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Statistical mechanical theories of freezing: An overview

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Abstract

Recent progress in the microscopic description of the liquid-solid coexistence is examined critically and put into historical perspective. The emphasis is on the density functional theories, including some of their more controversial aspects. The underlying physical freezing mechanism is discussed in detail.

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References

  1. W. Sutherland,Phil. Mag. Ser. 5 32:31 (1891); L. Brillouin, Phys. Rev.54:916 (1938); M. Born,J. Chem. Phys. 7:591 (1939).

    Google Scholar 

  2. R. Brout,Phase Transitions (Benjamin, New York, 1965), Section 4.1.

    Google Scholar 

  3. R. Lovett,J. Chem. Phys. 66:1225 (1977); T. Yoshida and H. Kudo, Prog. Theor. Phys.59:393 (1978); J. S. Hoye,Physica 91A:143 (1978); R. Lovett and F. P. Buff,J. Chem. Phys. 72:2425 (1980).

    Google Scholar 

  4. F. A. Lindemann,Phys. Z. 11:609 (1910).

    Google Scholar 

  5. J. P. Hansen and L. Verlet,Phys. Rev. 184:150 (1969).

    Google Scholar 

  6. D. Stroud and N. W. Ashcroft,Phys. Rev. B 5:371 (1972).

    Google Scholar 

  7. J. G. Kirkwood and E. Monroe,J. Chem. Phys. 8:845 (1940); J. G. Kirkwood and E. Monroe,J. Chem. Phys. 9:514 (1941); J. G. Kirkwood and E. W. Boggs,J. Chem. Phys. 10:307 (1942).

    Google Scholar 

  8. M. Baus,Mol. Phys. 53:183 (1984).

    Google Scholar 

  9. R. Brout,Physica 29:1041 (1963); B. Jancovici,Physica 31:1017 (1965); J. D. Weeks, S. A. Rice, and J. J. Kozak,J. Chem. Phys. 52:2416 (1970); H. J. Raveché and C. A. Stuart,J. Chem. Phys. 63:1099 (1975); H. J. Raveché and R. F. Kayser,J. Chem. Phys. 68:3632 (1978); J. J. Kozak,Adv. Chem. Phys. 40:229 (1979).

    Google Scholar 

  10. L. Feijoo and A. Rahman,J. Chem. Phys. 77:5687 (1982).

    Google Scholar 

  11. R. L. Jacobs,J. Phys. C 16:273 (1983); R. L. Jacobs and K. H. Cheung,J. Phys. C 19:129 (1986).

    Google Scholar 

  12. T. V. Ramakrishnan and M. Yussouff,Solid State Commun. 21:389 (1977); T. V. Ramakrishnan and M. Yussouff,Phys. Rev. B 19:2775 (1979); M. Yussouff,Phys. Rev. B 23:5871 (1981); T. V. Ramakrishnan,Phys. Rev. Lett. 48:541 (1982).

    Google Scholar 

  13. V. N. Ryzhov and E. E. Tareeva,Teor. Math. Phys. 48:835 (1981); V. N. Ryzhov,Teor. Math. Phys. 55:399 (1983).

    Google Scholar 

  14. N. H. March and M. P. Tosi,Phys. Chem. Liq. 11:79, 89, 129 (1981); B. d'Aguanno, M. Rovere, M. P. Tosi, and N. H. March,Phys. Chem. Liq. 13:113 (1983); M. Rovere and M. T. Tosi,J. Phys. C 18:3445 (1985); P.Ballone, G. Pastore, M. Rovere, and M. Tosi,J. Phys. C 18:4011 (1985).

    Google Scholar 

  15. A. D. J. Haymet and D. W. Oxtoby,J. Chem. Phys. 74:2559 (1981).

    Google Scholar 

  16. D. W. Oxtoby and A. D. J. Haymet,J. Chem. Phys. 76:6262 (1982).

    Google Scholar 

  17. A. D. J. Haymet,J. Chem. Phys. 78:4641 (1983).

    Google Scholar 

  18. A. D. J. Haymet,Phys. Rev. Lett. 52:1013 (1984); A. D. J. Haymet,J. Phys. Chem. 89:887 (1985); S. J. Smithline and A. D. J. Haymet,J. Chem. Phys. 83:4103 (1985).

    Google Scholar 

  19. P. R. Harrowell, D. W. Oxtoby, and A. D. J. Haymet,J. Chem. Phys. 83:6058 (1985).

    Google Scholar 

  20. A. D. J. Haymet and D. W. Oxtoby,J. Chem. Phys. 84:1769 (1986).

    Google Scholar 

  21. C. Marshall, B. B. Laird, and A. D. J. Haymet,Chem. Phys. Lett. 112:320 (1985).

    Google Scholar 

  22. B. Bagchi, C. Cerjan, and S. A. Rice,J. Chem. Phys. 79:5595, 6222 (1983);Phys. Rev. B 28:6411 (1983); B. Bagchi, C. Cerjan, U. Mohanty, and S. A. Rice,Phys. Rev. B 29:2857 (1984); P. L. Radloff, B. Bagchi, C. Cerjan, and S. A. Rice,J. Chem. Phys. 81:1406 (1984); C. Cerjan, B. Bagchi, and S. A. Rice,J. Chem. Phys. 83:2376 (1985).

