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Characteristic scale selection of lamellar spacings in binary eutectic solidification

Meng Guang-Hui Lin Xin

Characteristic scale selection of lamellar spacings in binary eutectic solidification

Meng Guang-Hui, Lin Xin
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  • The lamellar spacing, which is formed by solidified melt of eutectic or near-eutectic composition, plays a very important role in determining the properties of final products. In this study, the lamellar spacing of eutectic growth in steady-state is predicted by the method which is established based on the classical Jackson-Hunt theory, and completed by considering the free energy change during eutectic solidification at small undercooling. The density difference between the solid phases is also considered when calculating the diffusion field in the liquid. It is found that a band of lamellar spacings would be generally selected for a given alloy under fixed growth conditions. In addition, the lamellar spacing can be morphologically stable below the minimum undercooling value, and this overstabilization is only dependent on the intrinsic characteristic properties of a given system at a fixed growth velocity. The analysis results are found to be in reasonable agreement with experimental data of Al-Al2Cu, Sn-Pb and CBr4-C2Cl6 systems available from the literature.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 50971102, 50201012).
    [1]

    Pusztai T, Rátkai L, Szállás A, Gránásy L 2013 Phys. Rev. E 87 032401

    [2]

    Clopet C R, Cochrane R F, Mullins A M 2013 Appl. Phys. Lett. 102 031906

    [3]

    Bai B B, Lin X, Wang L L, Wang X B, Wang M, Huang W D 2013 Acta Phys. Sin. 62 218103 (in Chinese) [白贝贝, 林鑫, 王理林, 王贤斌, 王猛, 黄卫东 2013 物理学报 62 218103]

    [4]

    Wang L, Wang N, Ji L, Yao W J 2013 Acta Phys. Sin. 62 216801 (in Chinese) [王雷, 王楠, 冀林, 姚文静 2013 物理学报 62 216801]

    [5]

    Liu J M, Liu Z G, Wu Z C 1993 Chin. Phys. 2 782

    [6]

    Zhao S, Li J F, Liu L Zhou Y H 2009 Chin. Phys. B 18 1917

    [7]

    Liu X R, Cao C D, Wei B B 2003 Chin. Phys. 12 1266

    [8]

    Wang W M, Niu Y C, Chen J H, Bian X F, Liu J M 2004 Chin. Phys. B 13 1520

    [9]

    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]

    [10]

    Lewis D, Pusztai T, Gránásy L, Warren J, Boettinger W 2004 JOM 56 34

    [11]

    Zhu Y C, Wang J C, Yang G C, Zhao D W 2007 Chin. Phys. 16 805

    [12]

    Wu M W, Xiong S M 2011 Acta Phys. Sin. 60 058103 (in Chinese) [吴孟武, 熊守美 2011 物理学报 60 058103]

    [13]

    Li X M, Li W Q, Jin Q L, Zhou R 2013 Chin. Phys. B 22 078701

    [14]

    Jackson K A 1958 Can. J. Phys. 36 683

    [15]

    Kramer J J, Tiller W A 1965 J. Chem. Phys. 42 257

    [16]

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

    [17]

    Magnin P, Trivedi R 1991 Acta Metall. 39 453

    [18]

    Langer J S 1980 Phys. Rev. Lett. 44 1023

    [19]

    Datye V, Langer J S 1981 Phys. Rev. B 24 4155

    [20]

    Akamatsu S, Plapp M, Faivre G, Karma A 2004 Metall. Mater. Trans. A 35 1815

    [21]

    Akamatsu S, Bottin-Rousseau S, Perrut M, Faivre G, Witusiewicz V T, Sturz L 2007 J. Cryst. Growth 299 418

    [22]

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

    [23]

    Baker J C, Cahn J W 1971 Thermodynamics of Solidification in: Hughel T J, Boiling G F (eds) Solidification (Ohio: ASM, Metals Park) p23

    [24]

    Herlach D M 1994 Mater. Sci. Eng. R 12 177

    [25]

    Kim K B, Liu J, Marasli N, Hunt J D 1995 Acta Metall. Mater. 43 2143

    [26]

    Meng G H, Lin X, Huang W D 2007 Acta Metall. Sin. 43 1176 (in Chinese) [孟广慧, 林鑫, 黄卫东 2007 金属学报 43 1176]

    [27]

    Meng G H, Lin X, Huang W D 2008 Mater. Lett. 62 984

    [28]

    Hunt J D, Lu S Z 1994 Handbook of Crystal Growth. Vol.2, Part B: Bulk Crystal Growth: Growth Mechanism and Dynamics (Amsterdam: North Holland) p1111

    [29]

    Meng G H, Lin X, Huang W D 2007 J. Mater. Sci. Technol. 23 851

    [30]

    Ourdjini A, Liu J 1994 Mater. Sci. Techon. 10 312

    [31]

    Liu J, Elliott R 1995 Metall. Mater. Trans. A 26 471

    [32]

    Liu J, Elliott R 1995 J. Cryst. Growth 148 406

    [33]

    Cline H E 1984 Metall. Trans. A 15 1013

    [34]

    Akamatsu S, Bottin-Rousseau S, Faivre G 2004 Phys. Rve. Lett. 93 175701

    [35]

    Double D D 1973 Mater. Sci. Eng. 11 325

  • [1]

    Pusztai T, Rátkai L, Szállás A, Gránásy L 2013 Phys. Rev. E 87 032401

    [2]

