Skip to main content
SpringerLink
Log in

Solidification of Immiscible Alloys: A Review

  • Published:
Acta Metallurgica Sinica (English Letters) Aims and scope

Abstract

Immiscible alloys gained a considerable interest in last decades due to their valuable properties and potential applications. Many experimental and theoretical researches were carried out worldwide to investigate the solidification of immiscible alloys under the normal gravity and microgravity condition. The objective of this article is to review the research work in this field during the last few decades.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26
Fig. 27
Fig. 28
Fig. 29
Fig. 30

Similar content being viewed by others

Abbreviations

C :

Concentration (mole fraction)

C m :

Mean field concentration in the liquid matrix (mole fraction)

C d :

Concentration of the droplet (mole fraction)

C ∞ :

Equilibrium composition at a flat interface boundary (mole fraction)

C B :

Concentration of solute in the matrix at the interphase boundary (mole fraction)

C mix :

Concentration of the alloy (\( C_{\text{mix}} = \left( {1 - \phi } \right)C_{\text{m}} + \phi C_{\text{d}} \)) (mole fraction)

D :

Diffusion coefficient (m2/s)

D AB :

Diffusion coefficient of the solute A in the solvent B (m2/s)

D BB :

Self-diffusion coefficient of the solvent B (m2/s)

d :

Goldschmidt atomic diameter (m)

d A, d B :

Atomic diameter of the solute A and the solvent B (m)

d D :

Diameter of the droplet (m)

e z :

Unit vector in the z direction

e r :

Unit vector in the radial direction r of the sample

F :

Free energy function

f :

Radius distribution function of the MPDs

G (A+B) :

Gibbs free energy of the two unmixed components A and B (J/mol)

G alloy :

Gibbs free energy of an alloy (J/mol)

\( G_{\text{A}}^{0} \), \( G_{\text{B}}^{0} \) :

Gibbs free energy of the pure component A and B (J/mol)

\( \Delta G_{\text{v}} \) :

Gain in free energy per unit volume on nucleation (J/m3)

\( \Delta G_{\text{c}} \) :

Energy barrier for nucleation (J)

g :

Acceleration due to gravity (m/s2)

h :

Planck constant (6.626 × 10−34 J s)

\( \Delta H_{\text{mix}} \) :

Molar mixing enthalpy (J/mol)

ΔH 0 :

Constant term related to the interatomic interaction (J/mol)

I :

Nucleation rate of the MPDs [nuclei/(m3 s)]

J :

Molar flux of solute from or to a particle/droplet [mol/(m2 s)]

J D :

Molar flux from or to a particle/droplet due to pure diffusion [mol/(m2 s)]

k B :

Boltzmann’s constant (1.3807 × 10−23 J/K)

L1, L2 :

A-rich and B-rich liquid phases

M :

Atomic mass (amu)

N A :

Avogadro number (6.022 × 1023/mol)

N 0 :

Number density of atoms per unit volume (m−3)

n :

Number density of the MPDs (m−3)

R :

Radius of the minority phase droplet (m)

R g :

Gas constant (8.31447 J/mol K)

R*:

Critical radius for the nucleation of the MPDs (m)

r :

Radial position in a cylindrical sample (m)

S :

Supersaturation (\( S = C_{m} - C_{\infty } \)) (mole fraction)

S′:

Dimensionless supersaturation (\( \frac{{C_{\text{m}} - C_{\infty } }}{{C_{\text{d}} - C_{\infty } }} \))

S1, S2 :

Solid phase A and solid phase B

\( \Delta S_{\text{mix}} \) :

Molar mixing entropy (J/K)

T :

Absolute temperature (K)

T A, T B :

Melting temperature of the pure component A and B (K)

T C :

Critical temperature (K)

T M :

Monotectic temperature (K)

T E :

Eutectic temperature (K)

T W :

Wetting temperature (K)

T m :

Melting temperature (K)

t :

Time (s)

∇T :

Temperature gradient (K/m)

u :

Droplet/particle moving velocity (m/s)

u s :

Stokes velocity (m/s)

u M :

Marangoni velocity (m/s)

V :

Moving velocity of the matrix melt (V = V 0 + V c) (m/s)

V 0 :

Solidification velocity (m/s)

V C :

Convective velocity (m/s)

X A, X B :

Molar or atomic fraction of the component A and B

\( x_{{{\text{L}}_{ 1} }} \), \( x_{{{\text{L}}_{2} }} \) :

Composition of the liquid phase L1 and L2

x :

Distance (m)

σ :

L–L interfacial energy (J/m2)

Ω:

Molar volume (m3/mol)

\( \Omega _{\text{A}}^{{}} \), \( \Omega _{\text{B}}^{{}} \) :

Molar volume of the component A and B (m3/mol)

\( \Omega _{\text{d}} \) :

Molar volume in the droplet (m3/mol)

