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基于类似于Tersoff-Brenner模型的键级势架构, 从Sn的5种几何构型的基本物性第一性原理计算结果和实验结果出发, 通过Levenberg-Marquardt方法建立了Sn的分析型键级势.利用得到的相互作用势和分子动力学方法, 计算了Sn的β 相和体心四方晶体相的晶体结构、结合能、键距、键能以及体变模量, 并进而计算了Sn的α 和β 相的自由能、内能和熵随温度的变化.结果表明, β 相和体心四方晶体相的基本物性以及α↔β 相变温度计算结果与实验值符合良好, 建立的分析型键级势可用于Sn基钎料合金性质的大尺度分子动力学模拟.An analytical bond-order potential based on Tersoff-Brenner model for Sn is developed using the Levenberg-Marquardt optimization algorithm with the first-principles calculations on fundamental physical properties of five configurations of Sn, and with the available experimental results. The potential is used to determine the crystal structures, binding energies, bond distances and strengths, and bulk modulus of the β-Sn and body-centered-tetragonal Sn, and to predict the changes in free energy of the α and β phase with temperature. Result indicate that the calculated basic properties of the phases and the predicted transition temperature from α to β phase are in good agreement with the reported experimental data. The proposed interatomic potential is short-ranged and quickly evaluated, and it could be used to distinguish covalent bond from metallic bond in the phases, so it is very useful for large-scale molecular dynamics simulations of Sn-based solder.
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Keywords:
- interatomic potential /
- Sn /
- molecular dynamics /
- first-principles
[1] Huang M L, Chen L D, Zhou S M, Zhao N 2012 Acta Phys. Sin. 61 1981 (in Chinese) [黄明亮, 陈雷达, 周少明, 赵宁 2012 61 1981]
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[25] Cheong B H, Chang K J 1991 Phys. Rev. B 44 4103
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[29] Rayne J A, Chandrasekhar B S 1960 Phys. Rev. 120 1658
[30] Vaboya S N, Kennedy G C 1970 J. Phys. Chem. Solids. 31 2329
[31] Liu M, Liu L G 1986 High Temp-High Press 18 79
[32] Moré J J 1977 The Levenberg-Marquardt Algorithm: Implementation and Theory (Berlin: Springer Verlag) p105
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[1] Huang M L, Chen L D, Zhou S M, Zhao N 2012 Acta Phys. Sin. 61 1981 (in Chinese) [黄明亮, 陈雷达, 周少明, 赵宁 2012 61 1981]
[2] Lu Y D, He X Q, En Y F, Wang X, Zhuang Z Q 2009 Acta Phys. Sin. 58 1942 (in Chinese) [陆裕东, 何小琦, 恩云飞, 王歆, 庄志强 2009 58 1942]
[3] Liang Y F, Shui J P, Chen G, Zhu Z G 2000 Acta Phys. Sin. 49 1327 (in Chinese) [梁云峰, 水嘉鹏, 陈刚, 朱震刚 2000 49 1327]
[4] Zeng K, Tu K N 2002 Mater. Sci. Eng. R-Rep. 38 55
[5] Hou X H, Hu S J, Shi L 2010 Acta Phys. Sin. 59 2109 (in Chinese) [侯贤华, 胡社军, 石璐 2010 59 2109]
[6] Idota Y, Kubota T, Matsufuji A, Maekawa Y, Miyasaka T 1997 Science 276 1395
[7] Ravelo R, Baskes M 1997 Phys. Rev. Lett. 79 2482
[8] Bernard S, Maillet J B 2002 Phys. Rev. B 66 012103
[9] Dong H, Moon K S, Wong C P 2005 J. Electron. Mater. 34 40
[10] Brenner D W 2000 Phys. Status Solidi B 217 23
[11] Brenner D W 1989 Phys. Rev. Lett. 63 1022
[12] Tersoff J 1994 Phys. Rev. B 49 16349
[13] Brenner D W 1990 Phys. Rev. B 42 9458
[14] Khor K E, Sarma S D 1988 Phys. Rev. B 38 3318
[15] Oleinik I I, Pettifor D G 1999 Phys. Rev. B 59 8500
[16] Conrad D, Scheerschmidt K 1998 Phys. Rev. B 58 4538
[17] Aguado A 2003 Phys. Rev. B 67 212104
[18] Albe K 1997 Phys. Rev. B 55 6203
[19] Bondybey V E, Heaven M C, Miller T A 1983 J. Chem. Phys. 78 3593
[20] Jo C, Lee K 2000 J. Chem. Phys. 113 7268
[21] Majumder C, Kumar V, Mizuseki H, Kawazoe Y 2001 Phys. Rev. B 64 233405
[22] Majumder C, Kumar V, Mizuseki H, Kawazoe Y 2005 Phys. Rev. B 71 035401
[23] Buchenauer C J, Cardona M, Pollak F H 1971 Phys. Rev. B 3 1243
[24] Thewlis J, Davey A R 1954 Nature 174 1011
[25] Cheong B H, Chang K J 1991 Phys. Rev. B 44 4103
[26] Christensen N E, Methfessel M 1993 Phys. Rev. B 48 5797
[27] Pavone P, Baroni S, Gironcoli S D 1998 Phys. Rev. B 57 10421
[28] Ihm J, Cohen M L 1981 Phys. Rev. B 23 1576
[29] Rayne J A, Chandrasekhar B S 1960 Phys. Rev. 120 1658
[30] Vaboya S N, Kennedy G C 1970 J. Phys. Chem. Solids. 31 2329
[31] Liu M, Liu L G 1986 High Temp-High Press 18 79
[32] Moré J J 1977 The Levenberg-Marquardt Algorithm: Implementation and Theory (Berlin: Springer Verlag) p105
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