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The change of the interface kinetic coefficient with the interface temperature under the non-equilibrium solidification condition is considered in the growth model of a spherical crystal. The first-order approximation solutions of temperature and interface for the spherical crystal growth in the undercooled melt are obtained by the asymptotic analysis method. The effects of the nonlinear interface kinetic undercooling on the interface morphology and the growth velocity of the spherical crystal in the undercooled melt are studied. The results show that as the interface kinetic coefficient increases, the growth velocity of the spherical crystal increases; as the interface kinetic coefficient decreases, the growth velocity of the spherical crystal decreases. Compared with the situation of neglecting interface kinetics, the nonlinear interface kinetics during crystal growth significantly decreases the growth velocity of the spherical crystal.
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Keywords:
- spherical crystal /
- interfacial morphology /
- asymptotic analysis
[1] Mullins W W, Sekerka R F 1963 J. Appl. Phys. 34 323
[2] Golovin A A, Davis S H 1998 Phisica D 116 363
[3] Davis S H 2001 Theory of Solidification (Cambridge: Cambridge University Press)
[4] Maruyama M, Kawabata K 2002 J. Cryst.Growth 237—239 164
[5] Murray B T, Coriell S R, Chernov A A, McFadden G B 2000 J. Cryst. Growth 218 434
[6] Zhu Z H, Ge P W, Xu Z Y, Huo C R 1998 Chin. Phys. 7 801
[7] Liu Y C, Chen W C, Huo C R, Ge P W 1999 Chin. Phys. 8 881
[8] Yu Y M, Yang G C, Zhao D W, Lü Y L, Karma A, Beckermann C 2001 Acta Phys. Sin. 50 2423 (in Chinese) [于艳梅、 杨根仓、 赵达文、 吕衣礼、 Karma A, Beckermann C 2001 物理学报 50 2423]
[9] Zhu Z H, Hong Y, Ge P W, Yu Y D 2004 Chin. Phys. 13 1982
[10] 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]
[11] Xu J J 2006 Introduction to Kinetics of Solidification and Stability Theory of the Interface pp18—21, p58 (Beijing: Science Press) (in Chinese) [徐鉴君 2006 凝固过程动力学与交界面稳定性理论导引 (北京:科学出版社) 第18—21, 58页]
[12] Sekerka R F 2004 J. Cryst. Growth 264 530
[13] Cristini V, Lowengrub J 2002 J. Cryst. Growth 240 267
[14] Cristini V, Lowengrub J 2004 J. Cryst. Growth 266 552
[15] Li S W, Lowengrub J S, Leo P H, Cristini V 2005 J. Cryst. Growth 277 578
[16] Chen M W, Wang Z D, Sun R J 2007 Acta Phys. Sin. 56 1819 (in Chinese) [陈明文、 王自东、 孙仁济 2007 物理学报 56 1819]
[17] Chen M W, Wang Z D, Xu J J 2007 Sci. China E 37 644 [陈 明文、 王自东、 徐鉴君 2007 中国科学E 37 644] 〖18] Chen M W, Wang Z D, Xie J X, Xu J J 2008 Acta Mech. Sin. 24 681
[18] Chen M W, Lan M, Yuan L, Wang Y Y, Wang Z D, Xu J J 2009 Chin. Phys. B 18 1691
[19] Wang Z D, Wang X W, Wang Q S, Shi H I, Xu J J 2009 Nanotechnology 20 075605
[20] Turnbull D 1981 Metall. Trans. 12A 695
[21] Li J F, Yang G C, Zhou Y H 2000 Mater. Res. Bull. 35 1775
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[1] Mullins W W, Sekerka R F 1963 J. Appl. Phys. 34 323
[2] Golovin A A, Davis S H 1998 Phisica D 116 363
[3] Davis S H 2001 Theory of Solidification (Cambridge: Cambridge University Press)
[4] Maruyama M, Kawabata K 2002 J. Cryst.Growth 237—239 164
[5] Murray B T, Coriell S R, Chernov A A, McFadden G B 2000 J. Cryst. Growth 218 434
[6] Zhu Z H, Ge P W, Xu Z Y, Huo C R 1998 Chin. Phys. 7 801
[7] Liu Y C, Chen W C, Huo C R, Ge P W 1999 Chin. Phys. 8 881
[8] Yu Y M, Yang G C, Zhao D W, Lü Y L, Karma A, Beckermann C 2001 Acta Phys. Sin. 50 2423 (in Chinese) [于艳梅、 杨根仓、 赵达文、 吕衣礼、 Karma A, Beckermann C 2001 物理学报 50 2423]
[9] Zhu Z H, Hong Y, Ge P W, Yu Y D 2004 Chin. Phys. 13 1982
[10] 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]
[11] Xu J J 2006 Introduction to Kinetics of Solidification and Stability Theory of the Interface pp18—21, p58 (Beijing: Science Press) (in Chinese) [徐鉴君 2006 凝固过程动力学与交界面稳定性理论导引 (北京:科学出版社) 第18—21, 58页]
[12] Sekerka R F 2004 J. Cryst. Growth 264 530
[13] Cristini V, Lowengrub J 2002 J. Cryst. Growth 240 267
[14] Cristini V, Lowengrub J 2004 J. Cryst. Growth 266 552
[15] Li S W, Lowengrub J S, Leo P H, Cristini V 2005 J. Cryst. Growth 277 578
[16] Chen M W, Wang Z D, Sun R J 2007 Acta Phys. Sin. 56 1819 (in Chinese) [陈明文、 王自东、 孙仁济 2007 物理学报 56 1819]
[17] Chen M W, Wang Z D, Xu J J 2007 Sci. China E 37 644 [陈 明文、 王自东、 徐鉴君 2007 中国科学E 37 644] 〖18] Chen M W, Wang Z D, Xie J X, Xu J J 2008 Acta Mech. Sin. 24 681
[18] Chen M W, Lan M, Yuan L, Wang Y Y, Wang Z D, Xu J J 2009 Chin. Phys. B 18 1691
[19] Wang Z D, Wang X W, Wang Q S, Shi H I, Xu J J 2009 Nanotechnology 20 075605
[20] Turnbull D 1981 Metall. Trans. 12A 695
[21] Li J F, Yang G C, Zhou Y H 2000 Mater. Res. Bull. 35 1775
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