Journal of Engineering Physics and Thermophysics

, Volume 73, Issue 6, pp 1236–1246 | Cite as

Quasistationary Forms of Crystal Growth in Locally Nonequilibrium Diffusion of Impurity

  • P. K. Galenko
  • D. A. Danilov


Isoconcentration forms of crystal growth are obtained in a quasistationary approximation using a model of locally nonequilibrium diffusion in high‐speed solidification of a binary system. Four isoconcentration forms of growth (an elliptic paraboloid, a paraboloid of revolution, a parabolic cylinder, and a parabolic plate) are found for crystals that grow along a selected coordinate at a constant velocity. In the isothermal case of nondiffusion solidification, i.e., when the velocity of crystal growth is equal to or higher than the rate of impurity diffusion, these surfaces have an arbitrary configuration.


Statistical Physic Crystal Growth Binary System Constant Velocity Impurity Diffusion 
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  1. 1.
    A. Papapetrou, Z. Kristallographie, 92, 89-98 (1935).Google Scholar
  2. 2.
    G. P. Ivantsov, Dokl. Akad. Nauk SSSR, 58, 567-569 (1947).Google Scholar
  3. 3.
    G. P. Ivantsov, Dokl. Akad. Nauk SSSR, 83, 573-575 (1952).Google Scholar
  4. 4.
    G. P. Ivantsov, in: A. V. Shubnikov and N. N. Sheftal' (eds.), Crystal Growth [in Russian], Vol. 3, Moscow (1961), pp. 75-84.Google Scholar
  5. 5.
    G. Horvay and J. W. Cahn, Acta Metallurgica, 9, No. 7, 695-705 (1961).Google Scholar
  6. 6.
    J. Langer, Rev. Modern Phys., 52, No. 1, 1-28 (1980).Google Scholar
  7. 7.
    W. Kurz and D. J. Fisher, Fundamentals of Solidification, 3rd edn., Aedermannsdorf (1992).Google Scholar
  8. 8.
    P. K. Galenko and V. A. Zhuravlev, Phys. Dendrites, Singapore (1994).Google Scholar
  9. 9.
    H. Muller-Krumbhaar and W. Kurz, in: P. Haasen (ed.), Phase Transformations in Materials, Weinheim (1991), pp. 553-632.Google Scholar
  10. 10.
    D. M. Herlach, Mater. Sci. Eng., R 12, Nos. 4-5, 177-272 (1994).Google Scholar
  11. 11.
    P. K. Galenko, Kristallografia, 38, No. 6, 238-244 (1993).Google Scholar
  12. 12.
    P. K. Galenko, Dokl. Ross. Akad. Nauk, 334, No. 6, 707-709 (1994).Google Scholar
  13. 13.
    P. K. Galenko, Phys. Lett. A, 190, Nos. 3-4, 292-294 (1994).Google Scholar
  14. 14.
    P. K. Galenko, Zh. Tekh. Fiz., 65, No. 11, 110-119 (1995).Google Scholar
  15. 15.
    D. Jou, J. Casas-Vazquez, and G. Lebon, Extended Irreversible Thermodynamics, 2nd edn., Berlin (1996).Google Scholar
  16. 16.
    P. K. Galenko and S. Sobolev, Phys. Rev. E, 55, No. 1, 343-352 (1997).Google Scholar
  17. 17.
    P. K. Galenko and D. A. Danilov, Phys. Lett. A, 235, No. 3, 271-280 (1997).Google Scholar
  18. 18.
    L. E. Él'sgol'ts, Differential Equations and Variational Calculus [in Russian], Moscow (1969).Google Scholar
  19. 19.
    P. K. Galenko and D. A. Danilov, J. Crystal Growth, 197, No. 4, 992-1002 (1999).Google Scholar
  20. 20.
    J. S. Langer and H. Muller-Krumbhaar, Acta Metallurgica, 26, No. 6, 1681-1695 (1978).Google Scholar
  21. 21.
    P. Pelcé, Dynamics of Curved Front, New York (1988).Google Scholar
  22. 22.
    D. A. Kessler, J. Koplik, and H. Levine, Advanced Physics, 37, No. 2, 255-269 (1988).Google Scholar
  23. 23.
    J. J. Xu, Interfacial Wave Theory of Pattern Formation, Berlin (1997).Google Scholar

Copyright information

© Plenum Publishing Corporation 2000

Authors and Affiliations

  • P. K. Galenko
    • 1
  • D. A. Danilov
    • 1
  1. 1.Udmurt State UniversityIzhevskRussia

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