近年來隨著電能需求的提升，能更輕便、更有效率地充儲電力早已成為現代大型電力工具的瓶頸。鋰電池的發展雖然提供了解決問題的方向，不過基本的鋰電池存在許多缺點使其在應用上有所限制。像是以碳為陽極的電池有較低的電荷密度、以矽為陽極的電池因為體積及重複充放電後體積膨脹造成的結構缺陷而無法維持穩定。其中一種有效的解決方法是使用二元金屬間化合物。以Sb作為陽極的鋰電池在近年來獲得不少關注，其中Sb-Sn的組合也被發現可以在維持穩定重複充放電的條件下，依然提供足夠高的電荷密度及容量。因此，確立精確且完整的Li-Sb熱力學模型在發展材料的過程中起著關鍵作用。以可靠的計算方法研究材料除了可以縮短實驗所需的時間外，還可以將計算完成的資訊推向更高維度的運算，使得設計與發展材料的過程更有效率。
　　本實驗基於CALPHAD理論並以ab initio方法輔助運算，以ab initio 方法計算Li-Sb系統中金屬間化合物的形成焓並以結合可靠的熱力學性質數據，接著於Thermo-calc 軟體中計算Li-Sb系統的熱力學模型，並與文獻實驗數據比較達到擬合完成。此研究在CALPHAD理論的基礎下，Li-Sb系統的熱力學模型獲得新的描述。

　　In recent years, as the demand for electrical energy has increased, the ability to charge and store electricity more lightly and efficiently has long been a bottleneck for modern large-scale power tools. Although the development of lithium batteries provides a solution to the problem, the basic lithium batteries have many shortcomings that limit their application. For example, a battery with carbon as the anode has a lower charge density, and a battery with silicon as the anode cannot maintain stability due to the volume and structural defects caused by volume expansion after repeated charge and discharge. One effective solution is to use binary intermetallic compounds. Lithium batteries using Sb as the anode have received a lot of attention in recent years. Among them, the combination of Sb-Sn has also been found to provide a sufficiently high charge density and capacity while maintaining stability in charge and discharge. Therefore, establishing an accurate and complete Li-Sb thermodynamic model plays an important role in the development of materials. In addition to shortening the time required for experiments, researching materials with a reliable calculation method can not only push the completed information to higher-dimensional calculations but also making the process of designing and developing materials more efficient.
　　This work is based on the CALPHAD approach and assisted by the ab initio calculation. The ab initio is used to calculate the enthalpy of formation of intermetallic compounds in the Li-Sb system, and the reliable thermodynamic properties are used to assess the thermodynamic model.

1. Introduction 1
1.1 Preface. 1
1.2 Lithium-ion battery 2
1.3 Propose of study 3
2. Literature review 5
2.1 CALPHAD 5
2.1.1 Selection of Models for the Gibbs Energy Functions 6
2.1.2 Selection and Evaluation of Input Data 7
2.1.3 Optimization of model parameter 7
2.1.4 Calculations and Comparisons 7
2.1.5 Application 7
2.2 ab initio 9
2.3 Li-Sb 14
2.4 Phase diagram of Lithium-Antimony system 15
2.5 Activities of Lithium-Antimony system 21
2.6 Enthalpies of mixing of Lithium-Antimony system 22
3. Methodology 23
3.1 Ab initio calculation 23
3.2 CALPHAD thermodynamic modeling 25
3.2.1 Intermetallic phase 25
3.2.2 Liquid phase 26
4. Results and discussion 29
4.1 ab initio calculation 29
4.2 The CALPHAD calculation 34
5. Conclusion 41
5.1 Conclusion 41
6. Reference 43
Appendix A The input file 49
A.1 CIF file 49
A.1.1 Li 49
A.1.2 Sb 50
A.1.3 Li3Sb_C 51
A.1.4 Li3Sb_H 52
A.1.5 Li2Sb 53
A.2 Li-Sb binary system 54
A.2.1 TDB file 54
A.2.2 POP file 56

[1] Dima, A., Bhaskarla, S., Becker, C., Brady, M., Campbell, C., Dessauw, P., ... & Peskin, A. (2016). Informatics infrastructure for the materials genome initiative. Jom, 68(8), 2053-2064.
