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Kinetics of first-order phase transitions in the asymptotic stage

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Abstract

We construct an asymptotic theory that describes the kinetics of first-order phase transitions. The theory is a considerable refinement of the well-known Lifshits-Slezov theory. The main difference between the two is that the Lifshits—Slezov theory uses for the first integral of the kinetic equation an approximate solution of the characteristic equation, which is valid in the entire range of sizes except for the blocking point, i.e., it uses a nonuniformly applicable approximation. At the same time, the behavior of the characteristic solution near the blocking point determines the asymptotic behavior of the size distribution function of the nuclei for the new phase. Our theory uses a uniformly applicable solution of the characteristic equation, a solution valid at long times over the entire range of sizes. This solution is used to find the asymptotic behavior of all basic properties of first-order phase transitions: the size distribution function, the average nucleus size, and the nucleus density.

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References

  1. S. A. Kukushkin and A. V. Osipov, Prog. Surf. Sci. 51, 1 (1996).

    Article  Google Scholar 

  2. S. A. Kukushkin and A. V. Osipov, Khim. Fiz. 15, 5 (1996).

    Google Scholar 

  3. A. I. Olemskoi and I. V. Koplyk, Usp. Phys. Nauk 165, 1105 (1995) [Phys. Usp. 38, 1061 (1995)].

    Google Scholar 

  4. V. G. Boiko, Kh.-Í. Mogel’, V. M. Sysoev, and A. V. Chalyi, Usp. Phys. Nauk 161, No. 2, 77 (1991) [Sov. Phys. Usp. 34, 141 (1991)].

    Google Scholar 

  5. S. A. Kukushkin and V. V. Slezov, Dispersive Systems on Solid Surfaces: Mechanisms of Thin Film Formation [in Russian], Nauka, St. Petersburg (1996).

