二元层片共晶凝固过程的特征尺度选择

孟广慧; 林鑫

doi:10.7498/aps.63.068104

摘要

基于Jackson和Hunt二元规则共晶稳态生长理论，在共晶两相的界面溶质守恒条件中引入密度修正项，改进了共晶两相的界面溶质守恒条件. 在此基础上，根据二元层片共晶常规凝固过程中层片组织稳态生长时Gibbs自由能的变化，运用极值形态选择原理确定二元层片共晶凝固过程中层片间距特征尺度选择准则. 理论分析表明，对于给定二元共晶合金，在常规凝固条件下的层片间距选择通常为一有限区间. 此外，理论分析还表明，二元层片共晶稳态生长时其特征尺度的选择可以呈现超稳定性，而且在给定的凝固条件下超稳定性只和给定合金系的物性参数有关. 将该形态选择准则分别运用于物性参数精确已知的Al-Al2Cu，Sn-Pb 和CBr4-C2Cl6 合金系，表明计算结果与实验结果相符合.

关键词:

凝固 /
共晶 /
层片间距 /
超稳定性

Abstract

The lamellar spacing, which is formed by solidified melt of eutectic or near-eutectic composition, plays a very important role in determining the properties of final products. In this study, the lamellar spacing of eutectic growth in steady-state is predicted by the method which is established based on the classical Jackson-Hunt theory, and completed by considering the free energy change during eutectic solidification at small undercooling. The density difference between the solid phases is also considered when calculating the diffusion field in the liquid. It is found that a band of lamellar spacings would be generally selected for a given alloy under fixed growth conditions. In addition, the lamellar spacing can be morphologically stable below the minimum undercooling value, and this overstabilization is only dependent on the intrinsic characteristic properties of a given system at a fixed growth velocity. The analysis results are found to be in reasonable agreement with experimental data of Al-Al2Cu, Sn-Pb and CBr4-C2Cl6 systems available from the literature.

Keywords:

作者及机构信息

孟广慧¹,
林鑫²

1.
西安航空学院机械学院, 西安 710077;

2.
西北工业大学凝固技术国家重点实验室, 西安 710072

基金项目: 国家自然科学基金（批准号：50971102，50201012）资助的课题.

Authors and contacts

Meng Guang-Hui¹,
Lin Xin²

1.
Department of Mechanical Engineering, Xi’an Aeronautical University, Xi’an 710077, China;

2.
State Key Laboratory of Solidification Processing, Northwestern Polytechnical University, Xi’an 710072, China

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 50971102, 50201012).

参考文献

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[8]	Wang W M, Niu Y C, Chen J H, Bian X F, Liu J M 2004 Chin. Phys. B 13 1520
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[21]	Akamatsu S, Bottin-Rousseau S, Perrut M, Faivre G, Witusiewicz V T, Sturz L 2007 J. Cryst. Growth 299 418
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[23]	Baker J C, Cahn J W 1971 Thermodynamics of Solidification in: Hughel T J, Boiling G F (eds) Solidification (Ohio: ASM, Metals Park) p23
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[25]	Kim K B, Liu J, Marasli N, Hunt J D 1995 Acta Metall. Mater. 43 2143
[26]	Meng G H, Lin X, Huang W D 2007 Acta Metall. Sin. 43 1176 (in Chinese) [孟广慧, 林鑫, 黄卫东 2007 金属学报 43 1176]
[27]	Meng G H, Lin X, Huang W D 2008 Mater. Lett. 62 984
[28]	Hunt J D, Lu S Z 1994 Handbook of Crystal Growth. Vol.2, Part B: Bulk Crystal Growth: Growth Mechanism and Dynamics (Amsterdam: North Holland) p1111
[29]	Meng G H, Lin X, Huang W D 2007 J. Mater. Sci. Technol. 23 851
[30]	Ourdjini A, Liu J 1994 Mater. Sci. Techon. 10 312
[31]	Liu J, Elliott R 1995 Metall. Mater. Trans. A 26 471
[32]	Liu J, Elliott R 1995 J. Cryst. Growth 148 406
[33]	Cline H E 1984 Metall. Trans. A 15 1013
[34]	Akamatsu S, Bottin-Rousseau S, Faivre G 2004 Phys. Rve. Lett. 93 175701
[35]	Double D D 1973 Mater. Sci. Eng. 11 325