η :

Dynamic viscosity (Pa s)

\( \eta_{\text{m}}^{{}} \) :

Viscosity of the matrix (Pa s)

\( \eta_{\text{d}} \) :

Viscosity of the MPDs (Pa s)

\( \mu_{\text{A}} \), \( \mu_{\text{B}} \) :

Chemical potentials of the component A and B (J/mol)

υ :

Kinematic viscosity (m2/s)

\( \rho_{\text{m}} \) :

Density of the matrix (kg/m3)

\( \rho_{\text{d}} \) :

Density of the MPDs (kg/m3)

\( \rho^{\text{mix}} \) :

Density of the alloy (kg/m3)

\( \lambda_{\text{m}} \) :

Thermal conductivity of the matrix [W/(K m)]

\( \lambda_{\text{d}} \) :

Thermal conductivity of the MPDs [W/(K m)]

\( \lambda_{{}}^{\text{mix}} \) :

Thermal conductivity of the alloy [W/(K m)]

Φ:

Phase field variable

ϕ :

Volume fraction of the MPDs

References

  1. J. Chang, H.P. Wang, K. Zhou, B. Wei, Appl. Phys. A 109, 139 (2012)

    Article  Google Scholar 

  2. G.J. Feng, Z.R. Li, R.H. Liu, S.C. Feng, Acta Metall. Sin. (Engl. Lett.) 28, 405 (2015)

    Article  Google Scholar 

  3. A.P. Silva, A. Garcia, J.E. Spinelli, J. Mater. Sci. Technol. 30, 401 (2014)

    Article  Google Scholar 

  4. A.P. Silva, J.E. Spinelli, N. Mangelinck-Noel, A. Garcia, Mater. Des. 31, 4584 (2010)

    Article  Google Scholar 

  5. A. Inoue, N.J. Yano, J. Mater. Sci. 22, 123 (1987)

    Article  Google Scholar 

  6. S.Z. Hao, J. An, Y.B. Liu, Y. Lu, Mater. Des. 26, 181 (2005)

    Article  Google Scholar 

  7. J.G. Grolig, P. Alnegren, J. Froitzheim, J. Svensson, J. Power Sources 297, 534 (2015)

    Article  Google Scholar 

  8. R. Raghavan, T.P. Harzer, V. Chawla, S. Djaziri, B. Phillipi, J. Wehrs, J.M. Wheeler, J. Michler, G. Dehm, Acta Mater. 93, 175 (2015)

    Article  Google Scholar 

  9. J.Q. Wang, N. Yao, M. Li, J. Hu, J.W. Chen, Q.L. Hao, K.B. Wu, Y.K. Zhou, Microchim. Acta 182, 515 (2015)

    Article  Google Scholar 

  10. J.Z. Zhao, L. Ratke, J. Jia, Q.C. Li, J. Mater. Sci. Technol. 18, 197 (2002)

    Google Scholar 

  11. K. Murata, H. Tanaka, Nat. Mater. 11, 436 (2012)

    Article  Google Scholar 

  12. Y. Li, Y.X. Li, J.J. Guo, J. Jia, Y.Q. Su, H.S. Ding, Trans. Nonferrous Meterol. Soc. China 12, 357 (2002)

    Google Scholar 

  13. H. Tang, L.C. Wrobel, Z. Fan, Appl. Phys. A 81, 549 (2005)

    Article  Google Scholar 

  14. E. Bosco, P. Rizzi, M. Baricco, J. Magn. Magn. Mater. 262, 64 (2003)

    Article  Google Scholar 

  15. N. Harnby, M.F. Edward, A.W. Nienow, Mixing in the Process Industries, 2nd edn. (Butterworths-Heinemann Ltd., Oxford, 1985)

