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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]
[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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[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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