施引文献

[1]	Pusztai T, Rátkai L, Szállás A, Gránásy L 2013 Phys. Rev. E 87 032401
[2]	Clopet C R, Cochrane R F, Mullins A M 2013 Appl. Phys. Lett. 102 031906
[3]	Bai B B, Lin X, Wang L L, Wang X B, Wang M, Huang W D 2013 Acta Phys. Sin. 62 218103 (in Chinese) [白贝贝, 林鑫, 王理林, 王贤斌, 王猛, 黄卫东 2013 物理学报 62 218103]
[4]	Wang L, Wang N, Ji L, Yao W J 2013 Acta Phys. Sin. 62 216801 (in Chinese) [王雷, 王楠, 冀林, 姚文静 2013 物理学报 62 216801]
[5]	Liu J M, Liu Z G, Wu Z C 1993 Chin. Phys. 2 782
[6]	Zhao S, Li J F, Liu L Zhou Y H 2009 Chin. Phys. B 18 1917
[7]	Liu X R, Cao C D, Wei B B 2003 Chin. Phys. 12 1266
[8]	Wang W M, Niu Y C, Chen J H, Bian X F, Liu J M 2004 Chin. Phys. B 13 1520
[9]	Yang Y J, Wang J C, Zhang Y X, Zhu Y C, Yang G C 2009 Acta Phys. Sin. 58 2797 (in Chinese) [杨玉娟, 王锦程, 张玉祥, 朱耀产, 杨根仓 2009 物理学报 58 2797]
[10]	Lewis D, Pusztai T, Gránásy L, Warren J, Boettinger W 2004 JOM 56 34
[11]	Zhu Y C, Wang J C, Yang G C, Zhao D W 2007 Chin. Phys. 16 805
[12]	Wu M W, Xiong S M 2011 Acta Phys. Sin. 60 058103 (in Chinese) [吴孟武, 熊守美 2011 物理学报 60 058103]
[13]	Li X M, Li W Q, Jin Q L, Zhou R 2013 Chin. Phys. B 22 078701
[14]	Jackson K A 1958 Can. J. Phys. 36 683
[15]	Kramer J J, Tiller W A 1965 J. Chem. Phys. 42 257
[16]	Jackson K A, Hunt J D 1966 Trans. AIME 236 1129
[17]	Magnin P, Trivedi R 1991 Acta Metall. 39 453
[18]	Langer J S 1980 Phys. Rev. Lett. 44 1023
[19]	Datye V, Langer J S 1981 Phys. Rev. B 24 4155
[20]	Akamatsu S, Plapp M, Faivre G, Karma A 2004 Metall. Mater. Trans. A 35 1815
[21]	Akamatsu S, Bottin-Rousseau S, Perrut M, Faivre G, Witusiewicz V T, Sturz L 2007 J. Cryst. Growth 299 418
[22]	Akamatsu S, Plapp M, Faivre G, Karma A 2002 Phys. Rev. E 66 030501(R)
[23]	Baker J C, Cahn J W 1971 Thermodynamics of Solidification in: Hughel T J, Boiling G F (eds) Solidification (Ohio: ASM, Metals Park) p23
[24]	Herlach D M 1994 Mater. Sci. Eng. R 12 177
[25]	Kim K B, Liu J, Marasli N, Hunt J D 1995 Acta Metall. Mater. 43 2143
[26]	Meng G H, Lin X, Huang W D 2007 Acta Metall. Sin. 43 1176 (in Chinese) [孟广慧, 林鑫, 黄卫东 2007 金属学报 43 1176]
[27]	Meng G H, Lin X, Huang W D 2008 Mater. Lett. 62 984
[28]	Hunt J D, Lu S Z 1994 Handbook of Crystal Growth. Vol.2, Part B: Bulk Crystal Growth: Growth Mechanism and Dynamics (Amsterdam: North Holland) p1111
[29]	Meng G H, Lin X, Huang W D 2007 J. Mater. Sci. Technol. 23 851
[30]	Ourdjini A, Liu J 1994 Mater. Sci. Techon. 10 312
[31]	Liu J, Elliott R 1995 Metall. Mater. Trans. A 26 471
[32]	Liu J, Elliott R 1995 J. Cryst. Growth 148 406
[33]	Cline H E 1984 Metall. Trans. A 15 1013
[34]	Akamatsu S, Bottin-Rousseau S, Faivre G 2004 Phys. Rve. Lett. 93 175701
[35]	Double D D 1973 Mater. Sci. Eng. 11 325

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