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Phase-field Theory of Nucleation and Growth in Binary Alloys

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Interface and Transport Dynamics

Abstract

We present a phase field theory for binary crystal nucleation. Using the physical interface thickness, we achieve quantitative agreement with computer simulations and experiments for unary and binary substances. Large-scale numerical simulations are performed for multi-particle freezing in alloys. We deduce the Kolmogorov exponents for dendritic solidification and for the “soft-impingement” of crystallites interacting via diffusion fields.

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References

  1. Huisman, W. J., Peters, J. F., Zwanenburg, M. J., de Vries, S. A., Derry, T. E., Albernathy, D., van der Veen, J. F.: Layering of a liquid metal in contact with a hard wall. Nature 390 (1997) 379–381

    Article  Google Scholar 

  2. Davidchack, R. L., Laird, B. B.: Simulation of the hard-sphere crystal-melt interface. J. Chem. Phys. 108 (1998) 9452–9462

    Article  Google Scholar 

  3. Ohnesorge, R., Löwen, H., Wagner, H.: Density functional theory of crystal-fluid interfaces and surface melting. Phys. Rev. E 50 (1994) 4801–4809

    Article  Google Scholar 

  4. Granasy, L., Iglbi, F.: Comparison of experiments and modern theories of crystal nucleation. J. Chem. Phys. 107 (1997) 3634–3644

    Article  Google Scholar 

  5. Karma, A.: Phase–field formulation for quantitative modeling of alloy solidification. Phys. Rev. Lett. 87 (2001) 115701–1–115701–4

    Google Scholar 

  6. Warren, J. A., Boettinger, W. J.: Prediction of dendritic growth and microsegregation patterns in a binary alloy using the phase-field method. Acta Metall. Mater. 43 (1995) 689–703

    Google Scholar 

  7. Boettinger, W. J., Warren, J. A.: The phase-field method: Simulation of alloy dendritic solidification during recalescence. Metall. Mater. Trans. A 27 (1996) 657–669

    Article  Google Scholar 

  8. Broughton, J. Q., Gilmer G. H.: Molecular dynamics investigation of the crystal-fluid interface. I-VI. J. Chem. Phys. 79 (1983) 5090–5127

    Google Scholar 

  9. Grnasy, L.: Cahn—Hilliard-type density functional calculations for homogeneous ice nucleation in undercooled water. J. Mol. Struct. 485–486 (1999) 523–536

    Article  Google Scholar 

  10. Conti, M.: Growth of a needle crystal from an undercooled alloy melt. Phys. Rev. E 56 (1997) 3197–3202

    Article  Google Scholar 

  11. Kelton, K. F.: Crystal nucleation in liquids and glasses. Solid St. Phys. 45 (1991) 75–177

    Google Scholar 

  12. Kobayashi, R., Warren, J. A., Carter, W. C.: Vector-valued phase field model for crystallization and grain boundary formation. Physica D 119 (1998) 415–423

    Article  Google Scholar 

  13. Bâsz, L. A., Clancy, P.: The kinetics of crystal growth and dissolution from the melt in Lennard-Jones systems. J. Chem. Phys. 102 (1995) 8138–8148

    Article  Google Scholar 

  14. Taborek, P: Nucleation in emulsified supercooled water. Phys. Rev. B 32 (1985) 5902–5906

    Article  Google Scholar 

  15. Willnecker, R., Herlach, D. M., Feuerbacher, B.: Nucleation in bulk undercooled nickel-base alloys. Mater. Sci. Eng. 98 (1988) 85–88

    Article  Google Scholar 

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© 2003 Springer-Verlag Berlin Heidelberg

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Gránásy, L., Börzsönyi, T., Pusztai, T. (2003). Phase-field Theory of Nucleation and Growth in Binary Alloys. In: Emmerich, H., Nestler, B., Schreckenberg, M. (eds) Interface and Transport Dynamics. Lecture Notes in Computational Science and Engineering, vol 32. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-07969-0_18

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  • DOI: https://doi.org/10.1007/978-3-662-07969-0_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-07320-5

  • Online ISBN: 978-3-662-07969-0

  • eBook Packages: Springer Book Archive

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