Skip to main content
Log in

Computer Simulation of Nonequilibrium Growth of Crystals in a Two-Dimensional Medium with a Phase-Separating Impurity

  • Published:
Journal of Statistical Physics Aims and scope Submit manuscript

Abstract

Two-dimensional nonequilibrium growth of crystals (quasistable faceted and dendritic) in the presence of a phase separating impurity is studied by computer simulation. It is shown that there is a gradual modification in this system from quasistable faceted growth to the formation of dendrites when the impurity concentration increases. If there is dendritic growth in the presence of a phase-separating impurity, the cyclic changes in the morphology, expressed through the periodic occurrence of tertiary branches of a dendrite, are observed when the phase-separating impurity concentration is raised. This behavior of the morphology is considered as a reentrant nonequilibrium phase transition.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

REFERENCES

  1. H. Haken, Synergetics(Springer-Verlag, Berlin, 1978).

    Google Scholar 

  2. P. Glandsorff and I. Prigogine, Thermodynamic Theory of Structure, Stability and Fluctuations(Wiley, New York, 1971).

    Google Scholar 

  3. J. Feder, Fractals(Plenum Press, New York, 1988).

    Google Scholar 

  4. J. S. Langer, Instabilities and pattern formation in crystal growth, Rev. Mod. Phys. 52:1 (1980).

    Google Scholar 

  5. A. Sole, Stagoskopie(Franz Deuticke, Vienna, 1960).

    Google Scholar 

  6. L. M. Martyushev, V. D. Seleznev, and S. A. Skopinov, Tech. Phys. Lett. 22:648 (1996).

    Google Scholar 

  7. P. K. Galenko and V. A. Zhuravlev, Physics of Dendrites(World Scientific, Singapore, 1994); R. Sasikumar and R. Sreenivasan, Acta Metall. Mater. 42:2381 (1994); Shu-Zu Lu, J. D. Hung, P. Gilgien, and W. Kurz, Acta Metall. Mater. 42:1653 (1994).

    Google Scholar 

  8. S. G. R. Brown, T. Williams, and J. A. Spittle, Acta Metall. Mater. 42:2893 (1994); D. B. Berg, S. A. Skopinov, et al., Izv. Akad. Nauk. SSSR Ser. Fiz. 55:175 (1991).

    Google Scholar 

  9. L. M. Martyushev, V. D. Seleznev, and S. A. Skopinov, Tech. Phys. Lett. 22:146 (1996); L. M. Martiouchev, V. D. Seleznev, and S. A. Skopinov, Crystallogr. Rep. 42:735 (1997).

    Google Scholar 

  10. A. A. Chernov, Modern Crystallography III: Crystal Growth(Springer-Verlag, Berlin, 1984).

    Google Scholar 

  11. D. D. Saratovkin, Dendritic Crystallization(Metallurgizdat, Moscow, 1957).

    Google Scholar 

  12. W. N. Izmailova and P. A. Rehbinder, The Formation of Structures in Protein Systems(Nauka, Moscow, 1974).

    Google Scholar 

  13. G. H. Brown and J. J. Wolken, Liquid Crystals and Biological Structures(Academic Press, New York, 1979).

    Google Scholar 

  14. R. I. Mints, S. A. Skopinov, et al., Russ. J. Phys. Chem. 66:183 (1992); R. I. Mints and D. B. Berg, Russ. J. Phys. Chem. 69:48 (1995) [in Russian]; R. I. Mints and D. B. Berg, In Surface Phenomena, SPIE Proceedings, Vol. 2731, p. 74; R. I. Mints, S. A. Skopinov, S. V. Yakovleva, et al., Studia Biophys. 133:221 (1989); M. Yasui and M. Matsushita, J. Phys. Soc. Jpn. 61:2327 (1992).

    Google Scholar 

  15. R. I. Mints, S. A. Skopinov, and S. V. Yakovleva, Tech. Phys. Lett. 14:12 (1988).

    Google Scholar 

  16. K. Shinoda, T. Nakogawa, B. Tamamushi, et al., Colloidal Surfactants. Some Physicochemical Properties(Academic Press, New York, 1963); W. N. Izmailova, G. P. Jampolskaia, and B. D. Summ, Surface Phenomena in Protein Systems(Chemistry, Moscow, 1988).

    Google Scholar 

  17. B. Chalmers, Principles of Solidification(Wiley, New York, 1964).

    Google Scholar 

  18. S.-C. Huang and M. E. Glicksman, Acta Metall. 29:717 (1981).

    Google Scholar 

  19. P. E. Cladis, Phys. Rev. Lett. 35:48 (1975); P. E. Cladis, R. K. Bogardus, and D. Aadsen, Phys. Rev. A 18:2292 (1978).

    Google Scholar 

  20. P. E. Cladis, Mol. Cryst. Liquid Cryst. 67:177 (1981).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Martiouchev, L.M., Seleznev, V.D. & Skopinov, S.A. Computer Simulation of Nonequilibrium Growth of Crystals in a Two-Dimensional Medium with a Phase-Separating Impurity. Journal of Statistical Physics 90, 1413–1427 (1998). https://doi.org/10.1023/A:1023295815199

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1023295815199

Navigation