The Cluster Expansion Method
Chapter
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.
Keywords
Thermodynamic Limit Configurational Space Finite Order Cluster Algebra Cluster Expansion
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References
- 1.R. Kikuchi, Phys. Rev. 81, 988 (1951).MathSciNetADSMATHCrossRefGoogle Scholar
- 2.R. Kikuchi, Prog. Theor. Phys. Suppl. 35, 1 (1966).ADSGoogle Scholar
- 3.J. M. Sanchez, and D. de Fontaine Phys. Rev. B 17, 2926 (1978).MathSciNetADSCrossRefGoogle Scholar
- 4.J. M. Sanchez, and D. de Fontaine Phys. Rev. B 21, 216 (1980).ADSCrossRefGoogle Scholar
- 5.J.M. Sanchez, and D. de Fontaine Phys. Rev. B 25, 1759 (1982).ADSCrossRefGoogle Scholar
- 6.J. M. Sanchez, F. Ducastelle and D. Gratias, Physica A 128, 334 (1984).MathSciNetADSCrossRefGoogle 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)ADSCrossRefGoogle Scholar
- 11.C. Wolverton, M. Asta, H. Dreyssé, and D. de Fontaine Phys. Rev. B 44, 4914 (1991)ADSCrossRefGoogle Scholar
- 12.J. M. Sanchez Phys. Rev. B 48, 14013 (1993).ADSCrossRefGoogle Scholar
- 13.J. M. Sanchez, J. P Stark and V. L. Moruzzi Phys. Rev. B 44, 5411 (1991).ADSCrossRefGoogle Scholar
- 14.G. D. Garbulski and G. Ceder Phys. Rev. B 49, 6327 (1994).ADSCrossRefGoogle Scholar
- 15.A. Gonis, P. P. Singh, P. E. A. Turchi and X.-G. Zhang Phys. Rev. B 51, 2122 (1995).ADSCrossRefGoogle Scholar
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© Plenum Press, New York 1996