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Modeling of regular eutectic growth of binary alloy basedon cellular automaton method

Wu Meng-Wu Xiong Shou-Mei

Modeling of regular eutectic growth of binary alloy basedon cellular automaton method

Wu Meng-Wu, Xiong Shou-Mei
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  • Based on cellular automaton method, a numerical model was developed for the regular eutectic growth of binary alloy. By coupling with the macro-temperature field and considering the solute diffusion, the constitutional undercooling and the curvature undercooling, modeling of the steady-state lamellar eutectic growth was achieved. A systematic investigation on eutectic growth morphology and lamellar spacing of a model alloy was made under unidirectional solidification conditions with different undercoolings, initial lamellar spacings, temperature gradients and solidification rates. The results reproduced the adjustment of lamellar spacing of two eutectic phases under the interaction between solute diffusion and surface energy by mechanisms of nucleation, lamellar branching, lamellar termination and overgrowth. The simulated results were in agreement with those predicted by the Jackson-Hunt model and experimental results by other researchers. Finally, the model was extended to three dimensional systems, which verified its feasibility of modeling the three-dimensional eutectic growth.
    • Funds:
    [1]

    Rosa C D, Park C, Thomas E L, Lotz B 2000 Nature 405 433

    [2]

    Coriell S R, McFadden G B, Mitchell W F, Murray B T, Andrews J B, Arikawa Y 2001 J. Cryst. Growth 224 145

    [3]

    Himemiya T, Ohsasa K, Saga T 2010 Mater. Trans. 51 110

    [4]

    Seetharaman V, Trivedi R K 1988 Metall. Trans. A 19 2955

    [5]

    Jackson K A, Hunt J D 1966 Trans. Metal. Soc. AIME 236 1129

    [6]

    Donaghey L F, Tiller W A 1968 Mater. Sci. Eng. 3 231

    [7]

    Magnin P, Trivedi R 1991 Acta Metall. Mater. 39 453

    [8]

    Ma D, Jie W Q 1996 Acta Metall. Sin. 32 791 (in Chinese) [马 东、介万奇 1996 金属学报 32 791]

    [9]

    Akamatsu S, Plapp M, Faivre G, Karma A 2002 Phys. Rev. E 66 030501

    [10]

    Steinbach I, Pezzolla F 1999 Physica D 134 385

    [11]

    Kim S G, Kim W T, Suzuki T, Ode M 2004 J. Cryst. Growth 261 135

    [12]

    Folch R, Plapp M 2003 Phys. Rev. E 68 010602

    [13]

    Zhu Y C, Wang J C, Yang G C, Yang Y J 2007 Acta Phys. Sin. 56 5542 (in Chinese) [朱耀产、王锦程、杨根仓、杨玉娟 2007 物理学报 56 5542]

    [14]

    Yang Y J, Wang J C, Zhang Y X, Zhu Y C, Yang G C 2009 Acta Phys. Sin. 58 2797 (in Chinese) [杨玉娟、王锦程、张玉祥、朱耀产、杨根仓 2009 物理学报 58 2797]

    [15]

    Gandin C A, Rappaz M 1994 Acta Metall. Mater. 42 2233

    [16]

    Nastac L 1999 Acta Mater. 47 4253

    [17]

    Wang W, Lee P D, Mclean M 2003 Acta Mater. 51 2971

    [18]

    Brown S G R 1998 J. Mater. Sci. 33 4769

    [19]

    Zhu M F, Hong C P 2002 Phys. Rev. B 66 155428

    [20]

    Zhu M F, Hong C P 2004 Metall. Mater. Trans. A 35 1555

    [21]

    Charbon C, LeSar R 1997 Modell. Simul. Mater. Sci. Eng. 5 53

    [22]

    Cadirli E, Gündüz M 2000 J. Mater. Process. Tech. 97 74

  • [1]

    Rosa C D, Park C, Thomas E L, Lotz B 2000 Nature 405 433

    [2]

    Coriell S R, McFadden G B, Mitchell W F, Murray B T, Andrews J B, Arikawa Y 2001 J. Cryst. Growth 224 145

    [3]

    Himemiya T, Ohsasa K, Saga T 2010 Mater. Trans. 51 110

    [4]

