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An asymptotic solution of the concentration and interface morphology for a deep cellular crystal in directional solidification is obtained by using the matched asymptotic expansion method and multiple variable expansion method, and the effect of anisotropic surface tension on deep cellular crystal growth is studied. Results show that the anisotropic surface tension has a significant effect on the concentration and interface shape of deep cellular crystal growth in directional solidification. As the anisotropic surface tension parameter increases, the concentration near the front part of deep cellular crystal decays and the interface shrinks; when as the concentration near the root increases and the curvature of the interface near the root increases or the curvature radius decreases; and the amplitude of the deep cellular crystal increases. The concentration and interface shape of the deep cellular crystal in directional solidification can be calculated with the results obtained in this paper.
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Keywords:
- directional solidification /
- deep cellular crystal growth /
- anisotropic surface tension /
- asymptotic solution
[1] Mullins W W, Sekerka R F 1964 J. Appl. Phys. 35 444
[2] Mullins W W, Sekerka R F 1963 J. Appl. Phys. 34 323
[3] Langer J S, Turski L A 1977 Acta Metall 32 1
[4] Corell S R, McFadden G B 1993 Handbook of Crystal Growth (Berlin: Springer-Verlag), Chapter 12 785
[5] McFadden G B, Corell S R 1984 Physica D 12 253
[6] Coriell S R, McFadden G B 2002 J. Crystal Growth 237–239 8
[7] Boettinger W J, Coriell S R, Greer A L, Karma A, Kurz W, Rappaz M, Trivedi R 2000 Acta Materialia 48 43
[8] Xu J J 1998 Interfacial wave theory of pattern formation (Berlin: Springer-Verlag) pp79–242
[9] Davis S H 2001 Theory of Solidification (Cambridge, UK: Cambridge University Press) pp42–214
[10] Huang W D, Lin X, Li T, Wang L L 2004 Acta Phys. Sin. 57 3978 (in Chinese) [黄卫东, 林鑫, 李涛, 王琳琳, 2004 57 3978]
[11] Zhang Y P, Lin X, Wei L, Wang M, Peng D J, Huang W D 2012 Acta Phys. Sin. 61 228106 (in Chinese) [张云鹏, 林鑫, 魏雷, 王猛, 彭东剑, 黄卫东 2012 61 228106]
[12] Weeks J D, Saarloos W Van 1989 Phys. Rev. A 39(5) 2772
[13] Weeks J D, Saarloons W Van, Grant M 1991 J. Crystal Growth 112 244
[14] Chen Y Q, Xu J J 2011 Phys. Rev. E 83 041601
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[1] Mullins W W, Sekerka R F 1964 J. Appl. Phys. 35 444
[2] Mullins W W, Sekerka R F 1963 J. Appl. Phys. 34 323
[3] Langer J S, Turski L A 1977 Acta Metall 32 1
[4] Corell S R, McFadden G B 1993 Handbook of Crystal Growth (Berlin: Springer-Verlag), Chapter 12 785
[5] McFadden G B, Corell S R 1984 Physica D 12 253
[6] Coriell S R, McFadden G B 2002 J. Crystal Growth 237–239 8
[7] Boettinger W J, Coriell S R, Greer A L, Karma A, Kurz W, Rappaz M, Trivedi R 2000 Acta Materialia 48 43
[8] Xu J J 1998 Interfacial wave theory of pattern formation (Berlin: Springer-Verlag) pp79–242
[9] Davis S H 2001 Theory of Solidification (Cambridge, UK: Cambridge University Press) pp42–214
[10] Huang W D, Lin X, Li T, Wang L L 2004 Acta Phys. Sin. 57 3978 (in Chinese) [黄卫东, 林鑫, 李涛, 王琳琳, 2004 57 3978]
[11] Zhang Y P, Lin X, Wei L, Wang M, Peng D J, Huang W D 2012 Acta Phys. Sin. 61 228106 (in Chinese) [张云鹏, 林鑫, 魏雷, 王猛, 彭东剑, 黄卫东 2012 61 228106]
[12] Weeks J D, Saarloos W Van 1989 Phys. Rev. A 39(5) 2772
[13] Weeks J D, Saarloons W Van, Grant M 1991 J. Crystal Growth 112 244
[14] Chen Y Q, Xu J J 2011 Phys. Rev. E 83 041601
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