    Google Scholar 

  16. G.B. Rudrakshi, V.C. Srivastava, S.N. Ojha, Mater. Sci. Eng. A 457, 100 (2007)

    Article  Google Scholar 

  17. B. Prim, A. Romero, Immiscible Liquid Metals and Organics (DGM Informations gesellschaft, Oberursel, 1993), p. 281

    Google Scholar 

  18. T. Berrenberg, Immiscible Liquid Metals and Organics (DGM-Informations gesellschaft, Oberursel, 1993), p. 299

    Google Scholar 

  19. R.N. Singh, F. Sommer, Rep. Prog. Phys. 60, 57 (1997)

    Article  Google Scholar 

  20. A.W. Weeber, J. Phys. Met. Phys. 17, 809 (1987)

    Article  Google Scholar 

  21. D.H. Kim, W.T. Kim, E.S. Park, N. Mattern, J. Eckert, Prog. Mater. Sci. 58, 1103 (2013)

    Article  Google Scholar 

  22. L. Ratke, S. Diefenbach, Mater. Sci. Eng. R l5, 263 (1995)

    Article  Google Scholar 

  23. S.K. Yu, F. Sommer, Z. Metallkd. 87, 574 (1996)

    Google Scholar 

  24. Q. Chen, Z.P. Jin, Metall. Mater. Trans. A 26, 417 (1995)

    Article  Google Scholar 

  25. D.B. Thiessen, K.F. Man, Surface Tension Measurement, Copyright 2000 CRC Press LLC. http://www.engnetbase.com

  26. N. Uebber, L. Ratke, Scr. Metall. Mater. 25, 1133 (1991)

    Article  Google Scholar 

  27. J.B. Andrews, A.C. Sandlin, P.A. Curreri, Metall. Trans. A 19, 2645 (1988)

    Article  Google Scholar 

  28. M. Merkwitz, J. Weise, K. Thriemer, W. Hoyer, Z. Metallkd. 89, 247 (1998)

    Google Scholar 

  29. M. Merkwitz, J. Hoyer, Z. Metallkd. 90, 363 (1999)

    Google Scholar 

  30. W. Hoyer, I. Kaban, M. Merkwitz, J. Optoelectr. Adv. Mater. 5, 1069 (2003)

    Google Scholar 

  31. I. Kaban, S. Gruner, W. Hoyer, J. Non-Cryst. Sol. 353, 3717 (2007)

    Article  Google Scholar 

  32. I. Kaban, W. Hoyer, Mater. Sci. Eng. A 495, 3 (2008)

    Article  Google Scholar 

  33. I. Kaban, S. Curiotto, D. Chatain, W. Hoyer, Acta Mater. 58, 3406 (2010)

    Article  Google Scholar 

  34. I. Kaban, M. Kohler, L. Ratke, W. Hoyer, N. Mattern, J. Eckert, A.L. Greer, Acta Mater. 59, 6880 (2011)

    Article  Google Scholar 

  35. R. Becker, Proc. Phys. Soc. 52, 71 (1940)

    Article  Google Scholar 

  36. J.W. Cahn, J.E. Hilliard, J. Chem. Phys. 28, 258 (1958)

    Article  Google Scholar 

  37. M.R. Moldover, Phys. Rev. A 31, 1022 (1985)

    Article  Google Scholar 

  38. S.S. Rowlinson, B. Widom, Molecular Theory of Capillarity (Clarendon Press, Oxford, 1982)

    Google Scholar 

  39. G. Kaptay, Mater. Sci. Forum 508, 269 (2006)

    Article  Google Scholar 

  40. G. Kaptay, Calphad 32, 338 (2008)

    Article  Google Scholar 

  41. G. Kaptay, Acta Mater. 32, 6804 (2012)

    Article  Google Scholar 

  42. D. Chatain, N.J. Eustathopoulus, Chim. Phys. 81, 587 (1984)

    Google Scholar 

  43. D. Chatain, N.J. Eustathopoulus, Chim. Phys. 81, 599 (1984)

    Google Scholar 

  44. D. Chatain, N.J. Eustathopoulus, P.J. Desre, Coll. Interfacial Sci. 83, 384 (1981)

    Article  Google Scholar 

  45. A. Griesche, M.P. Macht, J.P. Grandet, G. Frohberg, J. Non-Cryst. Sol. 336, 173 (2004)

    Article  Google Scholar 

  46. A. Meyer, F. Kargl, Int. J. Microgravity Sci. Appl. 30, 30 (2013)

    Google Scholar 

  47. T. Masaki, T. Fukazawa, S. Matsumoto, T. Itami, S. Yoda, Meas. Sci. Technol. 16, 327 (2005)

    Article  Google Scholar 

  48. M.W. Ozelton, R.A. Swalin, Philos. Mag. 18, 441 (1968)

    Article  Google Scholar 

  49. S. Larsson, L. Broman, C. Roxbergh, A. Lodding, Z. Nat. Sch. 25, 1472 (1970)

    Google Scholar 

  50. G. Frohberg, K.H. Kraatz, H. Wever, Results of Spacelab-1, ESA-SP-222, 263 (1979)

  51. T. Itami, H. Aoki, M. Uchida, A. Sisa, S. Amano, O. Odawara, T. Masaki, T. Oida, H. Oda, Yoda, Micro. Sci. Lab. (MSL-1) Final Report NASA-CP 208868, 60 (1998)

