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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.
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Keywords:
- cellular automata /
- cellular growth /
- anisotropy.
[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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[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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