本研究使用第一原理分子動力學模擬材料性質與有限體積法研究電池模組性能，將現今已作為商業使用之鋰三元電池與各式內部新型材料做模擬以確定模式正確性，其目的在做可預見將來全固態鋰離子電池性能預測與分析，超前佈署其最佳化材料選配與模組設計。
固態電池方面，本研究首先使用α-MoO3作為陰極，Li6PS5Cl作為固態電解質，為基線研究材料，首先建立材料的分子結構，以第一原理模擬電子動態進行結構最佳化，從中獲得結構中鋰離子移動狀況，並依位移獲得其擴散係數。而後使用微擾理論計算聲子頻譜，評估原子晶格振盪之聲子頻率(能量變化)對應倒晶格波向量，由態密度積分得到材料的熱力性質(熱傳導係數、比熱容量等)，將原本難以用實驗取得的奈米材料參數，以第一原理量態分子動力學模擬計算方式求出。其後以有限體積法計算巨觀狀態下之熱傳與離子傳播，加上電化學理論，建立一系列電池模組模擬系統，故本研究可從基礎材料計算獲得關鍵物理性質，輸入電池模組設計進行全電池電化學性能模擬。經由改變充電與放電操作狀態與材料參數，並觀察比對模擬結果，進而最佳化鋰離子電池材料與模組設計。
α-MoO3作為陰極材料與使用固態電解質Li6PS5Cl皆會有比較高的鋰離子擴散係數(D)、比熱容量(Cv)與熱傳導率(k)，在實際充放電操作狀況下，電池的溫升降低、鋰離子在電池內擴散的速率提高，因此更適合做為將來極高充放電速率(10C以上)之超級電池內部材料，較不易發生熱崩潰與鋰長枝現象，其中陰極材料α-MoO3更有高達882.91 (mAh/g)的高比電容(為目前鋰三元電池五倍性能)，可有效增加新型鋰電池的容量與壽命，模組的設計亦可由此研究整合巨觀與微觀模擬，達成跨尺度從材料至系統的最佳化設計，為電動車全面商業化跨出重大進展。

This thesis employs the first principles calculation to predict material properties and finite volume methods to simulate the performance of Li-ion batteries (LiBs). Comparing simulation with experimental results using a commercial NMC LiB, this research has confirmed the accuracy of the simulation models. This thesis aims at optimal deign at microscopic material perspective and also the macroscopic module design of various LiBs, especially the state-of-the-art solid electrolyte LiBs.
The methodology of this research starts from the molecular structure construction to module design of various LiBs. Using the first principles molecular dynamics, diffusion coefficient (D) of Li ions can be obtained without the semi-empirical potential models. Specific heat capacity (Cv) and thermal conductivity (k) are calculated by phonon dispersion and phonon density of states which employs the density functional perturbation theory at the reciprocal lattice space. This research focuses on the material selection using solid electrolyte Li6PS5Cl, and the cathode material usingα-MoO3 (α-Molybdenum Oxide), which are the baseline of simulation cases.
Microscopic and macroscopic simulation results show that theα-MoO3 cathode has an extraordinary specific capacity of 882.91 (mAh/g), which is five times better than the current NMC commercial batteries, the latter range from 150 to 200 (mAh/g). This cathode has a high Li-ion diffusivity of 8.26x10-8 (cm2/s) and a high thermal conductivity at 24.8 (W/m·K). The solid electrolyte Li6PS5Cl has an extremely high thermal conductivity at 151.62 (W/m·K). All these make the future high C-rate super batteries tend to have much less charge time and longer life that make electric vehicles commercialization much sooner.

[1] Federal Ministry for Economic Affairs and Energy., “Time series for the development of renewable energy sources in Germany,” 2020.
[2] Taiwan Power Company (https://www.taipower.com.tw/tc/page.aspx?mid)
[3] KEMET Engineering Center(https://ec.kemet.com/blog/supercapacitors-vs-batteries/)
[4] Panasonic Cooperation., “Lithium-ion Handbook: Industrial batteries for professionals,” 2007.
[5] M. Freire, N. V. Kosova, C. Jordy., “A New Active Li–Mn–O Compound for High Energy Density Li-ion Batteries,” Nature Materials, 15, pp.173-177, 2016.
[6] Y. Zhang, Y. Li, & Li. D., “High-energy cathode materials for Li-ion batteries: A review of recent developments,” Science China Technological Sciences, 58(11), pp.1809-1828, 2015.
