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Ground State Analysis on the Fcc Lattice With Four Pair Interactions

Published online by Cambridge University Press:  01 January 1992

Gerardo D. Garbulsky ,
Patrick D. Tepesch  and
Gerbrand Ceder
Gerardo D. Garbulsky
Affiliation:
Massachusetts Institute of Technology, Department of Materials Science and Engineering, Cambridge, MA 02139
Patrick D. Tepesch
Affiliation:
Massachusetts Institute of Technology, Department of Materials Science and Engineering, Cambridge, MA 02139
Gerbrand Ceder
Affiliation:
Massachusetts Institute of Technology, Department of Materials Science and Engineering, Cambridge, MA 02139
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Abstract

We have partially solved the ground state problem of binary alloys on the fcc lattice with pair interactions up to the fourth nearest neighbor distance. Our results extend the study presented by Kanamori and Kakehashi [1], releasing the constraint they imposed on the nearest neighbor correlation. The solution we present increases the number of possible ground state structures by an order of magnitude with respect to previous results. We have applied both the polyhedron and the enumeration method. The latter proved more powerful when including interactions beyond the second nearest neighbor distance.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 291: Symposium O – Materials Theory and Modeling , 1992 , 259
Copyright
Copyright © Materials Research Society 1993

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References

1 Kanamori, J. and Kakehashi, Y., J.Phys. (Paris) Colloq. 38, C7–274 (1977).Google Scholar
2 Ceder, G., A Derivation of the Ising Model for the Computation of Phase Diagrams , to be published in Computational Materials Science (1992).Google Scholar
3 Wolverton, C., Ceder, G., de Fontaine, D. and Dreyssé, H. Phys.Rev. B 45, 13105 (1992).Google Scholar
4 Sanchez, J.M., Ducastelle, F., and Gratias, D., Physica A 128,334 (1984).Google Scholar
5 Kanamori, J., Prog. Theor. Phys. 35, 16 (1966).Google Scholar
6 Allen, S.M. and Cahn, J.W., Acta Metall. 20, 423 (1972).Google Scholar
7 Sanchez, J.M. and de Fontaine, D., Structure and Bonding in Crystals (Academic, New York, 1981), Vol.11 p. 117.Google Scholar
8 Ducastelle, F., Order and Phase Stability in Alloys , North Holland, New York (1991).Google Scholar
9 Chváltal, V., Linear Programming , W.H. Freeman and Company, New York (1983).Google Scholar
10A more limited version of this approach was applied in L.G. Ferreira, S.H. Wei and A. Zunger, Supercomputer Applications 5, 34 (1991). They were only interested in the ground state structures for a given set of interactions and they only included about 32,000 structures (up to volume 15).Google Scholar
11It could (and in fact does) happen that two different structures with the same volume have the same set of correlations. In this case we only keep one set of correlations to compute the ground states, but keep in mind that these two structures will be degenerated within the approximation used.Google Scholar