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Influence of a continuous quenching procedure on the initial stages of spinodal decomposition

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Zeitschrift für Physik B Condensed Matter

Abstract

Instead of the standard assumption in the theory of phase separation where an instantaneous quench from an initial equilibrium state to the final state in the two-phase region is assumed, we consider the more realistic situation that the change of the external control parameter (e.g. temperature) can only be performed with finite rates. During the initial stages of spinodal decomposition the system then has some “memory” of the states intermediate between the initial and the final one. This influence of the finite quench rate in continuous quenching procedures is studied within the linearized theory of spinodal decomposition, with the Langer-Baron-Miller decoupling, and with Monte Carlo simulations. Both the case of thermally activated mobilities (applicable to solid metallic alloys) and the case of nearly temperature-independent mobilities (applicable to fluid polymer mixtures) are treated, and possible experimental applications are discussed. We find drastic deviations from the standard instantaneous quench situations in all cases of experimental interest.

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References

  1. Recent reviews can be found in Refs. 2–4

  2. Gunton, J.D., San Miguel, M., Sahni, P.S.: In: Phase transitions and critical phenomena. Domb, C., Lebowitz, J.L. (eds.), Vol. 8, p. 267. New York, London: Academic Press 1983

    Google Scholar 

  3. Binder, K.: In: Condensed matter research using neutrons. Lovesey, S.W., Scherm, R. (eds.), p. 1. New York: Plenum Publ. Corp. 1984

    Google Scholar 

  4. Binder, K., Heermann, D.W.: In: Scaling phenomena in disordered systems. Pynn, R., Skjeltorp, T. (eds.), New York: Plenum Publ. Corp. 1985

    Google Scholar 

  5. Snyder, H.L., Meakin, P.A.: J. Chem. Phys.79, 5588 (1983)

    Google Scholar 

  6. Cahn, J.W., Hilliard, J.E.: J. Chem. Phys.28, 258 (1958); Cahn, J.W.: Trans. Metall. Soc. AIME242, 166 (1968)

    Google Scholar 

  7. Marro, J., Bortz, A.B., Kalos, M.H., Lebowitz, J.L.: Phys. Rev. B12, 2000 (1975)

    Google Scholar 

  8. Langer, J.S., Baron, M., Miller, H.D.: Phys. Rev. A11, 1417 (1975)

    Google Scholar 

  9. Billotet, C., Binder, K.: Z. Phys. B — Condensed Matter and Quanta32, 195 (1979)

    Google Scholar 

  10. Binder, K., Billotet, C., Mirold, P.: Z. Phys. B — Condensed Matter and Quanta30, 183 (1978)

    Google Scholar 

  11. Binder, K.: Phys. Rev. A29, 341 (1984)

    Google Scholar 

  12. Binder, K.: J. Chem. Phys.79, 6387 (1983)

    Google Scholar 

  13. Snyder, H.L., Meakin, P., Reich, S.: Macromolecules16, 757 (1983)

    Google Scholar 

  14. Hashimoto, T., Kumaki, J., Kawai, H.: Macromolecules16, 641 (1983)

    Google Scholar 

  15. Hashimoto, T., Sasaki, T., Kawai, H.: Macromolecules,17, 2812 (1984)

    Google Scholar 

  16. Sasaki, K., Hashimoto, T.: Macromolecules17, 2818 (1984)

    Google Scholar 

  17. Izumitani, T., Hashimoto, T.: J. Chem. Phys.83, 3694 (1985)

    Google Scholar 

  18. E.g. Agarwal, H., Herman, H.: Scr. Metall.7, 503 (1973)

    Google Scholar 

  19. Craievich, A.F., Olivieri, J.R.: J. Appl. Cryst.14, 444 (1981)

    Google Scholar 

  20. Acuna, R.J., Craievich, A.F.: J. Non-Cryst. Solids34, 13 (1979) Yokota, H.: J. Phys. Soc. Jpn.45, 29 (1978)

    Google Scholar 

  21. Heermann, D.W.: Phys. Rev. Lett.52, 1126 (1984); Z. Phys. B — Condensed Matter61, 311 (1985)

    Google Scholar 

  22. Grant, M., San Miguel, M., Vinals, S., Gunton, J.D.: Phys. Rev. B31, 302 (1985)

    Google Scholar 

  23. Cook, H.E.: Acta Metall.18, 297 (1970)

    Google Scholar 

  24. Houston, E.L., Cahn, J.W., Hilliard, J.E.: Acta Metall.14, 1685 (1966); for related later work, see also Craievich, A.F.: Phys. Status Solidi (a)28, 609 (1975)

    Google Scholar 

  25. For more details see Carmesin, H.-O.: Diplomarbeit, Johannes-Gutenberg-Universität, Mainz 1986 (unpublished)

  26. An alternative formulation more appropriate to describe coarsening is found in Horner, H., Jüngling, K.: Z. Phys. B — Condensed Matter and Quanta36, 97 (1979)

  27. Le Gouillou, J.C., Zinn-Justin, J.: Phys. Rev. B21, 3976 (1980)

    Google Scholar 

  28. Kawasaki, K.: In Phase transitions and critical phenomena. Domb, C., Green, M.S. (eds.), Vol. 2. New York: Academic Press 1972

    Google Scholar 

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Carmesin, H.O., Heermann, D.W. & Binder, K. Influence of a continuous quenching procedure on the initial stages of spinodal decomposition. Z. Physik B - Condensed Matter 65, 89–102 (1986). https://doi.org/10.1007/BF01308403

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  • DOI: https://doi.org/10.1007/BF01308403

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