[7] Cadex Electronics Inc. “Types of Lithium-ion Battery”
(https://battery university .com/learn/article/types_of_lithium_ion)
[8] K. Mortensen, W. Brown, “Structure of PS-PEO Diblock Copolymers in Solution and the Bulk State Probed Using Dynamic Light-Scattering and Small-Angle Neutron-Scattering and Dynamic Mechanical Measurements” Langmuir, 13, pp.3635-3645, 1997.
[9] L. O. Valøen, J. N. Reimers, “Transport Properties of LiPF6-Based Li-Ion Battery Electrolytes,” Journal of The Electrochemical Society, 152(5), pp.882-891, 2005.
[10] W. Zhao, J. Yi, P. He, H. Zhou., “Solid‑State Electrolytes for Lithium‑Ion Batteries: Fundamentals, Challenges and Perspectives” Electrochemical Energy Reviews, 2, pp.574-605, 2019.
[11] J. Haruyama, K. Sodeyama, L. Han, K. Takada, and Y. Tateyama., “Space−Charge Layer Effect at Interface between Oxide Cathode and Sulfide Electrolyte in All-Solid-State Lithium-Ion Battery,” Chemistry of Materials, 26, pp.4248-4255, 2014.
[12] K. Hosoi, “Aiming for a Breakthrough in the Transition to a Low-Carbon Society Advanced Batteries,” Focus NEDO, 69, pp.8-11, 2018.
[13] Timo D., Madhav S., Simon H and Arnulf L., “Thick electrodes for Li-ion batteries: A model based analysis,” Journal of Power Sources, vol.334, pp.191-201, 2016.
[14] Bin W., Sangwoo H., Kang G. S., and Wei L., “Application of Artificial Neural Networks in Design of Lithium-ion Batteries,” Journal of Power Sources, 395, pp.128-136, 2018.
[15] M. Doyle, and J. Newman., “Comparison of Modeling Predictions with Experimental Data from Plastic Lithium Ion Cells,” Journal of the Electrochemical Society, 143(6), pp.1890-1903, 1996.
[16] L. Cai, R. E. White., “Mathematical Modeling of a Lithium Ion Battery,” Journal of Power Sources, 196, pp.5985-5989, 2011.
[17] M. Torchio, Lalo M, R. Bhushan and G. Richard D. B., “LIONSIMBA: A Matlab Framework Based on a Finite Volume Model Suitable for Li-Ion Battery Design, Simulation, and Control,” Journal of The Electrochemical Society, 163(7), pp.A1192-A1205, 2016.
[18] R. G. Parr., Yang W. (1994)., Density-Functional Theory of Atoms and Molecules., New York: Oxford University Press Inc.
[19] W. Kohn, and L. J. Sham, “Self-Consistent Equations Including Exchange and Correlation Effects,” Physical Review, 140(4A), pp.A1133, 1965.
[20] P. Giannozzi, S. Baroni, “Density-Functional Perturbation Theory,” Handbook of Materials Modeling, pp.195-214, 2005.
[21] WIKIPEDIA (https://en.wikipedia.org/wiki/Pseudopotential)
[22] M.T. Dove, “Introduction to the Theory of Lattice Dynamics,” Collection SFN, vol.12, pp.123-159, 2011.
[23] B. V. Troeye, M. Torrent and X. Gonze1, “Interatomic Force Constants Including the DFT-D Dispersion Contribution,” Physical Review B, 93, 144304, 2016.
[24] H. Ibach, H. Lüth, Solid-State Physics: An Introduction to Theory and Experiment., Berlin: Springer, pp.51-65, 1991.
[25] D. C. Wallace, Thermodynamics of Crystals., New York: Dover, 1998
[26] J. Morris, Nanopackaging: Nanotechnologies and Electronics Packaging., New York: Springer, pp.831, 2008.
[27] Andreas N., Mårten B and Göran L., “Electrochemical Characterization and Modelling of the Mass Transport Phenomena in LiPF6–EC–EMC Electrolyte,” Electrochimica Acta, 53, pp.6356-6365, 2008.
[28] Perdew J. P., and Wang Y., “Parameter Estimation of an Electrochemistry-based Lithium-ion Battery Model Using a Two-step Procedure and a Parameter Sensitivity Analysis,” International Journal of Energy Research, 42(7), pp.2417-2430, 2018.
