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Morphological phase diagram of a spherical crystal growing under nonequilibrium conditions at the growth rate as a quadratic function of supersaturation

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Abstract

The complete morphological diagram of a spherical nucleus growing from a solution under nonequilibrium conditions at a local growth rate as a quadratic function of supersaturation is calculated for the first time on the basis of a linear analysis for morphological stability and the principle of maximum entropy production. The results of calculations are compared with those obtained previously for a spherical particle in the case of a linear dependence of the growth rate on the supersaturation.

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References

  1. M. C. Cross and P. C. Hohenberg, Rev. Mod. Phys. 65(1), 851 (1993).

    ADS  Google Scholar 

  2. E. Ben-Jacob and P. Garik, Nature 343, 523 (1990).

    Article  ADS  Google Scholar 

  3. W. Kurz and D. J. Fisher, Fundamentals of Solidification (Trans. Tech., Zurich, 1992).

    Google Scholar 

  4. L. M. Martyushev and V. D. Seleznev, Dokl. Akad. Nauk 371(4), 466 (2000) [Dokl. Phys. 45, 129 (2000)].

    Google Scholar 

  5. L. M. Martyushev, V. D. Seleznev, and I. E. Kuznetsova, Zh. Éksp. Teor. Fiz. 118(1), 149 (2000) [JETP 91, 132 (2000)].

    Google Scholar 

  6. H. Ziegler, in Progress in Solid Mechanics, Ed. by I. N. Sneddon and R. Hill (North-Holland, Amsterdam, 1963; Mir, Moscow, 1966), Vol. 4.

    Google Scholar 

  7. H. Ziegler, An Introduction to Thermomechanics (North-Holland, Amsterdam, 1983).

    Google Scholar 

  8. Y. Sawada, J. Stat. Phys. 34, 1039 (1984).

    Article  MathSciNet  Google Scholar 

  9. L. M. Martyushev, I. E. Kuznetsova, and V. D. Seleznev, Zh. Éksp. Teor. Fiz. 121(2), 363 (2002) [JETP 94, 307 (2002)].

    Google Scholar 

  10. L. M. Martyushev and E. M. Sal’nikova, Pis’ma Zh. Tekh. Fiz. 28(6), 57 (2002) [Tech. Phys. Lett. 28, 242 (2002)].

    Google Scholar 

  11. L. M. Martyushev and E. M. Sal’nikova, J. Phys.: Condens. Matter 15, 1137 (2003).

    ADS  Google Scholar 

  12. J. W. Cahn, W. B. Hillig, and G. W. Seers, Usp. Fiz. Nauk 91(4), 691 (1967); Acta Metall. 12, 1421 (1964).

    Google Scholar 

  13. A. A. Chernov, Kristallografiya 16(4), 842 (1971) [Sov. Phys. Crystallogr. 16, 734 (1971)].

    MathSciNet  Google Scholar 

  14. S. Corill and R. Parker, in Proceedings of International Conference on Crystal Growth, Boston, 1966 (London, 1967; Mir, Moscow, 1968).

  15. W. W. Mullins and R. F. Sekerka, J. Appl. Phys. 34, 323 (1963).

    Article  Google Scholar 

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Translated from Fizika Tverdogo Tela, Vol. 46, No. 11, 2004, pp. 2045–2050.

Original Russian Text Copyright © 2004 by Martyushev, Kuznetsova, Nazarova.

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Martyushev, L.M., Kuznetsova, I.E. & Nazarova, A.S. Morphological phase diagram of a spherical crystal growing under nonequilibrium conditions at the growth rate as a quadratic function of supersaturation. Phys. Solid State 46, 2115–2120 (2004). https://doi.org/10.1134/1.1825558

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  • DOI: https://doi.org/10.1134/1.1825558

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