用CA方法模拟界面能各向异性对胞晶生长形态的影响

张云鹏; 林鑫; 魏雷; 王猛; 彭东剑; 黄卫东

doi:10.7498/aps.61.228106

摘要

用元胞自动机(Cellular Automaton, CA)模型研究了界面能各向异性对二维定向凝固胞晶的生长形态的影响, 建立了判定胞晶生长达到稳态的判据.结果显示, 当界面能各向异性强度非常小时, 胞晶尖端很容易分岔, 胞晶形态不容易稳定.而当界面能各向异性强度足够大时, 容易形成稳定的胞晶形态, 同时界面能各向异性强度会显著影响稳定胞晶的形态, 界面能各向异性越强, 稳态胞晶间距越小, 胞晶尖端半径越小, 尖端半径与胞晶间距的比值越小, 固液界面前沿的浓度与过冷度越小.

关键词:

元胞自动机 /
胞晶 /
各向异性

Abstract

The growth patterns of cellulars in directional solidification are investigated numerically using the cellular automata (CA) model in two dimensions. A criterion which determine whether the cellulars reach stable state is derived from the analysis of simulated results. The simulated results also show that it is easy for tip splitting to appear for cellulars when the surface tention anisotropy is very small. So it is hard to obtain stable cellular arrays. However, if the amplitude of surface tention anisotropy is strong enough, it is easy to obtain stable cellular arrays. And the intensity of surface energy anisotropy can considerably influence the stable cellular patterns. The stronger the surface energy anisotropy, the smaller the stable cellular spacing and the cellular tip radius are, and the smaller the ratio between tip radius and cellular spacing, the smaller the tip concentration and the tip undercooling are.

Keywords:

作者及机构信息

1.
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, 50901061), 国家重点基础研究发展计划(973) (批准号: 2011CB610402)，高等学校学科创新引智计划 (批准号: 08040)和西北工业大学凝固技术国家重点实验室基金 (批准号: 02-TZ-2008)资助的课题.

Authors and contacts

1.
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 and 50901061), the National Basic Research Program of China (Grant No. 2011CB610402), the Programme of Introducing Talents of Discipline to Universities (Grant No. 08040), and the Fund of the State Key Laboratory of Solidification Processing in NWPU (Grant No. 02-TZ-2008).

参考文献

[1]	Akamatsu S, Faivre G 1998 Phys. Rev. E 58 3302
[2]	Zhao D W, Li J F 2009 Acta Phys. Sin. 58 7094 (in Chinese) [赵达文, 李金富 2009 物理学报 58 7094]
[3]	Li M E, Yang G C 2007 Acta Metall. Sin. 20 258
[4]	Kessler D A, Levine H 1986 Phys. Rev. B 33 7868
[5]	Amar M B, Pomeau Y 1986 Euro. Phys. Lett. 2 307
[6]	Langer J S 1986 Phys. Rev. A 33 435
[7]	Brener E A 1991 Adv. Phys. 40 53
[8]	Jamgotchian H, Trivedi R, Billia B 1993 Phys. Rev. E 47 4313
[9]	Ben-Jacob E, Deutscher G, Garik P, Goldenfeld N D, Lareah Y 1986 Phys. Rev.Lett. 57 1903
[10]	Steinbach I 2008 Acta Mater. 56 4965
[11]	Provatas N, Wang Q, Haataja M, Grant M 2003 Phys. Rev. Lett. 91 155502
[12]	Wang Z J 2009 Ph. D. Dissertation (Xi'an: Northwestern Polytechnical University) (in Chinese) [王志军 2009 博士学位论文 (西安: 西北工业大学)]
[13]	Trivedi R, Seetharaman V, Eshelman M A 1991 Metall. Trans. A 22A 585
[14]	Coriell S R, Sekerka R F 1976 J. Cryst. Growth 34 157
[15]	Zhu M F, Stefanescu D M 2007 Acta Mater. 55 1741
[16]	Beltran-Sanchez L, Stefanescu D M 2004 Metall. Mater. Trans. A 35 2471
[17]	Wei L, Lin X, Wang M, Huang W D 2011 Appl. Phys. A 103 123
[18]	Wei L, Lin X, Wang M, Huang W D 2012 Physica B 407 2471
[19]	Lipton J, Glicksman M E, Kurz W 1987 Metall. Trans. A 18A 341
[20]	Tiller W A, Jackson K A, Rutter J W, Chalmers B 1953 Acta Metall. 1 428
[21]	Kurz W, Fisher D.J 1981 Acta Metall. 29 11
[22]	Huang W D, Geng X G, Zhou Y H 1993 J. Cryst. Growth 134 105
[23]	Laxmanan V 1985 Acta. Metall. 33 1023
[24]	Lu S Z, Hunt J D 1992 J. Cryst. Growth 123 17
[25]	Mullins W W, Sekerka R F 1964 J. Appl. Phys. 35 444

施引文献

[1]	Akamatsu S, Faivre G 1998 Phys. Rev. E 58 3302
[2]	Zhao D W, Li J F 2009 Acta Phys. Sin. 58 7094 (in Chinese) [赵达文, 李金富 2009 物理学报 58 7094]
[3]	Li M E, Yang G C 2007 Acta Metall. Sin. 20 258
[4]	Kessler D A, Levine H 1986 Phys. Rev. B 33 7868
[5]	Amar M B, Pomeau Y 1986 Euro. Phys. Lett. 2 307
[6]	Langer J S 1986 Phys. Rev. A 33 435
[7]	Brener E A 1991 Adv. Phys. 40 53
[8]	Jamgotchian H, Trivedi R, Billia B 1993 Phys. Rev. E 47 4313
[9]	Ben-Jacob E, Deutscher G, Garik P, Goldenfeld N D, Lareah Y 1986 Phys. Rev.Lett. 57 1903
[10]	Steinbach I 2008 Acta Mater. 56 4965
[11]	Provatas N, Wang Q, Haataja M, Grant M 2003 Phys. Rev. Lett. 91 155502
[12]	Wang Z J 2009 Ph. D. Dissertation (Xi'an: Northwestern Polytechnical University) (in Chinese) [王志军 2009 博士学位论文 (西安: 西北工业大学)]
[13]	Trivedi R, Seetharaman V, Eshelman M A 1991 Metall. Trans. A 22A 585
[14]	Coriell S R, Sekerka R F 1976 J. Cryst. Growth 34 157
[15]	Zhu M F, Stefanescu D M 2007 Acta Mater. 55 1741
[16]	Beltran-Sanchez L, Stefanescu D M 2004 Metall. Mater. Trans. A 35 2471
[17]	Wei L, Lin X, Wang M, Huang W D 2011 Appl. Phys. A 103 123
[18]	Wei L, Lin X, Wang M, Huang W D 2012 Physica B 407 2471
[19]	Lipton J, Glicksman M E, Kurz W 1987 Metall. Trans. A 18A 341
[20]	Tiller W A, Jackson K A, Rutter J W, Chalmers B 1953 Acta Metall. 1 428
[21]	Kurz W, Fisher D.J 1981 Acta Metall. 29 11
[22]	Huang W D, Geng X G, Zhou Y H 1993 J. Cryst. Growth 134 105
[23]	Laxmanan V 1985 Acta. Metall. 33 1023
[24]	Lu S Z, Hunt J D 1992 J. Cryst. Growth 123 17
[25]	Mullins W W, Sekerka R F 1964 J. Appl. Phys. 35 444

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