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The dendritic growth patterns in directional solidification with different amplitudes of solid-liquid interface energy anisotropy were investigated using the two-dimensional cellular automata (CA) model. It is shown that when the preferred growth direction of the crystal was the same as the direction of thermal gradient, the solidification pattern would transform from seaweed to dendrite with the increase of amplitude of interface energy anisotropy. The amplitude of interface energy anisotropy could also influence the morphology of dendritic tips. As the amplitude of interface energy anisotropy increased, the dendritic tip radius, the liquid concentration ahead of the tip and the tip undercooling decreased. A power law relationship evisted between the stability parameter of dendritic tip and the amplitude of interface energy anisotropy in directional solidification. The primary arm spacing changed little with the increase of interface energy anisotropy. When the angle between the preferred growth direction of the crystals and the direction of thermal gradient was-40, and the amplitude of interface energy anisotropy increased, the solidification pattern would transform from seaweed to degenerated dendrite and finally to tilted dendrite.
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Keywords:
- cellular automata model /
- dendrite /
- interface energy anisotropy
[1] Yokoyama E, Sekeka R F 1992 J. Cryst. Growth 125 389
[2] Kessler D A, Levine H 1986 Phys. Rev. B 33 7868
[3] Amar M B, Pomeau Y 1986 Euro. Phys. Lett. 2 307
[4] Langer J S 1986 Phys. Rev. A 33 435
[5] Brener E A 1991 Adv. Phys. 40 53
[6] Lin H K, Chen C C, Lan C W 2011 J. Cryst. Growth 318 51
[7] 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]
[8] Spencer B J, Huppert H E 1999 J. Cryst. Growth 200 287
[9] Trivedi R 1980 J. Cryst. Growth 49 219
[10] Akamatsu S, Faivre G 1998 Phys. Rev. E 58 3302
[11] Lu S Z, Hunt J D 1992 J. Cryst. Growth 123 17
[12] Steinbach I 2008 Acta Materialia 56 4965
[13] Zhang Y P, Lin X 2012 Acta Phys. Sin. 61 228106 (in Chinese) [张云鹏, 林鑫 2012 物理学报 61 228106]
[14] Wei L,Lin X, Wang M, Huang W D 2011 Appl. Phys. A 103 123
[15] Beltran-Sanchez L, Stefanescu D M 2004 Metall. Mater. Trans. A 35 2471
[16] Zhu M F, Stefanescu D M 2007 Acta Mater. 55 1741
[17] Wei L, Lin X, Wang M, Huang W D 2012 Acta Phys. Sin. 61 098104 (in Chinese) [魏雷, 林鑫, 王猛, 黄卫东 2012 物理学报 61 098104]
[18] Lipton J, Glicksman M E, Kurz W 1987 Metall. Trans. A 18 341
[19] Kurz W, Fisher D J 1981 Acta Metall. 29 11
[20] Ihle T, Muller-krumbhaar 1993 Phys. Rev. Lett. 70 3083
[21] Ihle T, Muller-krumbhaar 1994 Phys. Rev. E 49 2972
[22] Akamatsu S, Faivre G, Ihle T 1995 Phys. Rev. E 51 4751
[23] Langer J S 1980 Rev. Mod. Phys. 52 1
[24] Langer J S, Muller-krumbhaar 1978 Acta Metall. 26 1681
[25] Langer J S, Muller-krumbhaar 1978 Acta Metall. 26 1689
[26] Langer J S, Muller-krumbhaar 1978 Acta Metall. 26 1691
[27] Xu J J 1996 Phys. Rev. E 53 5051
[28] Warren J A, Langer J S 1993 Phys. Rev. E 47 2702
[29] Hunt J D 1979 Solidification of Casting of Metals. (London: The Metals Society) p3
[30] 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)]
[31] Akamatsu S, Faivre G, Ihle T 1995 Phys. Rev. E 51 4751
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[1] Yokoyama E, Sekeka R F 1992 J. Cryst. Growth 125 389
[2] Kessler D A, Levine H 1986 Phys. Rev. B 33 7868
[3] Amar M B, Pomeau Y 1986 Euro. Phys. Lett. 2 307
[4] Langer J S 1986 Phys. Rev. A 33 435
[5] Brener E A 1991 Adv. Phys. 40 53
[6] Lin H K, Chen C C, Lan C W 2011 J. Cryst. Growth 318 51
[7] 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]
[8] Spencer B J, Huppert H E 1999 J. Cryst. Growth 200 287
[9] Trivedi R 1980 J. Cryst. Growth 49 219
[10] Akamatsu S, Faivre G 1998 Phys. Rev. E 58 3302
[11] Lu S Z, Hunt J D 1992 J. Cryst. Growth 123 17
[12] Steinbach I 2008 Acta Materialia 56 4965
[13] Zhang Y P, Lin X 2012 Acta Phys. Sin. 61 228106 (in Chinese) [张云鹏, 林鑫 2012 物理学报 61 228106]
[14] Wei L,Lin X, Wang M, Huang W D 2011 Appl. Phys. A 103 123
[15] Beltran-Sanchez L, Stefanescu D M 2004 Metall. Mater. Trans. A 35 2471
[16] Zhu M F, Stefanescu D M 2007 Acta Mater. 55 1741
[17] Wei L, Lin X, Wang M, Huang W D 2012 Acta Phys. Sin. 61 098104 (in Chinese) [魏雷, 林鑫, 王猛, 黄卫东 2012 物理学报 61 098104]
[18] Lipton J, Glicksman M E, Kurz W 1987 Metall. Trans. A 18 341
[19] Kurz W, Fisher D J 1981 Acta Metall. 29 11
[20] Ihle T, Muller-krumbhaar 1993 Phys. Rev. Lett. 70 3083
[21] Ihle T, Muller-krumbhaar 1994 Phys. Rev. E 49 2972
[22] Akamatsu S, Faivre G, Ihle T 1995 Phys. Rev. E 51 4751
[23] Langer J S 1980 Rev. Mod. Phys. 52 1
[24] Langer J S, Muller-krumbhaar 1978 Acta Metall. 26 1681
[25] Langer J S, Muller-krumbhaar 1978 Acta Metall. 26 1689
[26] Langer J S, Muller-krumbhaar 1978 Acta Metall. 26 1691
[27] Xu J J 1996 Phys. Rev. E 53 5051
[28] Warren J A, Langer J S 1993 Phys. Rev. E 47 2702
[29] Hunt J D 1979 Solidification of Casting of Metals. (London: The Metals Society) p3
[30] 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)]
[31] Akamatsu S, Faivre G, Ihle T 1995 Phys. Rev. E 51 4751
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