計算得到了在充放電時鋰離子擴散所需克服之活化能能障，但在分子動力學模擬中之兩相介面無法穩定存在，經過驗證發現界面處之電荷不均勻分布為界面處結構改變之原因。

Due to the minimal volume change that occurs during lithium-ion intercalation and de-intercalation, lithium titanate (LTO) and graphite are currently the two most widely used anode materials for lithium-ion batteries. However, previous research has primarily focused on the diffusion behavior of lithium ions within these materials, with very few studies investigating the phase separation phenomenon between the two coexisting phases-????????? and ?????????-during charging and discharging. Furthermore, the significant difference in electrical conductivity between these two phases, attributed to the mixed valence states of titanium ions, makes understanding the movement of the phase boundaries a crucial challenge. We augmented the existing fixed-charge molecular dynamics simulations with the charge equilibration (Qeq) method. By adjusting parameters provided in the literature, we successfully obtained a set of Qeq parameters that accurately describe both pure phases. Applying this set of parameters to two-phase separation simulations resulted in a two-phase ratio close to the preset value, and cluster analysis also showed aggregation within the same phase; however, no obvious phase separation phenomenon was observed. The adhesion energies between the two phases, calculated using both empirical potentials and first-principles methods, were positive, demonstrating the significant referential value of this set of Qeq parameters. First-principles NEB calculations yielded the activation energy barrier that lithium ions must overcome for diffusion during charging and discharging. However, the two-phase interface in the molecular dynamics simulations could not be stably maintained. Upon verification, it was found that the uneven charge distribution at the interface was the cause of the structural changes at the interface.

[1] B. L. Ellis, K. T. Lee, and L. F. Nazar, "Positive electrode materials for Li-ion and Li-batteries," Chemistry of materials, vol. 22, no. 3, pp. 691-714, 2010.
[2] V. Aravindan, Y. S. Lee, and S. Madhavi, "Research progress on negative electrodes for practical Li‐ion batteries: beyond carbonaceous anodes," Advanced Energy Materials, vol. 5, no. 13, p. 1402225, 2015.
[3] 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.
[4] J. R. Dahn, "Phase diagram of ????6," Physical Review B, vol. 44, no. 17, pp. 9170-9177, 11/01/ 1991, doi: 10.1103/PhysRevB.44.9170.
[5] M. Obrovac and L. Christensen, "Structural changes in silicon anodes during lithium insertion/extraction," Electrochemical and solid-state letters, vol. 7, no. 5, p. A93, 2004.
[6] M. Obrovac and L. Krause, "Reversible cycling of crystalline silicon powder," Journal of The Electrochemical Society, vol. 154, no. 2, p. A103, 2006.
[7] T. Ohzuku, A. Ueda, and N. Yamamoto, "Zero‐strain insertion material of Li [Li1/3Ti5/3] O 4 for rechargeable lithium cells," Journal of the Electrochemical Society, vol. 142, no. 5, p. 1431, 1995.
[8] P.-c. Tsai et al., "Ab initio phase stability and electronic conductivity of the doped-Li4Ti5O12 anode for Li-ion batteries," Acta Materialia, vol. 175, pp. 196-205, 2019.
[9] 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.
[10] 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.
[11] M. Vijayakumar et al., "Lithium diffusion in Li4Ti5O12 at high temperatures," Journal of Power Sources, vol. 196, no. 4, pp. 2211-2220, 2011.
[12] M. Kitta, T. Akita, S. Tanaka, and M. Kohyama, "Two-phase separation in a lithiated spinel Li4Ti5O12 crystal as confirmed by electron energy-loss spectroscopy," Journal of Power Sources, vol. 257, pp. 120-125, 2014.
[13] 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.
[14] M. Ding, H. Liu, X. Zhao, L. Pang, L. Deng, and M. Li, "Composite with TiO 2 and extension of discharge voltage range for capacity enhancement of a Li 4 Ti 5 O 12 battery," RSC Advances, vol. 7, no. 69, pp. 43894-43904, 2017.
[15] C. Han et al., "Large polarization of Li4Ti5O12 lithiated to 0 V at large charge/discharge rates," ACS Applied Materials & Interfaces, vol. 8, no. 29, pp. 18788-18796, 2016.
[16] M. Wagemaker et al., "A kinetic two‐phase and equilibrium solid solution in spinel Li4+ xTi5O12," Advanced Materials, vol. 18, no. 23, pp. 3169-3173, 2006.
[17] D. Young, A. Ransil, R. Amin, Z. Li, and Y. M. Chiang, "Electronic conductivity in the Li4/3Ti5/3O4–Li7/3Ti5/3O4 system and variation with state‐of‐charge as a Li battery anode," Advanced energy materials, vol. 3, no. 9, pp. 1125-1129, 2013.
[18] D. Wolf, P. Keblinski, S. Phillpot, and J. Eggebrecht, "Exact method for the simulation of Coulombic systems by spherically truncated, pairwise r− 1 summation," The Journal of chemical physics, vol. 110, no. 17, pp. 8254-8282, 1999.
