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Coherent Phase Diagrams in the Cluster Variation Approximation

Published online by Cambridge University Press:  15 February 2011

Didier De Fontaine
Didier De Fontaine*
Affiliation:
University of California, Department of Materials Science and Mineral Engineering, Berkeley, California, USA
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Abstract

Coherent phase diagrams are defined as pertaining to equilibria between phases which differ from one another merely by the distribution of different types of atoms on fixed crystallographic sites. Resulting ordered structures must then all be superstructures of one parent lattice, and corresponding phase diagrams are isomorphous to those of the Ising model with non–vanishing magnetic field. Rather complex phase diagrams can then be obtained from a single free energy functional by means of the cluster variation method. Calculated phase diagrams will be shown for the case of the fcc parent lattice with various positive and negative ratios of the values of second-to-first-neighbor pair interactions, this ratio being the only parameter which enters the calculation. Results will be compared to those of Monte Carlo calculations. The possibility of performing these first-principle calculations of coherent phase diagrams will be briefly touched upon.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 19: Symposium E – Alloy Phase Diagrams , 1982 , 149
Copyright
Copyright © Materials Research Society 1983

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References

REFERENCES

1. Faulkner, J. S. in: Progress in Materials Science, Christian, J. W., Haasen, P., Massalski, T. B. eds. (Pergamon, Oxford 1982) pp. 1–187 .Google Scholar
2. Moruzzi, V. L., Janak, J. F. and Williams, A. R., Calculated Electronic Properties of Metals (Pergamon, Oxford 1978).Google Scholar
3. Lam, P. K. and Cohen, M. L., Phys. Rev. B 24, 4224 (1981).CrossRefGoogle Scholar
4. Gautier, F., Ducastelle, F. and Giner, J., Phil. Mag. 31, 1373 (1975).CrossRefGoogle Scholar
5. Ducastelle, F. and Gautier, F., J. Phys. F 6, 2039 (1979).CrossRefGoogle Scholar
6. Bieber, A., Gautier, F., Treglia, G. and Ducastelle, F., Solid State Comm., 39, 149 (1981).CrossRefGoogle Scholar
7. Bieber, A. and Gautier, F., Solid State Comm., 38, 1219 (1981).CrossRefGoogle Scholar
8. Sanchez, J. M. and de Fontaine, D., Phys. Rev. B, 21, 216 (1980).CrossRefGoogle Scholar
9. Sanchez, J. M. and de Fontaine, D. in: Structure and Bonding in Crystals, O'Keeffe, M. and Navrotsky, A. eds. (Academic, N.Y. 1981) Vol II, pp.117-132.Google Scholar
10. Kanamori, J., Progr. Theor. Phys. 35, 66 (1966).CrossRefGoogle Scholar
11. Kanamori, J. and Kakehashi, Y., J. Phys. (Paris) 38, C7–C274 (1977).CrossRefGoogle Scholar
12. Allen, S. M. and Cahn, J. W., Acta Metall. 20, 423 (1970).CrossRefGoogle Scholar
13. Kudō, T. and Katsura, S., Progr. Theor. Phys. 56, 435 (1976).CrossRefGoogle Scholar
14. Kikuchi, R., Phys. Rev. 81, 988 (1951).CrossRefGoogle Scholar
15. Gratias, D., Sanchez, J. M. and de Fontaine, D., Physica (Utrecht) 113A, 315 (1982).Google Scholar
16. de Fontaine, D., Acta Metall. 23, 553 (1975).CrossRefGoogle Scholar
17. de Fontaine, D. in: Solid State Physics, Ehrenreich, H., Seitz, F., Turnbull, D. eds. (Academic, N.Y. 1979) Vol. 34, pp. 73–274.Google Scholar
18. Lifshitz, E. M., J. Phys. USSR, 7, 61, 251 (1942).Google Scholar
19. Sanchez, J. M., Gratias, D. and de Fontaine, D., Acta Cryst. A 38, 214 (1982).CrossRefGoogle Scholar
20. Sanchez, J. M. and de Fontaine, D., Phys. Rev. B, 25, 1759 (1982).CrossRefGoogle Scholar
21. de Fontaine, D. and Kikuchi, R. in: NBS Publication SP-496 (1978) pp. 99-103.Google Scholar
22. Kikuchi, R., Sanchez, J. M., de Fontaine, D. and Yamauchi, H., Acta Metall. 28, 651 (1980).CrossRefGoogle Scholar
23. Sanchez, J. M. and de Fontaine, D., Phys. Rev. B, 17, 2926 (1978).CrossRefGoogle Scholar
24. Sanchez, J. M., de Fontaine, D. and Teitler, W., Phys. Rev. B, 26, 1465 (1982).CrossRefGoogle Scholar
25. van Baal, C. M., Physica (Utrecht) 64, 571 (1973).CrossRefGoogle Scholar
26. Binder, K., Lebowitz, J. L., Phani, M. K. and Kalos, M. H., Acta Metall. 29, 1655 (1981).CrossRefGoogle Scholar
27. Bond, R. A. and Ross, D. K., J. Phys. F, 12, 597 (1982).CrossRefGoogle Scholar
28. Büth, J. and Inden, G., Acta Metall. 30, 213 (1982).CrossRefGoogle Scholar