Hierarchy of Cluster Variational Methods on 3-Dimensional Lattices and Application to the Study of FCC Phase Diagrams

  • A. Finel
Part of the NATO ASI Series book series (NSSE, volume 163)


Closed form approximations for statistical systems, such as mean field theories or cluster variational technics, are very useful to calculate phase diagrams. The most popular and succesful closed form technic to date is Kikuchi’s Cluster Variation Method (CVM) [1]. The variety of problems that have been analysed with the CVM shows the importance of that technic (for a recent review, see [2]).


Free Energy Basic Cluster Calculate Phase Diagram Approximate Entropy Cluster Variation Method 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Kikuchi R., Phys. Rev., 81,988 (1951)MathSciNetADSzbMATHCrossRefGoogle Scholar
  2. 2.
    Mohri T., Sanchez J.M. and De Fontaine D., Acta Metall., 33, 1171 (1985)CrossRefGoogle Scholar
  3. 3.
    Finel A. and Ducastelle F., Europhys. Lett., 1, 135 (1986)ADSCrossRefGoogle Scholar
  4. 4.
    Diep H.T., Ghazali A., Berge B. and Lallemand P., Europhys. Lett., 2, 603 (1986)ADSCrossRefGoogle Scholar
  5. 5.
    Finel A., Thèse de Doctorat d’Etat, Université Paris VI, 1987Google Scholar
  6. 6.
    Kikuchi R. and Brush S.G., J. Chem. Phys., 47, 195 (1967)ADSCrossRefGoogle Scholar
  7. 7a.
    Schlijper A.G., J. Stat. Phys., 35, 285 (1984)MathSciNetADSCrossRefGoogle Scholar
  8. 7b.
    Schlijper A.G., J. Stat. Phys., 40, 1 (1985)MathSciNetADSCrossRefGoogle Scholar
  9. 8.
    Mackenzie N.D., J. Phys., A8, 102 (1975)ADSGoogle Scholar
  10. 9a.
    Shockley W., J. Chem. Phys. 6, 130 (1938)ADSCrossRefGoogle Scholar
  11. 9b.
    Gahn U., Z. Metallkunde, 64, 268 (1973)Google Scholar
  12. 9c.
    Buth J. and Inden G., Acta Met., 30, 213 (1982)CrossRefGoogle Scholar
  13. 10.
    Sanchez J. M., De Fontaine D. and Teitler W., Phys. Rev. B, 26, 1465 (1982)ADSCrossRefGoogle Scholar
  14. 11.
    Binder K., Z. Phys. B., 45, 61 (1981)ADSCrossRefGoogle Scholar
  15. 12a.
    Binder K., Lebowitz J. L., Phani M. K. and Kalos M. H., Acta Met., 29, 1655 (1981)CrossRefGoogle Scholar
  16. 12b.
    Binder K., Phys. Rev. Lett., 45, 811 (1980)ADSCrossRefGoogle Scholar
  17. 13.
    Lebowitz J. L., Phani M. K. and Styer D. F., J. Stat. Phys., 38, 413 (1985)ADSCrossRefGoogle Scholar
  18. 14.
    Styer D. F., Phani M. K. and Lebowitz J. L., Phys. Rev. B, 34, 3361 (1986)ADSCrossRefGoogle Scholar
  19. 15.
    Ackermann H., Crusius S. and Inden G., Acta Met., 34, 2311 (1986)CrossRefGoogle Scholar
  20. 16.
    Gahn U., J. Phys. Chem. Solids, 47, 1153 (1986)ADSCrossRefGoogle Scholar
  21. 17.
    Slawny J., J. Stat. Phys., 20, 711 (1979)MathSciNetADSCrossRefGoogle Scholar
  22. 18.
    Mackenzie N. D. and Young A. P., J. Phys. C, 14, 3927 (1981)ADSCrossRefGoogle Scholar
  23. 19.
    Styer D. F., Phys. Rev. B, 32, 393 (1985)ADSCrossRefGoogle Scholar
  24. 20.
    Kikuchi R., Prog. Th. Phys. Japan (in press)Google Scholar
  25. 21.
    Sanchez J. M. and De Fontaine D., Phys. Rev. B, 17, 2926 (1978)MathSciNetADSCrossRefGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1989

Authors and Affiliations

  • A. Finel
    • 1
  1. 1.Office National d’Etudes et de Recherches AérospatialesONERAChatillon CedexFrance

Personalised recommendations