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Phase Transformations in Hexagonal-Close-Packed Alloys: Analysis with the Cluster Variation Method

Published online by Cambridge University Press:  01 January 1992

Ryan Mccormack
Affiliation:
Department of Materials Science and Mineral Engineering, University of California, and Materials Sciences Division, Lawrence Berkeley Laboratory, Berkeley, California 94720
Mark Asta
Affiliation:
Department of Materials Science and Mineral Engineering, University of California, and Materials Sciences Division, Lawrence Berkeley Laboratory, Berkeley, California 94720
Gerbrand Ceder
Affiliation:
Department of Materials Science, Massachusetts Institute of Technology, Cambridge, MA 02139
Didier de Fontaine
Affiliation:
Department of Materials Science and Mineral Engineering, University of California, and Materials Sciences Division, Lawrence Berkeley Laboratory, Berkeley, California 94720
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Abstract

We present a study of the hexagonal close-packed (hcp) Ising model for binary alloys within the cluster variation approximation. Groundstates of order stabilized by nearest-neighbor (NN) pair, triplet, and tetrahedron interactions were determined using the cluster configuration polyhedron method; no previous hcp ground-state study has considered all of these interactions. We predict physically realizable groundstates with stoichiometries A, AB (3 distinct structures), A2B, A3B, and A4B3. The previously unpredicted A4B3 structure is stabilized by multiatom (i.e. triplet, tetrahedron) interactions, while the others are stabilized by the two NN pair interactions. The Cluster Variation Method (CVM) was used to calculate the finite-temperature phase-equilibria for prototypical binary alloys. We present the first ordering phase diagrams computed with the CVM which contain all relevant groundstates for both isotropic and anisotropic NN pair interactions.

Type
Research Article
Copyright
Copyright © Materials Research Society 1993

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References

REFERENCES

1. Allen, S. M. and Cahn, J.W., Acta Met., 20, 423 (1972)Google Scholar
2. Kanamori, J., Progr. Theor. Phys., 35, 16 (1966)Google Scholar
3. Ducastelle, F., Order and Phase Stability in Alloys, Cohesion and Structure, Vol. 3, Eds. de Boer, F.R. and Pettifor, D.G. (North-Holland, Amsterdam, 1991)Google Scholar
4. Kikuchi, R., Phys. Rev., 81, 988 (1951)Google Scholar
5. Sanchez, J.M., Ducastelle, F., and Gratias, D., Physica 128A, 334 (1984)Google Scholar
6. Ceder, G., Thesis, PhD, Berkeley, U.C., 1991, (#9203517) available from University Microfilms International, 300 N. Zeeb Rd., Ann Arbor, MI 48106Google Scholar
7. Kikuchi, R. and Cahn, J.W., User Applications of Alloy Phase Diagrams. Ed. Kaufmann, L. (ASM International, 1987)Google Scholar
8. Gratias, D., Sanchez, J.M., and de Fontaine, D., Physica 113A, 315 (1982)Google Scholar
9. Mattheiss, T.H., Operations Research, 121, 247 (1973)Google Scholar
10. Kudō, T. and Katsura, S., Progr. Theor. Phys., 56(2), 435 (1976)Google Scholar
11. Kanamori, J., J. Phys. Soc. Jpn., 53(1), 250 (1984)Google Scholar
12. Singh, A.K. and Lele, S., Phil. Mag. B, 65(5), 967 (1992)Google Scholar
13. Singh, A.K. and Lele, S., Phil. Mag. B, 64(3), 275 (1991)Google Scholar
14. Singh, A.K., Singh, V., and Lele, S., Acta Metall. Mater., 39(11), 2847 (1991)Google Scholar
15. Bichara, C., Crusius, S., and Inden, G., Physica B, 182, 42 (1992)Google Scholar
16. Crusius, S. and Inden, G., Proc. Int'l Symp, on Ordering in Cond. Matter, ed. by Komura, S. and Furukawa, H. (Plenum Press, New York, 1988) p. 139 Google Scholar
17. Van Baal, C.M., Physica, 64, 571 (1973)Google Scholar
18. Sanchez, J.M., de Fontaine, D., and Teitler, W., Phys. Rev. B, 26(3), 1465 (1982)Google Scholar
19. Burley, D. M, Proc. Phys. Soc., 85, 1163 (1965)Google Scholar
20. Metcalf, B.D., Phys. Letters, 45A, 1 (1973)Google Scholar
21. Wannier, G.H., Phys. Rev., 79, 357 (1950)Google Scholar