[19] D. Adams, "On the use of the Ewald summation in computer simulation," The Journal of Chemical Physics, vol. 78, no. 5, pp. 2585-2590, 1983.
[20] S. I. NOSÉ, "A molecular dynamics method for simulations in the canonical ensemble," Molecular physics, vol. 100, no. 1, pp. 191-198, 2002.
[21] S. Nosé, "A unified formulation of the constant temperature molecular dynamics methods," The Journal of chemical physics, vol. 81, no. 1, pp. 511-519, 1984.
[22] W. G. Hoover, "Canonical dynamics: Equilibrium phase-space distributions," Physical review A, vol. 31, no. 3, p. 1695, 1985.
[23] A. K. Rappe and W. A. Goddard III, "Charge equilibration for molecular dynamics simulations," The Journal of Physical Chemistry, vol. 95, no. 8, pp. 3358-3363, 1991.
[24] W. Kohn, "Nobel Lecture: Electronic structure of matter—wave functions and density functionals," Reviews of modern physics, vol. 71, no. 5, p. 1253, 1999.
[25] 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.
[26] P. Hohenberg and W. Kohn, "Inhomogeneous electron gas," Physical review, vol. 136, no. 3B, p. B864, 1964.
[27] W. Kohn and L. J. Sham, "Self-consistent equations including exchange and correlation effects," Physical review, vol. 140, no. 4A, p. A1133, 1965.
[28] A. D. Becke, "Density-functional exchange-energy approximation with correct asymptotic behavior," Physical review A, vol. 38, no. 6, p. 3098, 1988.
[29] D. M. Ceperley and B. J. Alder, "Ground state of the electron gas by a stochastic method," Physical review letters, vol. 45, no. 7, p. 566, 1980.
[30] S. L. Dudarev, G. A. Botton, S. Y. Savrasov, C. Humphreys, and A. P. Sutton, "Electron-energy-loss spectra and the structural stability of nickel oxide: An LSDA+ U study," Physical Review B, vol. 57, no. 3, p. 1505, 1998.
[31] I.-H. Lee and R. M. Martin, "Applications of the generalized-gradient approximation to atoms, clusters, and solids," Physical Review B, vol. 56, no. 12, p. 7197, 1997.
[32] J. P. Perdew et al., "Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation," Physical review B, vol. 46, no. 11, p. 6671, 1992.
[33] G. Kresse and D. Joubert, "From ultrasoft pseudopotentials to the projector augmented-wave method," Physical review b, vol. 59, no. 3, p. 1758, 1999.
[34] Y. Liu, J. Lian, Z. Sun, M. Zhao, Y. Shi, and H. Song, "The first-principles study for the novel optical properties of LiTi2O4, Li4Ti5O12, Li2Ti2O4 and Li7Ti5O12," Chemical Physics Letters, vol. 677, pp. 114-119, 2017.
[35] F. Richard and R. Bader, "Atoms in molecules: a quantum theory," ed: Oxford University Press, Oxford, 1990.
[36] G. Henkelman, A. Arnaldsson, and H. Jónsson, "A fast and robust algorithm for Bader decomposition of charge density," Computational Materials Science, vol. 36, no. 3, pp. 354-360, 2006.
[37] G. Henkelman, B. P. Uberuaga, and H. Jónsson, "A climbing image nudged elastic band method for finding saddle points and minimum energy paths," The Journal of chemical physics, vol. 113, no. 22, pp. 9901-9904, 2000.
[38] G. Henkelman and H. Jónsson, "Improved tangent estimate in the nudged elastic band method for finding minimum energy paths and saddle points," The Journal of chemical physics, vol. 113, no. 22, pp. 9978-9985, 2000.
[39] A. P. Thompson et al., "LAMMPS-a flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales," Computer physics communications, vol. 271, p. 108171, 2022.
[40] Y. K. Shin et al., "Development of a ReaxFF reactive force field for lithium ion conducting solid electrolyte Li 1+ x Al x Ti 2− x (PO 4) 3 (LATP)," Physical Chemistry Chemical Physics, vol. 20, no. 34, pp. 22134-22147, 2018.
[41] S.-y. Kim, "Development Of A Reaxff Reactive Force Field For Titanium Dioxide/Water Systems And Its Applications To Etching, Nanoparticles With Organic Solvents And Ion Adsorptions On Nanocrystalline Surfaces," 2013.
[42] B. Narayanan, A. C. Van Duin, B. B. Kappes, I. E. Reimanis, and C. V. Ciobanu, "A reactive force field for lithium–aluminum silicates with applications to eucryptite phases," Modelling and Simulation in Materials Science and Engineering, vol. 20, no. 1, p. 015002, 2011.
[43] S.-Y. Kim, A. C. Van Duin, and J. D. Kubicki, "Molecular dynamics simulations of the interactions between TiO 2 nanoparticles and water with Na+ and Cl−, methanol, and formic acid using a reactive force field," Journal of Materials Research, vol. 28, pp. 513-520, 2013.
[44] W. Zhang et al., "Kinetic pathways of ionic transport in fast-charging lithium titanate," Science, vol. 367, no. 6481, pp. 1030-1034, 2020.