  52. S. Yoda, T. Masaki, H. Oda, Micro. Sci. Lab. (MSL-1) Final Report, NASA-CP 208868, 86 (1998)

  53. S. Suzuki, K.H. Kraatz, G. Frohberg, Microgravity. Sci. Technol. XVIII-3/4, 82–85 (2006)

    Article  Google Scholar 

  54. F.A.L. Dullien, Trans. Faraday Soc. 59, 586 (1963)

    Article  Google Scholar 

  55. W. Sutherland, Philos. Mag. 9, 781 (1905)

    Article  Google Scholar 

  56. G. Kaptay, Z. Metallkd. 99, 14 (2008)

    Google Scholar 

  57. X.P. Su, S. Yang, J. Phase Equilib. Differ. 31, 333 (2010)

    Article  Google Scholar 

  58. R.A. Swalin, V.G. Leak, Acta Meter. 13, 471 (1965)

    Article  Google Scholar 

  59. V.G. Leak, R.A. Swalin, J. Chem. Phys. 18, 747 (1964)

    Google Scholar 

  60. R.J. Reynik, Trans. Met. Soc. AIME 245, 75 (1969)

    Google Scholar 

  61. A.K. Roy, R.P. Chhabra, Metall. Mater. Trans. A 19, 273 (1988)

    Article  Google Scholar 

  62. R.C. Reied, J.M. Pransuitz, B.E. Poling, The Properties of Gases and Liquids (McGraw-Hill, New York, 1987)

    Google Scholar 

  63. R.H. Perry, D. Green (eds.), Chemical Engineers Handbook, 6th edn. (McGraw-Hill, New York, 1984)

    Google Scholar 

  64. H. Fukuyama, Y. Waseda, High-Temperature Measurements of Materials (Springer, Berlin, 2009)

    Book  Google Scholar 

  65. L.G. Rong, B.X. Fang, S.M. Hua, Chin. Phys. Lett. 20, 1326 (2003)

    Article  Google Scholar 

  66. Y. Plevachuk, V. Sklyarchuk, O. Alekhin, L. Bulavin, O. Bilous, J. Phys.: Conference Series 98, 02 (2008)

  67. Y. Plevachuka, V. Sklyarchuka, O. Alekhinb, O. Bilous, J. Non-Cryst. Sol. 391, 12 (2014)

    Article  Google Scholar 

  68. Y. Wu, C. Li, J. Appl. Phys. 111, 073521 (2012)

    Article  Google Scholar 

  69. E.N. Andrade, Philos. Mag. 17, 497 (1934)

    Article  Google Scholar 

  70. Y.S. Touloukian, S.C. Sexena, P. Hestermans, Thermophysical Properties of Matter, vol. 11, Viscosity (IFI/Plenum, New-York, 1975)

    Google Scholar 

  71. L. Battezzati, A.L. Greer, Acta Meter. 37, 1791 (1989)

    Article  Google Scholar 

  72. T. Iida, R.I.L. Guthrie, The Physical Properties of Liquid Metals (Clarendon Press, Oxford, 1993)

    Google Scholar 

  73. A.J. Batchinski, Z. Phys. Chem. 84, 643 (1913)

    Google Scholar 

  74. J.H. Hildebrand, Viscosity and Diffusivity: A predictive Treatment (Wiley, New York, 1977)

    Google Scholar 

  75. G. Kaptay, Z. Metallkd. 96, 24 (2005)

    Article  Google Scholar 

  76. S. Glasstone, K.J. Laidler, H. Eyring, The Theory of Rate Processes (McGraw-Hill, New-York, 1941)

    Google Scholar 

  77. M.H. Cohen, D. Turnbull, J. Chem. Phys. 31, 1164 (1959)

    Article  Google Scholar 

  78. M. Born, H.S. Green, A General Kinetic Theory of Liquids (University Press, Cambridge, 1949)

    Google Scholar 

  79. G.A. Chadwick, Brit. J. Appl. Phys. 16, 1095–1097 (1965)

    Article  Google Scholar 

  80. J.W. Cahn, Metall. Trans. A 10, 119 (1979)

    Article  Google Scholar 

  81. R.N. Grugel, A. Hellawell, Metall. Trans. A 12, 669 (1981)

    Article  Google Scholar 

  82. R.N. Grugel, T.A. Lograsso, A. Hellawell, Metall. Trans. A 15, 1003 (1984)

    Article  Google Scholar 

  83. C. Schafer, M.H. Johnston, R.A. Parr, Acta Mater. 31, 1221 (1983)

    Article  Google Scholar 

  84. K.A. Jackson, J.D. Hunt, Trans. AIME 236, 843 (1986)

    Google Scholar 

  85. B. Majumdar, K. Chattopadhyay, Metall. Mater. Trans. A 31, 1 (2000)

    Article  Google Scholar 

  86. N.B. Singh, U.S. Rai, O.P. Singh, J. Cryst. Growth 71, 353 (1985)

    Article  Google Scholar 

  87. B. Derby, J.J. Favier, Acta Metall. 31, 1123 (1983)

    Article  Google Scholar 

  88. C. Ang, L. Lacy: NASA Document, TMX 58173 (1976)

  89. K. Lohberg, V. Dietl, H. Ahlborn: NASA Technical Memorandum 78125 (1977)

  90. C. Portard, Technical Report: NASA, Washington Microgravity Science and Application Program Tasks 81–82 (1985)

  91. S.H. Gelles, A.J. Mark-worth, J. AIAA 16, 431 (1978)

    Article  Google Scholar 

  92. T. Carlberg, H. Frederickson, Metall. Trans. A 11, 1665 (1980)

    Article  Google Scholar 

  93. H.U. Walter, in Workshop on Effect of Gravity on the Solidification of Immiscible Alloys, Stockholm, Sweden, ESA SP-219, 1984, pp. 47–67