[2] C.-M. Park, J.-H. Kim, H. Kim, H.-J. Sohn, Li-alloy based anode materials for Li secondary batteries, Chem. Soc. Rev. 39 (2010) 3115-3141.
[3] J.M. Tarascon, M. Armand, Issues and challenges facing rechargeable lithium batteries, Nature 414 (2001) 359-367.
[4] Beutl1, A., Cupid, D.2, Flandorfer, H.1* The Li-Sb Phase Diagram Part I: New Experimental Results
[5] Wachtler, M., Winter, M., & Besenhard, J. O. (2002). Anodic materials for rechargeable Li-batteries. Journal of Power Sources, 105(2), 151–160. doi:10.1016/s0378-7753(01)00934-x
[6] J. Sangster, A.D. Pelton, The Li-Sb (lithium-antimony) system, J. Phase Equilib. 14 (4) (1993) 514–517
[7] P.I. Fedorov, Lithium-antimony system, Zh. Neorg. Khim+ 40 (1995) 844-846
[8] M.M. Kane, J.M. Newhouse, D.R. Sadoway, Electrochemical determination of the thermodynamic properties of lithium-antimony alloys, J. Electrochem. Soc. 162 (2015) A421–A425..
[9] Experimental investigation and thermodynamic assessment of the Li-Sb system Fan Zhang, Shuhong Liua,⁎, Jianchuan Wanga, Yong Dua,⁎, Lixian Sunb
[10] Li, D., Beutl, A., Flandorfer, H., & Cupid, D. M. (2017). The Li-Sb phase diagram part II: Calorimetry and thermodynamic assessment. Journal of Alloys and Compounds, 701, 186-199.
[11] Terlicka, S., Dębski, A., & Fima, P. (2016). Enthalpy of formation of Li2Sb and Li3Sb and mixing enthalpy of liquid Li–Sb alloys. Journal of Alloys and Compounds, 673, 272-277.
[12]https://www.thermocalc.com/products-services/databases/the-calphad-methodology/
[13] Kaufman, L.; Bernstein, H. Computer calculation of phase diagrams. With special reference to refractory metals, Refractory Materials. A Series of Monographs. Volume 4; 1970; 344 p; Academic Press Inc; New York
[14] Cacciamani, G. (2016). An introduction to the calphad method and the compound energy formalism (CEF). Tecnologia em Metalurgia, Materiais e Mineração, 13(1), 16-24.
[15] H. F. Schaefer, III, “Critical Evaluation of Chemical and Physical Structural Informaron”, D. R. Lide and M. A. Paul, Ed., National Academy of Sciences, Washington, D.C., 1974, p 591
[16] Reed, A. E., Curtiss, L. A., & Weinhold, F. (1988). Intermolecular interactions from a natural bond orbital, donor-acceptor viewpoint. Chemical Reviews, 88(6), 899-926.
[17] Pokluda, J., Černý, M., Šob, M., & Umeno, Y. (2015). Ab initio calculations of mechanical properties: Methods and applications. Progress in Materials Science, 73, 127-158.
[18] V. Fock, Z.phys. Chem, pp. 126-148,1930.
[19] https://www.iue.tuwien.ac.at/phd/goes/dissse14.html
[20] Slater, J. C. (1951). A simplification of the Hartree-Fock method. Physical review, 81(3), 385.
[21] Abadir, G. B. B. (2010). Simulation studies of the mechanisms of interaction between carbon nanotubes and amino acids (Doctoral dissertation, University of British Columbia).
[22] Stokbro, K., Taylor, J., Brandbyge, M., & Guo, H. O. N. G. (2006). Ab-initio non-equilibrium Green’s function formalism for calculating electron transport in molecular devices. In Introducing Molecular Electronics (pp. 117-151). Springer, Berlin, Heidelberg.