    Clopet C R, Cochrane R F, Mullins A M 2013 Appl. Phys. Lett. 102 031906

    [3]

    Bai B B, Lin X, Wang L L, Wang X B, Wang M, Huang W D 2013 Acta Phys. Sin. 62 218103 (in Chinese) [白贝贝, 林鑫, 王理林, 王贤斌, 王猛, 黄卫东 2013 物理学报 62 218103]

    [4]

    Wang L, Wang N, Ji L, Yao W J 2013 Acta Phys. Sin. 62 216801 (in Chinese) [王雷, 王楠, 冀林, 姚文静 2013 物理学报 62 216801]

    [5]

    Liu J M, Liu Z G, Wu Z C 1993 Chin. Phys. 2 782

    [6]

    Zhao S, Li J F, Liu L Zhou Y H 2009 Chin. Phys. B 18 1917

    [7]

    Liu X R, Cao C D, Wei B B 2003 Chin. Phys. 12 1266

    [8]

    Wang W M, Niu Y C, Chen J H, Bian X F, Liu J M 2004 Chin. Phys. B 13 1520

    [9]

    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]

    [10]

    Lewis D, Pusztai T, Gránásy L, Warren J, Boettinger W 2004 JOM 56 34

    [11]

    Zhu Y C, Wang J C, Yang G C, Zhao D W 2007 Chin. Phys. 16 805

    [12]

    Wu M W, Xiong S M 2011 Acta Phys. Sin. 60 058103 (in Chinese) [吴孟武, 熊守美 2011 物理学报 60 058103]

    [13]

    Li X M, Li W Q, Jin Q L, Zhou R 2013 Chin. Phys. B 22 078701

    [14]

    Jackson K A 1958 Can. J. Phys. 36 683

    [15]

    Kramer J J, Tiller W A 1965 J. Chem. Phys. 42 257

    [16]

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

    [17]

    Magnin P, Trivedi R 1991 Acta Metall. 39 453

    [18]

    Langer J S 1980 Phys. Rev. Lett. 44 1023

    [19]

    Datye V, Langer J S 1981 Phys. Rev. B 24 4155

    [20]

    Akamatsu S, Plapp M, Faivre G, Karma A 2004 Metall. Mater. Trans. A 35 1815

    [21]

    Akamatsu S, Bottin-Rousseau S, Perrut M, Faivre G, Witusiewicz V T, Sturz L 2007 J. Cryst. Growth 299 418

    [22]

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

    [23]

    Baker J C, Cahn J W 1971 Thermodynamics of Solidification in: Hughel T J, Boiling G F (eds) Solidification (Ohio: ASM, Metals Park) p23

    [24]

    Herlach D M 1994 Mater. Sci. Eng. R 12 177

    [25]

    Kim K B, Liu J, Marasli N, Hunt J D 1995 Acta Metall. Mater. 43 2143

    [26]

    Meng G H, Lin X, Huang W D 2007 Acta Metall. Sin. 43 1176 (in Chinese) [孟广慧, 林鑫, 黄卫东 2007 金属学报 43 1176]

    [27]

    Meng G H, Lin X, Huang W D 2008 Mater. Lett. 62 984

    [28]

    Hunt J D, Lu S Z 1994 Handbook of Crystal Growth. Vol.2, Part B: Bulk Crystal Growth: Growth Mechanism and Dynamics (Amsterdam: North Holland) p1111

    [29]

    Meng G H, Lin X, Huang W D 2007 J. Mater. Sci. Technol. 23 851

    [30]

    Ourdjini A, Liu J 1994 Mater. Sci. Techon. 10 312

    [31]

    Liu J, Elliott R 1995 Metall. Mater. Trans. A 26 471

    [32]

    Liu J, Elliott R 1995 J. Cryst. Growth 148 406

    [33]

    Cline H E 1984 Metall. Trans. A 15 1013

    [34]

    Akamatsu S, Bottin-Rousseau S, Faivre G 2004 Phys. Rve. Lett. 93 175701

    [35]

    Double D D 1973 Mater. Sci. Eng. 11 325

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  • Received Date:  13 October 2013
  • Accepted Date:  27 November 2013
  • Published Online:  05 March 2014

Characteristic scale selection of lamellar spacings in binary eutectic solidification

  • 1. Department of Mechanical Engineering, Xi’an Aeronautical University, Xi’an 710077, China;
  • 2. State Key Laboratory of Solidification Processing, Northwestern Polytechnical University, Xi’an 710072, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant Nos. 50971102, 50201012).

Abstract: The lamellar spacing, which is formed by solidified melt of eutectic or near-eutectic composition, plays a very important role in determining the properties of final products. In this study, the lamellar spacing of eutectic growth in steady-state is predicted by the method which is established based on the classical Jackson-Hunt theory, and completed by considering the free energy change during eutectic solidification at small undercooling. The density difference between the solid phases is also considered when calculating the diffusion field in the liquid. It is found that a band of lamellar spacings would be generally selected for a given alloy under fixed growth conditions. In addition, the lamellar spacing can be morphologically stable below the minimum undercooling value, and this overstabilization is only dependent on the intrinsic characteristic properties of a given system at a fixed growth velocity. The analysis results are found to be in reasonable agreement with experimental data of Al-Al2Cu, Sn-Pb and CBr4-C2Cl6 systems available from the literature.

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