    Google Scholar 

  23. P. Tarazona,Mol. Phys. 52:81 (1984).

    Google Scholar 

  24. P. Tarazona,Phys. Rev. A 31:2672 (1985).

    Google Scholar 

  25. M. Baus and J. L. Colot,Mol. Phys. 55:653 (1985).

    Google Scholar 

  26. J. L. Colot and M. Baus,Mol. Phys. 56:807 (1985).

    Google Scholar 

  27. M. Baus and J. L. Colot,J. Phys. C 18:L365 (1985).

    Google Scholar 

  28. J. L. Colot, M. Baus, and H. Xu,Mol. Phys. 57:809 (1986).

    Google Scholar 

  29. M. Baus and J. L. Colot,J. Phys. C 19:L135 (1986); J. L. Barrat, M. Baus, and J. P. Hansen,Phys. Rev. Lett. 56:1063 (1986); H. Xu and M. Baus,Phys. Lett. A 117:127 (1986); M. Baus and J. L. Colot,J. Phys. C 19:L643 (1986); J. L. Barrat and J. P. Hansen,J. Phys. (Paris) 47:1547 (1986); J. L. Barrat, M.Baus, and J. P. Hansen,J. Phys. C 20:1413 (1987); J. L. Colot and M. Baus,Phys. Lett. A 119:135 (1986); J. L. Barrat,J. Phys. C 20:1031 (1987); J. L. Barrat,Europhys. Lett. 3:523 (1987).

    Google Scholar 

  30. G. J. Jones and U. Mohanty,Mol. Phys. 54:1241 (1985); G. J. Jones, preprint; M. V. Jaric and U. Mohanty,Phys. Rev. Lett. 58:230 (1987).

    Google Scholar 

  31. W. A. Curtin and N. W. Ashcroft,Phys. Rev. A 32:2909 (1985);Phys. Rev. Lett. 56:2775 (1986).

    Google Scholar 

  32. Y. Singh, J. P. Stoessel, and P. G. Wolynes,Phys. Rev. Lett. 54:1059 (1985).

    Google Scholar 

  33. J. P. Stoessel and P. G. Wolynes,J. Chem. Phys. (to appear).

  34. F. Igloi and J. Hafner,J. Phys. C 19:5799 (1986); F. Igloi,J. Phys. C 19:6907 (1986).

    Google Scholar 

  35. S. M. Moore and H. J. Raveché,J. Chem. Phys. 85:6039 (1986).

    Google Scholar 

  36. N. N. Bogoliubov,Problems of a Dynamical Theory in Statistical Physics (Gostekhidzdat, Moscow, 1946); inStudies in Statistical Mechanics, Vol. 1 (North-Holland, Amsterdam, 1962), Chapter 1; E. A. Arinshtein,Dokl. Akad. Nauk. SSSR 112:615 (1957); B. Zumino,Phys. Fluids 2:20 (1959); R. J. Lewis,J. Math. Phys. 2:222 (1961); T. Morita and K. Hiroike,Prog. Theor. Phys. 25:537 (1961); C. De Dominicis,J. Math. Phys. 3:983 (1962); F. H. Stillinger and F. P. Buff,J. Chem. Phys. 37:1 (1962); J. L. Lebowitz and J. K. Percus,J. Math. Phys. 4:116 (1963).

    Google Scholar 

  37. N. D. Mermin,Phys. Rev. 137:A1441 (1965).

    Google Scholar 

  38. C. Ebner, W. F. Saam, and D. Stroud,Phys. Rev. A 14:2264 (1976); A. J. M. Yang, P. D. Fleming, and J. H. Gibbs,J. Chem. Phys. 64:3732 (1976); W. F. Saam and C. Ebner,Phys. Rev. A 15:2566 (1977).

    Google Scholar 

  39. R. Evans,Adv. Phys. 28:143 (1979).

    Google Scholar 

  40. J. K. Percus, inStudies in Statistical Mechanics, Vol. 8 (North-Holland, Amsterdam, 1982).

    Google Scholar 

  41. J. S. Rowlinson and B. Widom,Molecular Theory of Capillarity (Clarendon Press, 1982).

  42. M. Baus,Mol. Phys. 50:543 (1983).

    Google Scholar 

  43. P. Hohenberg and W. Kohn,Phys. Rev. 136:B864 (1964).

    Google Scholar 

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  1. Chimie-Physique II, Université Libre de Bruxelles, B-1050, Bruxelles, Belgium

    M. Baus

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Baus, M. Statistical mechanical theories of freezing: An overview. J Stat Phys 48, 1129–1146 (1987). https://doi.org/10.1007/BF01009537

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