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Abstract

The Cluster Expansion Method leading to the formal description of configurational functions in alloys is reviewed in the context of several recent developments, modifications and numerous applications. A general and rigorous formulation of the method is shown to unify the approaches proposed by the author and collaborators in 1984 with the concentration restricted sum method of Asta and co-workers.

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References

  1. R. Kikuchi, Phys. Rev. 81, 988 (1951).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  2. R. Kikuchi, Prog. Theor. Phys. Suppl. 35, 1 (1966).

    ADS  Google Scholar 

  3. J. M. Sanchez, and D. de Fontaine Phys. Rev. B 17, 2926 (1978).

    Article  MathSciNet  ADS  Google Scholar 

  4. J. M. Sanchez, and D. de Fontaine Phys. Rev. B 21, 216 (1980).

    Article  ADS  Google Scholar 

  5. J.M. Sanchez, and D. de Fontaine Phys. Rev. B 25, 1759 (1982).

    Article  ADS  Google Scholar 

  6. J. M. Sanchez, F. Ducastelle and D. Gratias, Physica A 128, 334 (1984).

    Article  MathSciNet  ADS  Google Scholar 

  7. K. Kawasaki, in Phase Transitions and Critical Phenomena, edited by C. Domb and M. S. Green, (Academic Press, New York, 1973), Vol. 2, p. 465.

    Google Scholar 

  8. F. Ducastelle, Order and Phase Stability in Alloys, (North Holland, Amsterdam, 1991).

    Google Scholar 

  9. D. de Fontaine, in Solid State Physics, edited by H. Ehrenreich and D. Turnbull, (Academic Press, New York, 1994), Vol. 47, p. 33.

    Google Scholar 

  10. A. Zunger, in Static and Dinamics of Alloy Phase Transformations, edited by P. E. A. Turchi and A. Gonis, NATO ASI Series. Series B, Physics. (Plenum Press, New York, 1994), Vol. 319, p. 361.

    Google Scholar 

  11. M. Asta, C. Wolverton, D. de Fontaine, and H. Dreyssé Phys. Rev. B 44, 4907 (1991)

    Article  ADS  Google Scholar 

  12. C. Wolverton, M. Asta, H. Dreyssé, and D. de Fontaine Phys. Rev. B 44, 4914 (1991)

    Article  ADS  Google Scholar 

  13. J. M. Sanchez Phys. Rev. B 48, 14013 (1993).

    Article  ADS  Google Scholar 

  14. J. M. Sanchez, J. P Stark and V. L. Moruzzi Phys. Rev. B 44, 5411 (1991).

    Article  ADS  Google Scholar 

  15. G. D. Garbulski and G. Ceder Phys. Rev. B 49, 6327 (1994).

    Article  ADS  Google Scholar 

  16. A. Gonis, P. P. Singh, P. E. A. Turchi and X.-G. Zhang Phys. Rev. B 51, 2122 (1995).

    Article  ADS  Google Scholar 

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© 1996 Plenum Press, New York

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Sanchez, J.M. (1996). The Cluster Expansion Method. In: Morán-López, J.L., Sanchez, J.M. (eds) Theory and Applications of the Cluster Variation and Path Probability Methods. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0419-7_11

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  • DOI: https://doi.org/10.1007/978-1-4613-0419-7_11

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-8043-6

  • Online ISBN: 978-1-4613-0419-7

  • eBook Packages: Springer Book Archive

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