  94. S. Ozawa, T. Motegi, Mater. Lett. 58, 2548 (2004)

    Article  Google Scholar 

  95. H. Yusuda, I. Ohnka, O. Kawakami, K. Ueno, K. Kishio, ISIJ Int. 43, 942 (2003)

    Article  Google Scholar 

  96. J. Gao, Y.P. Wang, Z.M. Zhou, M. Kolbe, Mater. Sci. Eng. A 449–451, 654 (2007)

    Article  Google Scholar 

  97. Y.K. Zhang, J. Gao, D. Nagamatsu, T. Fukud, H. Yasuda, M. Kolbe, J.C. He, Scr. Mater. 59, 1002 (2008)

    Article  Google Scholar 

  98. H. Li, J.Z. Zhao, Comp. Mater. Sci. 46, 1069 (2009)

    Article  Google Scholar 

  99. J. He, J.Z. Zhao, H. Li, X.F. Zhang, Q.X. Zhang, Metall. Trans. A 39, 1174 (2008)

    Article  Google Scholar 

  100. J. Zhu, T.M. Wang, F. Cao, H.W. Fu, Y.N. Fu, H.L. Xie, T.Q. Xiao, JMEPEG 22, 1319 (2013)

    Article  Google Scholar 

  101. H.X. Jiang, J.Z. Zhao, Chin. Phys. Lett. 29, 088104 (2012)

    Article  Google Scholar 

  102. H.X. Jiang, J.Z. Zhao, J. He, J. Mater. Sci. Technol. 30, 1027 (2014)

    Article  Google Scholar 

  103. H.X. Jiang, J.Z. Zhao, C.P. Wang, X.J. Liu, Mater. Lett. 132, 66 (2014)

    Article  Google Scholar 

  104. H.X. Jiang, H. Jie, J.Z. Zhao, Sci. Rep. 5, 1 (2015)

    Google Scholar 

  105. H.R. Kotadiaa, A. Dasb, E. Doernbergc, R. Schmid-Fetzerc, Mater. Chem. Phys. 131, 241 (2011)

    Article  Google Scholar 

  106. W. Zhai, H.M. Liu, B. Wei, Mater. Lett. 141, 221 (2015)

    Article  Google Scholar 

  107. W. Zhai, H.M. Liu, P. Zuo, X. Zhu, B. Wei, Prog. Nat. Sci. Mater. Inter. 25, 471 (2015)

    Article  Google Scholar 

  108. D.Q. Wan, Rare Met. 34, 560 (2015)

    Article  Google Scholar 

  109. Z. Fan, S. Ji, J. Zhang, Mater. Sci. Technol. 17, 837 (2001)

    Article  Google Scholar 

  110. H.R. Kotadia, J.B. Patel, Z. Fan, E. Doernberg, R. Schmid-Fetzer, Aluminum Alloys: Fabrication, Characterization and Applications II (TMS Warrendale, San Francisco, PA, 2009), pp. 81–86