    Seetharaman V, Trivedi R K 1988 Metall. Trans. A 19 2955

    [5]

    Jackson K A, Hunt J D 1966 Trans. Metal. Soc. AIME 236 1129

    [6]

    Donaghey L F, Tiller W A 1968 Mater. Sci. Eng. 3 231

    [7]

    Magnin P, Trivedi R 1991 Acta Metall. Mater. 39 453

    [8]

    Ma D, Jie W Q 1996 Acta Metall. Sin. 32 791 (in Chinese) [马 东、介万奇 1996 金属学报 32 791]

    [9]

    Akamatsu S, Plapp M, Faivre G, Karma A 2002 Phys. Rev. E 66 030501

    [10]

    Steinbach I, Pezzolla F 1999 Physica D 134 385

    [11]

    Kim S G, Kim W T, Suzuki T, Ode M 2004 J. Cryst. Growth 261 135

    [12]

    Folch R, Plapp M 2003 Phys. Rev. E 68 010602

    [13]

    Zhu Y C, Wang J C, Yang G C, Yang Y J 2007 Acta Phys. Sin. 56 5542 (in Chinese) [朱耀产、王锦程、杨根仓、杨玉娟 2007 物理学报 56 5542]

    [14]

    Yang Y J, Wang J C, Zhang Y X, Zhu Y C, Yang G C 2009 Acta Phys. Sin. 58 2797 (in Chinese) [杨玉娟、王锦程、张玉祥、朱耀产、杨根仓 2009 物理学报 58 2797]

    [15]

    Gandin C A, Rappaz M 1994 Acta Metall. Mater. 42 2233

    [16]

    Nastac L 1999 Acta Mater. 47 4253

    [17]

    Wang W, Lee P D, Mclean M 2003 Acta Mater. 51 2971

    [18]

    Brown S G R 1998 J. Mater. Sci. 33 4769

    [19]

    Zhu M F, Hong C P 2002 Phys. Rev. B 66 155428

    [20]

    Zhu M F, Hong C P 2004 Metall. Mater. Trans. A 35 1555

    [21]

    Charbon C, LeSar R 1997 Modell. Simul. Mater. Sci. Eng. 5 53

    [22]

    Cadirli E, Gündüz M 2000 J. Mater. Process. Tech. 97 74

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    [9] SUN XIA, WU ZI-QIN. FRACTAL AND MULTIFRACTAL DESCRIPTION OF SURFACE TOPOGRAPHY. Acta Physica Sinica, 2001, 50(11): 2126-2131. doi: 10.7498/aps.50.2126
    [10] Yuan Hui-Bo, Li Lin, Zeng Li-Na, Zhang Jing, Li Zai-Jin, Qu Yi, Yang Xiao-Tian, Chi Yao-Dan, Ma Xiao-Hui, Liu Guo-Jun. Morphology characterization and growth mechanism of Au-catalyzed GaAs and GaAs/InGaAs nanowires. Acta Physica Sinica, 2018, 67(18): 188101. doi: 10.7498/aps.67.20180220
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Publishing process
  • Received Date:  06 July 2010
  • Accepted Date:  22 August 2010
  • Published Online:  15 May 2011

Modeling of regular eutectic growth of binary alloy basedon cellular automaton method

  • 1. State Key Laboratory of Automobile Safety and Energy, Department of Mechanical Engineering,Tsinghua University, Beijing 100084, China

Abstract: Based on cellular automaton method, a numerical model was developed for the regular eutectic growth of binary alloy. By coupling with the macro-temperature field and considering the solute diffusion, the constitutional undercooling and the curvature undercooling, modeling of the steady-state lamellar eutectic growth was achieved. A systematic investigation on eutectic growth morphology and lamellar spacing of a model alloy was made under unidirectional solidification conditions with different undercoolings, initial lamellar spacings, temperature gradients and solidification rates. The results reproduced the adjustment of lamellar spacing of two eutectic phases under the interaction between solute diffusion and surface energy by mechanisms of nucleation, lamellar branching, lamellar termination and overgrowth. The simulated results were in agreement with those predicted by the Jackson-Hunt model and experimental results by other researchers. Finally, the model was extended to three dimensional systems, which verified its feasibility of modeling the three-dimensional eutectic growth.

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