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Directional Solidification: Theoretical Methods and Current Understanding

  • Herbert Levine
Chapter
Part of the NATO ASI Series book series (NSSE, volume 183)

Abstract

The patterns formed via the directional solidification of binary mixtures are paradigmatic of the type of structures which can arise in non-equilibrium dissipative systems. This paper will review the current status of our attempts to understand these patterns. We will focus in turn on phenomena in shallow cell systems, the highly non-equilibrium deep cell regime and the transition to dendritic growth.

Keywords

Directional Solidification Amplitude Equation Crystal Anisotropy Oscillatory Instability Deep Cell 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Systems Far From Equilibrium, J.E. Wesfried, ed., Springer-Verlar, 1988.Google Scholar
  2. 2.
    For an introduction, see Langer, J.S., Rev. Mod. Phys. 52, 1 (1980).CrossRefGoogle Scholar
  3. 3.
    Mullins, W.W. and Sekerka, R.F., J. Appl. Phys. 34, 323 (1964).CrossRefGoogle Scholar
  4. 4.
    Levine, H., Rappel, W.J. and Riecke, H., ‘Resonant interactions and travelling solidification cells’, preprint.Google Scholar
  5. 5.
    Simon, A., Bechhoefer, J. and Libchaber, A., Phys. Rev. Lett. 61, 2574 (1988).CrossRefGoogle Scholar
  6. 6.
    Kessler, D., Koplik, J. and Levine, H., Adv. Phys. 37, 255 (1988); Langer, J.S., Chance and Matter, J. Souletie, ed., ( North-Holland, 1987 ); Brener, E. and Melnikov, V.I., preprint.CrossRefGoogle Scholar
  7. 7.
    Kessler, D. and Levine, H., ‘Linear stability of directional solidification cells’, preprint.Google Scholar
  8. 8.
    de Cheveigne, S., Guthmann, C. and Lebrun, M.M., J. de Physique 47, 2095 (1986).CrossRefGoogle Scholar
  9. 9.
    See C. Guthmann, this volume.Google Scholar
  10. 10.
    Kessler, D. and Levine, H., Phys. Rev. A 39, 3041 (1989).CrossRefGoogle Scholar
  11. 11.
    Misbah, C., Saito, Y. and Muller-Krumbhaar, H., preprint.Google Scholar
  12. 12.
    Wollkind, D.J., Oulton, D.B. and Sriranganthan, R., J. de Physique 45, 505 (9184) and references therein.CrossRefGoogle Scholar
  13. 13.
    See Brown, R., et al in Supercomputer Research in Chemistry and Chemical Engineering, K. Jensen, ed., ( ACS, Washington, 1987 ).Google Scholar
  14. 14.
    Riecke, H. and Papp, H.G., Phys. Rev. A 33, 547 (1987).CrossRefGoogle Scholar
  15. 15.
    See G. Faivre, this volume.Google Scholar
  16. 16.
    Rabaud, M., Mich all and, S. and Couder, Y., preprint.Google Scholar
  17. 17.
    Coullet, P., Gunratne, G. and Goldstein, R., preprint (1989).Google Scholar
  18. 18.
    Haug, P., preprint (1989).Google Scholar
  19. 19.
    Jones, G.A. and Proctor, M.R.E., Phys. Lett. A 121, 224 (1987).CrossRefGoogle Scholar
  20. 20.
    Ben-Amar, M. and Moussallam, B., Phys. Rev. Lett. 60, 317 (1988).CrossRefGoogle Scholar
  21. 21.
    Pelce, P. and Pumir, A., J. Cryst. Growth 73, 357 (1985).CrossRefGoogle Scholar
  22. 22.
    Kessler, D., Koplik, J. and Levine, H., Phys. Rev. A 34, 4980 (1986).CrossRefGoogle Scholar
  23. 23.
    Maashall, M., Ben-Amar, M. and Hakim, V. (preprint, 1989 ).Google Scholar
  24. 24.
    Dombre, T. and Hakim, V., Phys. Rev. A 36, 2811 (1987); Ben-Amar, M. and Moussallam, B., Phys. Rev. Lett. 60, 317 (1988).CrossRefGoogle Scholar
  25. 25.
    Karma, A. and Pelce, P., preprint (1989).Google Scholar
  26. 26.
    Pieters, R. and Langer, J.S., Phys. Rev. Lett. 56, 1948 (1986); Kessler, D. and Levine, H., Europhys. Lett. 4, 215 (1987).CrossRefGoogle Scholar
  27. 27.
    Kessler, D. and Levine, H., Phys. Rev. A 33, 2621, 2634 (1986); Bensimon, D., Phys. Rev. A 33, 1302 (1986).CrossRefGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1990

Authors and Affiliations

  • Herbert Levine
    • 1
  1. 1.Department of Physics and Institute for Nonlinear ScienceUniversity of California, San DiegoLa JollaUSA

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