    Google Scholar 

  111. H.R. Kotadia, E. Doernberg, J.B. Patel, Z. Fan, R. Schmid-Fetzer, Metall. Trans. A 40, 2202 (2009)

    Article  Google Scholar 

  112. P.L. Schaffer, R.H. Mathiesen, L. Arnberg, Acta Mater. 57, 2887 (2009)

    Article  Google Scholar 

  113. P.L. Schaffer, R.H. Mathiesen, L. Arnberg, Trans. Indian Inst. Met. 62, 437 (2009)

    Article  Google Scholar 

  114. R. Dai, S.G. Zhang, Y.B. Li, X. Guo, J.G. Li, Mater. Lett. 65, 322 (2011)

    Article  Google Scholar 

  115. R. Dai, S.G. Zhang, Y.B. Li, X. Guo, J.G. Li, J. Alloys Compd. 509, 2289 (2011)

    Article  Google Scholar 

  116. R. Dai, J.F. Zhang, S.G. Zhang, J.G. Li, Mater. Character. 81, 49 (2013)

    Article  Google Scholar 

  117. B. Ma, J. Li, Z. Peng, G. Zhang, J. Alloys Compd. 535, 95 (2012)

    Article  Google Scholar 

  118. J. Li, B. Ma, S. Min, J. Lee, Z. Yuan, L. Zang, Mater. Lett. 64, 814 (2010)

    Article  Google Scholar 

  119. H.X. Zheng, H. Xie, X.F. Guo, Acta Metall. Sin. (Engl. Lett.) 14, 72 (2001)

  120. G.C. Yang, H. Xie, W.X. Hao, Z.M. Zhang, X.F. Guo, Trans. Nonferrous Met. Soc. China 16, 290 (2006)

    Article  Google Scholar 

  121. H. Xie, J. Sun, G.C. Yang, Y.Z. Chen, Z.L. Lu, Mater. Sci. Eng. A 457, 33 (2007)

    Article  Google Scholar 

  122. B.C. Luo, X.R. Liu, B. Wei, J. Appl. Phys. 106, 053523 (2009)

    Article  Google Scholar 

  123. N. Wang, L. Zhang, Y.L. Peng, W.J. Yao, J. Alloys Compd. 663, 379 (2016)

    Article  Google Scholar 

  124. J.T. Zhang, Y.H. Wang, X.C. Cui, J.B. Lin, Mater. Sci. (MEDŽIAGOTYRA) 19, 373 (2013)

    Google Scholar 

  125. N. Liu, J. Non-Cryst. Sol. 358, 196 (2012)

    Article  Google Scholar 

  126. N. Liu, F. Liu, Z. Chen, G. Yang, C. Yang, Y. Zhou, J. Mater. Sci. Technol. 28, 622 (2012)

    Article  Google Scholar 

  127. J.B. Guo, C.D. Cao, S.L. Gong, R.B. Song, X.J. Bai, Trans. Nonferrous Met. Soc. China 23, 731 (2013)

    Article  Google Scholar 

  128. J. He, J.Z. Zhao, L. Ratke, Acta Mater. 54, 1749 (2006)

    Article  Google Scholar 

  129. J.Z. Zhao, Mater. Sci. Eng. A 454–455, 637 (2007)

    Article  Google Scholar 

  130. L. Zhao, J.Z. Zhao, Metall. Mater. Trans. A 43, 5019 (2012)

    Article  Google Scholar 

  131. L. Zhao, J.Z. Zhao, J. Mater. Res. 28, 1203–1210 (2013)

    Article  Google Scholar 

  132. C. Tian, G. Chen, L. Yang, J.Z. Zhao, Y.C. Zhang, Chin. J. Mater. Res. 18, 102 (2004). (in Chinese)

    Google Scholar 

  133. C. Tian, L. Yang, G. Chen, J.Z. Zhao, Chin. J. Mater. Res. 19, 639 (2005). (in Chinese)

    Google Scholar 

  134. X.F. Wang, J.Z. Zhao, J. He, Mater. Sci. Eng. A 460–461, 69 (2007)

    Google Scholar 

  135. J. He, H.Q. Li, J.Z. Zhao, C.L. Dai, Appl. Phys. Lett. 93, 131907 (2008)

    Article  Google Scholar 

  136. J. He, H.Q. Li, B.J. Yang, J.Z. Zhao, H.F. Zhang, Z.Q. Hu, J. Alloys Compd. 489, 535 (2010)

    Article  Google Scholar 

  137. J. He, H.X. Jiang, S. Chen, J.Z. Zhao, L. Zhao, J. Non-Cryst. Sol. 357, 3561 (2011)

    Article  Google Scholar 

  138. J. He, H.X. Jiang, J.Z. Zhao, N. Mattern, J. Eckert, Metall. Mater. Trans. A 42, 4100 (2011)

    Article  Google Scholar 

  139. J. He, N. Mattern, J. Tan, J.Z. Zhao, I. Kaban, Z. Wang, L. Ratke, D.H. Kim, W.T. Kim, J. Eckert, Acta Mater. 61, 2102 (2013)

    Article  Google Scholar 

  140. L. Granasy, L. Ratke, Scr. Metall. Mater. 28, 1329 (1993)

    Article  Google Scholar 

  141. J.H. Perepezko, C. Gaoup, K.P. Cooper, in Materials Processing in Reduced Gravity Environment of Space, 1982, p. 491

  142. M. Kohler, L. Ratke, I. Kaban, W. Hoyer, in 3rd International Conference on Advances in Solidification Processes, IOP Conf. Series: Mater. Sci. Eng. 27, 012005 (2011)

  143. Q. Sun, H.X. Jiang, J.Z. Zhao, J. He, Mater. Des. 91, 361 (2016)

    Google Scholar 

  144. C. Zener, J. Appl. Phys. 20, 950 (1949)

    Article  Google Scholar 

  145. P. Brian, H. Hales, AIChE J. 15, 419 (1969)

    Article  Google Scholar 

  146. L. Ratke, Prog. Astron. Aeron. AIAA 130, 661 (1990)

    Google Scholar 

  147. J.Z. Zhao, L. Ratke, B. Feuerbacher, Mod. Simul. Mater. Sci. Eng. 6, 123 (1998)

    Article  Google Scholar 

  148. I. Lifshitz, V. Slyozov, J. Phys. Chem. Solids 19, 35 (1961)

    Article  Google Scholar 

  149. A. Kneissl, H. Fischmeister, in 5th European Symposium on Materials Science under Microgravity, ESA SP-222, 1984, p. 63