[23] Ohno, K., Esfarjani, K., & Kawazoe, Y. (2018). Computational materials science: from ab initio to Monte Carlo methods. Springer.

[24] Langreth, D. C., & Perdew, J. P. (1980). Theory of nonuniform electronic systems. I. Analysis of the gradient approximation and a generalization that works. Physical Review B, 21(12), 5469.
[25] Langreth, D. C., & Mehl, M. J. (1983). Beyond the local-density approximation in calculations of ground-state electronic properties. Physical Review B, 28(4), 1809.
[26] Perdew, J. P., & Yue, W. (1986). Accurate and simple density functional for the electronic exchange energy: Generalized gradient approximation. Physical review B, 33(12), 8800.
[27] Perdew, J. P. (1986). Density-functional approximation for the correlation energy of the inhomogeneous electron gas. Physical Review B, 33(12), 8822.
[28] Becke, A. D. (1988). Density-functional exchange-energy approximation with correct asymptotic behavior. Physical review A, 38(6), 3098.
[29] Becke, A. D. (1993). A new mixing of Hartree–Fock and local density‐functional theories. The Journal of chemical physics, 98(2), 1372-1377.
[30] https://www.quantum-espresso.org/
[31] Park, C. M., & Jeon, K. J. (2011). Porous structured SnSb/C nanocomposites for Li-ion battery anodes. CheYang, J., Wachtler, M., Winter, M., & Besenhard, J. O. (1999).
[32] Sub‐Microcrystalline Sn and Sn‐SnSb powders as lithium storage materials for Lithium‐ion batteries. Electrochemical and Solid-State Letters, 2(4), 161.mical Communications, 47(7), 2122-2124.
[33] Thermodynamic description of the Cu–Sb binary system Wojciech Gierlotka∗, Dominika Jendrzejczyk-Handzlik
[34] G. Brauer, E. Zintl, Constitution of phosphides, arsenides, antimonides, and bismuthides of Li, Na K, Z. Phys. Chem. B 37 (5–6) (1937) 323–352.
[35] W. Weppner, R.A. Huggins, Thermodynamic properties of the intermetallic systems Li-Sb and Li-Bi, J. Electrochem. Soc. 125 (1) (1978) 7–14.
[36] Morachevskii, A.G., Thermodynamic Analysis of Alloys of the Lithium-Antimony System. Zhurnal Prikladnoi Khimii, 2002. 75(3): p.380-382; TR: Russian Journal of Applied Chemistry, 2002. 75(3): p. 367-369.
[37] Okamoto, H., Li-Sb (Lithium-Antimony). Journal of Phase Eqilibria, 1996. 17(3): p.271.
[38] Liu, Z. K. (2009). First-principles calculations and CALPHAD modeling of thermodynamics. Journal of phase equilibria and diffusion, 30(5), 517.
[39] U.S. Department of Energy Office of Scientific and Technical Information
[40] Schmid, R., & Chang, Y. A. (1985). A thermodynamic study on an associated solution model for liquid alloys. Calphad, 9(4), 363-382.
[41] Shchukarev, S. A., Vol'f, E., & Morozova, M. P. (1954). ENTHALPY OF FORMATION OF LITHIUM ANTIMONIDE. Zhur. Obshchei Khim., 24.
[42] Kubaschewski, O., & Catterall, J. A. (1956). Thermochemical data of alloys (Vol. 3). Pergamon Press.
[43] Nikitin, A. V., Demidov, A. I., Morachevskii, A. G., Matveev, V. A., & Il’ina, O. I. (1972). Thermodynamics of solid alloys in the Li-Sb system. Zh. Prikl. Khim.(Leningrad), 55(4), 915-916.
[44] A. Jain*, S.P. Ong*, G. Hautier, W. Chen, W.D. Richards, S. Dacek, S. Cholia, D. Gunter, D. Skinner, G. Ceder, K.A. Persson (*=equal contributions)
The Materials Project: A materials genome approach to accelerating materials innovation
APL Materials, 2013, 1(1), 011002.