[29] M. Rousseau, O. Cerdan, O. Delestre and F. Dupros, “Overland Flow Modeling with the Shallow Water Equations Using a Well-Balanced Numerical Scheme: Better Predictions or Just More Complexity,” Journal of Hydrologic Engineering, vol.20(10), pp.04015012, 2015.
[30] 王顗智 (指導教授 洪哲文)，“固態物理分析以氧空缺方法增進超級電池陰極鋰離子嵌入性能，” 清華大學動力機械工程學系碩士論文，07/2019
[31] G. Kresse, and J. Furthmüller, “Efficient Iterative Schemes for Ab Initio Total-Energy Calculations Using a Plane-Wave Basis Set,” Physical Review B, 54(16), pp.11169, 1996.
[32] G. Kresse, and D. Joubert, “From Ultrasoft Pseudopotentials to the Projector Augmented-Wave Method,” Physical Review B, 59(3), pp.1758, 1999.
[33] A. Togo, I. Tanaka, “First Principles Phonon Calculations in Materials Science,” Scripta Materialia, 108, pp.1-5, 2015.
[34] Z. Sun, and T. Sugie, “Identification of Hessian Matrix in Distributed Gradient-based Multi-agent Coordination Control Systems,” Numerical Algebra, Control and Optimization, 9(3), pp.297-318, 2019.
[35] W. Jones, Theoretical solid state physics., New York: Dover Publications, 1985.
[36] C. Kittel, Introduction to Solid State Physics. 8th ed. New York: Wiley, 2005.
[37] Q. Wang, D. J. Keffer, S. Petrovan, and J. Brock Thomas, “Molecular Dynamics Simulation of Poly(ethylene terephthalate) Oligomers,” The Journal of Physical Chemistry B, 114(2), pp.786-795, 2010.
[38] P. Debye, “Zur Theorie der Spezifischen Waerme,” Annalen der Physik, 39 (4), pp.789–839, 1912.
[39] Tanvir R. T., Christopher D. R., and Chao-Yang W., “A Temperature Dependent, Single Particle, Lithium Ion Cell Model Including Electrolyte Diffusion,” Journal of Dynamic Systems Measurement and Contro., 137(1), 011005, 2015.
[40] C. Julien, “Lithium Intercalation in MoO3 : A Comparison Between Crystalline and Disordered Phases,” Applied Physics A, 59(2), pp.173-178, 1994
[41] M. A. Cabañero, “Direct Determination of Diffusion Coefficients in Commercial Li-Ion Batteries,” Journal of the Electrochemical Society, vol.165(5), pp. A847-A855, 2018.
[42] J. Zheng, X. Li, Z. Wang., “Characteristics of xLiFePO4·y Li3V2(PO4)3 Electrodes for Lithium Batteries,” Ionics, 15, pp753-759, 2009
[43] S. Yu, “Prediction of Lithium Diffusion Coefficient and Rate Performance by Using the Discharge Curves of LiFePO4 Materials,” Bulletin of the Korean Chemical Society, vol.32(3), pp.852-856, 2011.
[44] 彭立函 (指導教授 洪哲文)，“鋰電池以h-BN作為固態電解質Li6PS5Cl單層鍍膜Ab Initio分子動力學分析，” 清華大學動力機械工程學系碩士論文，07/2020
[45] Chase M.W. Jr., “NIST-JANAF Thermochemical Tables, Fourth Edition”, J. Phys. Chem. Ref. Data, Monograph 9, 1-1951, 1998
[46] O. Kamoun, A. Mami, M. A. Amara, R. Vidu, and M. Amlouk., “Nanostructured Fe, Co-Codoped MoO3 Thin Films,” Micromachines, 10, pp.138, 2019
[47] F. Richtera, P. J. S. Vieb, S. Kjelstrupa and O. S. Burheimc, “Measurements of Ageing and Thermal Conductivity in a Secondary NMC-hard Carbon Li-ion Battery and the Impact on Internal Temperature Profiles,” Electrochimica Acta, 250, pp.228-237, 2017.
[48] T. S. Pathan, M. Rashid, M. Walker, W. D. Widanage and Emma Kendrick, “Active Formation of Li-ion Batteries and its Effect on Cycle Life,” J. Phys.: Energy, vol.1, 044003, 2019.
[49] P. Chen, F. Sun, H. He., “An Electro-Thermal Model for Li-ion Battery under Different Temperature,” Advances in Energy, Environment and Materials Science, pp.635-639, 2016.