  150. K. Torssell, Jernkno Ann. 151, 890 (1967)

    Google Scholar 

  151. S. Bergh, Jernkno Ann. 146, 862 (1962)

    Google Scholar 

  152. V. Levich, Physicochemical Hydrodynamics (Prentice Hall, Englewood Cliffs, NJ, 1962)

    Google Scholar 

  153. J.Z. Zhao, Ph.D. Thesis, Harbin Institute of Technology, 1994 (in Chinese)

  154. A. Bergman, H. Fredriksson, in Materials Processing in the Reduced Gravity Environment of Space, ed. by G.E. Rindone, 1982, p. 563

  155. H. Ahlborn, K. Lohberg, in 5th European Symposium on Materials Science under Microgravity, ESA SP-222, 1984, p. 55

  156. H. Ahlborn, S. Diefenbach, Mater. Sci. Eng. A 173, 133 (1993)

    Article  Google Scholar 

  157. K. Togano, Y. Yoshida, in Summary Review of Sounding Rocket Experiments, ed. by O. Minster, ESA SP-1132, 1991, p. 274

  158. L. Ratke, Mater. Sci. Eng. A 203, 399 (1995)

    Article  Google Scholar 

  159. H.J. Kang, P. Zhou, F. Cao, J. Zhu, Y.N. Fu, W.X. Huang, T.Q. Xiao, T.M. Wang, Acta Metall. Sin. (Engl. Lett.) 28, 940 (2015)

  160. H. Tang, L.C. Wrobel, Int. J. Eng. Sci. 43, 1234 (2005)

    Article  Google Scholar 

  161. H. Tang, L.C. Wrobel, in Surface Tension-Driven Flows and Applications, ed. by R. Savino (Research Signpost, Trivandrum-695, Kerla, India, 2006), p. 227

  162. L. Ratke, S. Diefenbach, B. Prinz, H. Ahlborn, in 8th European Symposium on Material Science under Microgravity Condition, ESA SP-333, 1992, pp. 495–501

  163. S. Diefenbach, Ph.D. Thesis, Ruhr-Universitat Bochum, 1994

  164. A. Ludwig, M. Wu, Metall. Mater. Trans. A 33, 3673 (2002)

    Article  Google Scholar 

  165. M. Wu, A. Ludwig, Adv. Eng. Mater. 5, 62 (2003)

    Article  Google Scholar 

  166. M. Wu, A. Ludwig, A. Bührig-Polaczek, M. Fehlbier, P.R. Sahm, Int. J. Heat Mass Transf. 46, 2819 (2003)

    Article  Google Scholar 

  167. M. Wu, A. Ludwig, L. Ratke, Metall. Mater. Trans. A 34, 3009 (2003)

    Article  Google Scholar 

  168. M. Wu, A. Ludwig, L. Ratke, Model. Simul. Mater. Sci. Eng. 11, 755 (2003)

    Article  Google Scholar 

  169. S. Taniguchi, J.K. Brimacombe, ISIJ Int. 34, 722 (1994)

    Article  Google Scholar 

  170. J. Rogers, R. Davis, Meter. Trans. A 21, 59 (1990)

    Article  Google Scholar 

  171. L. Ratke, H. Fischmeister, A. Kneissl, in 6th European Symposium on Material Science under Microgravity Condition, ESA SP-256, 1987, pp. 161–165

  172. L. Ratke, H. Frschmerister, A. Kneissl, in 7th European Symposium on Material Science under Microgravity Condition, ESA SP-295, 1989, pp. 135–139

