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各向异性表面张力对定向凝固中深胞晶生长的影响

陈明文 陈弈臣 张文龙 刘秀敏 王自东

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各向异性表面张力对定向凝固中深胞晶生长的影响

陈明文, 陈弈臣, 张文龙, 刘秀敏, 王自东

Effect of anisotropic surface tension on deep cellular crystal growth in directional solidification

Chen Ming-Wen, Chen Yi-Chen, Zhang Wen-Long, Liu Xiu-Min, Wang Zi-Dong
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  • 利用匹配渐近展开法和多变量展开法求出定向凝固深胞晶生长的浓度场和界面形态的全局渐近解,研究各向异性表面张力对定向凝固深胞晶生长的影响. 结果表明,各向异性表面张力对定向凝固过程深胞晶生长有显著的影响. 随着各向异性表面张力增大,胞晶前端部分浓度减小而胞晶界面收缩;胞晶根部的浓度增大而界面曲率增大或根部的曲率半径减小,各向异性表面张力使得深胞晶界面振幅增加. 本文结果能够计算定向凝固过程中深胞晶生长的浓度、界面形态.
    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.
    • 基金项目: 教育部海外名师项目(批准号:MS2010BJKJ005))、国家自然科学基金(批准号:10972030)和中央高校基础研究基金(批准号:FRF-BR-11-034B)资助的课题.
    • Funds: Project supported by the Overseas Distinguished Scholar Program by the Ministry of Education of the People’s Republic of China (Grant No. MS2010BJKJ005), the National Natural Science Foundation of China (Grant No. 10972030), and the Fundamental Research Funds for the Central University (Grant No. FRF-BR-11-034B).
    [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 物理学报 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 物理学报 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

  • [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 物理学报 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 物理学报 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

计量
  • 文章访问数:  4945
  • PDF下载量:  420
  • 被引次数: 0
出版历程
  • 收稿日期:  2013-08-29
  • 修回日期:  2013-11-05
  • 刊出日期:  2014-02-05

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