    Google Scholar 

  6. J. J. Kozak, Adv. Chem. Phys. 40, 229 (1979).

    Google Scholar 

  7. K. Binder and D. Stauffer, Adv. Phys. 25, 343 (1976).

    Article  ADS  Google Scholar 

  8. Yu. M. Mikhailova and L. A. Maksimov, Zh. Éksp. Teor. Fiz. 59, 1368 (1970) [Sov. Phys. JETP 32, 747 (1971)].

    Google Scholar 

  9. V. P. Skripov and A. V. Skripov, Usp. Phys. Nauk 128, 193 (1979) [Sov. Phys. Usp. 22, 389 (1979)].

    Google Scholar 

  10. A. V. Osipov, Thin Solid Films 227, 111 (1993).

    Article  Google Scholar 

  11. A. V. Osipov, Thin Solid Films 231, 173 (1995).

    Google Scholar 

  12. S. A. Kukushkin and A. V. Osipov, Phys. Rev. E 53, 4964 (1996).

    Article  ADS  Google Scholar 

  13. S. A. Kukushkin and A. V. Osipov, J. Chem. Phys. 107, 3247 (1997).

    Article  ADS  Google Scholar 

  14. S. A. Kukushkin and A. V. Osipov, J. Phys. Chem. Solids 58, 1115 (1997).

    Google Scholar 

  15. A. S. Zel’tser, T. K. Soboleva, and A. É. Filippov, Zh. Éksp. Teor. Fiz. 108, 356 (1995) [JETP 81, 193 (1995)].

    Google Scholar 

  16. S. A. Kukushkin and A. V. Osipov, Thin Solid Films 227, 119 (1993).

    Article  Google Scholar 

  17. S. A. Kukushkin and A. V. Osipov, Surf. Sci. 329, 135 (1995).

    Article  Google Scholar 

  18. L. D. Landau, Zh. Éksp. Teor. Fiz. 7, 627 (1937).

    Google Scholar 

  19. Ya. B. Zel’dovich, Zh. Éksp. Teor. Fiz. 12, 525 (1942).

    Google Scholar 

  20. C. N. Yang and T. D. Lee, Phys. Rev. 87, 404 (1952).

    Article  ADS  MathSciNet  Google Scholar 

  21. J. W. Cahn, Acta Metall. 3, 255 (1961).

    Google Scholar 

  22. N. G. van Kampen, Phys. Rev. 135, A362 (1964).

    Google Scholar 

  23. J. S. Langer, Ann. Phys. (N.Y.) 41, 108 (1967).

    Article  Google Scholar 

  24. M. E. Fisher, Physics (Long Island City, NY) 3, 255 (1967).

    Google Scholar 

  25. A. Z. Patashinskii and B. I. Shumilo, Zh. Éksp. Teor. Fiz. 77, 1417 (1979) [Sov. Phys. JETP 50, 712 (1979)].

    Google Scholar 

  26. A. A. Chernov, in Modern Crystallography, Vol. 3, Nauka, Moscow (1980), p. 7 [English transl.: Springer, Berlin (1984)].

    Google Scholar 

  27. E. M. Lifshitz and L. P. Pitaevskii, Physical Kinetics [in Russian], Nauka, Moscow (1979) [English transl.: Pergamon Press, Oxford (1981)].

    Google Scholar 

  28. A. V. Osipov, Fiz. Tverd. Tela (St. Petersburg) 36, 1213 (1994) [Phys. Solid State 36, 664 (1994)].

    Google Scholar 

  29. A. V. Osipov, J. Phys. D 28, 1670 (1995).

    Article  ADS  Google Scholar 

  30. O. M. Todes, Zh. Fiz. Khim. 20, 630 (1946).

    Google Scholar 

  31. I. M. Lifshits and V. V. Slezov, Zh. Éksp. Teor. Fiz. 35, 479 (1958) [Sov. Phys. JETP 8, 331 (1959)].

    Google Scholar 

  32. I. M. Lifshits and V. V. Slezov, Fiz. Tverd. Tela (Leningrad) 1, 1401 (1959).

    Google Scholar 

  33. C. Z. Wagner, Elektrochem. 65, 581 (1961).

    Google Scholar 

  34. M. Kahlweit, Appl. Radiat. Isot. 5, 1 (1975).

    Google Scholar 

  35. K. Binder, Phys. Rev. B 15, 4425 (1977).

    Article  ADS  Google Scholar 

  36. J. A. Marquese and J. J. Ross, Chem. Phys. 79, 373 (1983).

    ADS  Google Scholar 

  37. M. Tokuyama and K. Kawasaki, Physica A 123, 386 (1984).

    Article  ADS  Google Scholar 

  38. G. Venzl, Phys. Rev. A 31, 3431 (1985).

    Article  ADS  Google Scholar 

  39. P. W. Voorhees, J. Stat. Phys. 38, 231 (1985).

    Article  Google Scholar 

  40. M. Marder, Phys. Rev. A 36, 858 (1987).

    ADS  Google Scholar 

  41. A. Nakahara, T. Kawakatsu, and K. Kawasaki, J. Chem. Phys. 95, 4407 (1991).

    Article  ADS  Google Scholar 

  42. S. A. Kukushkin, Acta Metall. Mater. 43, 1484 (1994).

    Google Scholar 

  43. V. V. Slezov, Phys. Rev. 17, 1 (1995).

    Google Scholar 

  44. A. H. Nayfeh, Perturbation Methods, Wiley, New York (1973).

    Google Scholar 

  45. V. V. Slezov, J. Phys. Chem. Solids 39, 367 (1978).

    Google Scholar 

  46. F. M. Kuni and A. P. Grinin, Kolloidn. Zh. 46, 460 (1984).

    Google Scholar 

  47. R. E. Langer, Trans. Am. Math. Soc. 67, 461 (1949).

    MATH  MathSciNet  Google Scholar 

  48. I. Imai, Phys. Rev. 80, 1112 (1950).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  49. H. J. Moriguchi, J. Phys. Soc. Jpn. 14, 1771 (1959).

    MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, 199178, St. Petersburg, Russia

    S. A. Kukushkin & A. V. Osipov

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  1. S. A. Kukushkin
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  2. A. V. Osipov
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Zh. Éksp. Teor. Fiz. 113, 2193–2208 (June 1998)

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Kukushkin, S.A., Osipov, A.V. Kinetics of first-order phase transitions in the asymptotic stage. J. Exp. Theor. Phys. 86, 1201–1208 (1998). https://doi.org/10.1134/1.558591

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  • DOI: https://doi.org/10.1134/1.558591

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