  173. J. Alkemper, L. Ratke, Z. Metallkd. 85, 365 (1994)

    Google Scholar 

  174. T. Carberg, H. Fredriksson, Metall. Trans. A 11, 1665 (1982)

    Article  Google Scholar 

  175. H. Ahlborn, H. Neumann, H.J. Schott, Z. Metallkd. 84, 748 (1993)

    Google Scholar 

  176. J.Z. Zhao, J.J. Guo, J. Jia, Q.C. Li, Trans. Nonferrous Met. Soc. China 5, 67 (1995)

    Google Scholar 

  177. J.Z. Zhao, J.J. Guo, J. Jia, Q.C. Li, Trans. Nonferrous Met. Soc. China 5, 85 (1995)

    Google Scholar 

  178. J.Z. Zhao, J.J. Guo, J. Jia, Q.C. Li, Trans. Nonferrous Met. Soc. China 5, 105 (1995)

    Google Scholar 

  179. J.Z. Zhao, L. Ratke, Z. Metallkd. 89, 241 (1998)

    Google Scholar 

  180. J.Z. Zhao, L. Ratke, Mater. Lett. 38, 235 (1999)

    Article  Google Scholar 

  181. J.Z. Zhao, S. Drees, L. Ratke, Mater. Sci. Eng. A 282, 262 (2000)

    Article  Google Scholar 

  182. J.Z. Zhao, L. Ratke, Scr. Mater. 50, 543 (2004)

    Article  Google Scholar 

  183. H. Li, J.Z. Zhao, Q. Zhang, Jie He. Metall. Mater. Trans. A 39, 3308 (2008)

    Article  Google Scholar 

  184. H.L. Li, J.Z. Zhao, Appl. Phys. Lett. 92, 241902 (2008)

    Article  Google Scholar 

  185. J.Z. Zhao, Scr. Mater. 54, 247 (2006)

    Article  Google Scholar 

  186. J.Z. Zhao, H.L. Li, Q.L. Wang, J. He, Comp. Mater. Sci. 44, 400 (2008)

    Article  Google Scholar 

  187. Y. Liu, J.J. Guo, J. Jia, Y.Q. Su, H.S. Ding, J.Z. Zhao, X. Xue, J. Mater. Sci. Technol. 18, 241 (2002)

    Google Scholar 

  188. S. Chen, J.Z. Zhao, H.X. Jiang, J. He, Acta Metall. Sin. (Engl. Lett.) 28, 316 (2015)

  189. L.X. Lv, L. Zhen, C.Y. Xu, X.Y. Sun, J. Magn. Magn. Mater. 322, 978 (2010)

    Article  Google Scholar 

  190. B. Nestler, A.A. Wheeler, L. Ratke, C. Stocker, Phys. D 141, 133 (2000)

    Article  Google Scholar 

  191. G. Tegze, L. Granasy, in Modeling of Casting, Welding and Advanced Solidification Processes-XI, TMS (The Minerals, Metals and Materials Society), 2006

  192. J.C.R.E. Oliveira, M.H. Braga, R.D.M. Travasso, J. Non-Cryst. Sol. 354, 5340 (2008)

    Article  Google Scholar 

  193. M.H. Braga, J.C.R.E. Oliveira, L.F. Malheiros, J.A. Ferreira, Comp. Coup. Phase Diag. Thermochem. 33, 237 (2009)

    Article  Google Scholar 

  194. C.P. Wang, X.J. Liu, R.P. Shi, Appl. Phys. Lett. 91, 141904 (2007)

    Article  Google Scholar 

  195. R.P. Shi, Y. Wang, C.P. Wang, X.J. Liu, Appl. Phys. Lett. 98, 204106 (2011)

    Article  Google Scholar 

  196. R.P. Shi, C.P. Wang, D. Wheeler, X.J. Liu, Y. Wang, Acta Mater. 61, 1229 (2013)

    Article  Google Scholar 

  197. B.C. Luo, H.P. Wang, B.B. Wei, Chin. Sci. Bull. 54, 183 (2009)

    Google Scholar 

  198. W.L. Wang, Z.Q. Li, B. Wei, Acta Mater. 59, 5482 (2011)

    Article  Google Scholar 

  199. F. Wang, A. Choudhury, B. Nestler, in 3rd International Conference on Advances in Solidification Processes, 27, 2011, p. 012027

  200. F. Wang, A. Choudhury, C. Strassacker, B. Nestler, J. Chem. Phys. 137, 034702 (2012)

    Article  Google Scholar 

  201. W.J. Boettinger, J.A. Warren, C. Beckermann, A. Karma, Annu. Rev. Mater. Res. 32, 163 (2002)

    Article  Google Scholar 

  202. L.A. Susana, E.O. Aviala-Davila, V.M. lopez-Hirata, J. Mater. Res. 16, 975–981 (2013)

    Article  Google Scholar 

Download references

Acknowledgements

The authors are grateful for financial support from the National Natural Science Foundation of China (Grant Nos. 51271185, 51471173 and 51501207) and the China Manned Space Engineering (Grant No. TGJZ800-2-RW024).

Author information

Authors and Affiliations

  1. Institute of Metal Research, Chinese Academy of Sciences, Shenyang, 110016, China

    Jiu-Zhou Zhao, Tauseef Ahmed, Hong-Xiang Jiang, Jie He & Qian Sun

Authors
  1. Jiu-Zhou Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tauseef Ahmed
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hong-Xiang Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jie He
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Qian Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jiu-Zhou Zhao.

Additional information

Available online at http://link.springer.com/journal/40195

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhao, JZ., Ahmed, T., Jiang, HX. et al. Solidification of Immiscible Alloys: A Review. Acta Metall. Sin. (Engl. Lett.) 30, 1–28 (2017). https://doi.org/10.1007/s40195-016-0523-x

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40195-016-0523-x

Keywords

Search

Navigation