Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-25T15:42:41.610Z Has data issue: false hasContentIssue false
  • English
  • Français

Phase Stability and Diagrams from First Principles

Published online by Cambridge University Press:  01 January 1992

J.M. Sanchez  and
J.D. Becker
J.M. Sanchez
Affiliation:
Center for Materials Science and Engineering, The University of Texas at Austin, Austin, Texas 78712
J.D. Becker
Affiliation:
Center for Materials Science and Engineering, The University of Texas at Austin, Austin, Texas 78712
Get access

Abstract

First principles theories of alloy phase equilibrium have been successfully used in recent years to compute temperature-composition phase diagrams for solid state phases. One particular approach, originating with the successful phenomenological Ising models to describe the alloy Hamiltonian, uses a cluster expansion of the configurational energy in terms of short-ranged pair and many-body interactions. The approach is deeply rooted in our ability to compute accurate total energies of relatively complex compounds, using density functional theory in the local approximation, from which effective interactions may be obtained. Fundamental aspects of the method which include convergence of the cluster expansion, treatment of the configurational entropy and description of vibrational modes are reviewed. Applications of the theory are given for binary alloys in the Ru-Zr-Nb system using the Linear Muffin Tin Orbital method for the total energy calculations, the Cluster Variation method for the description of the configurational entropy, and the Debye-Gruneisen approximation for the vibrational modes. The results are used to compute the equilibrium phase diagram for the Zr-Nb system and to assess current experimental data on phase stability in the Ru-Nb system. In the latter case, the calculations indicate that the DO19 structure is a likely candidate structure for the experimentally observed hexagonal-based compound Ru3Nb. Investigation of the energies and interactions of tetragonal structures as a function of the c/a ratio suggest the L10 structure as a likely candidate for the observed tetragonal phase near 1:1 stoichiometry.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 291: Symposium O – Materials Theory and Modeling , 1992 , 115
Copyright
Copyright © Materials Research Society 1993

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1. Sanchez, J.M. and de Fontaine, D., Phys. Rev. B 17, 2926 (1978).Google Scholar
2. Kikuchi, R., Sanchez, J.M., de Fontaine, D., and Yamauchi, H., Acta Metall. 28, 651 (1980).Google Scholar
3. Sigli, C. and Sanchez, J.M., Acta Metall. 33, 1097 (1985).Google Scholar
4. Sanchez, J.M., Barefoot, J.R., Jarret, R.N., and Tien, J.K., Acta Metall. 32, 1519 (1984).Google Scholar
5. Dahmani, C.E, Cadeville, M.C., Sanchez, J.M., and Moran-Lopez, J.L., Phys. Rev. Lett. 55, 1208 (1985).Google Scholar
6. Kikuchi, R., Phys. Rev. 81, 988 (1951); J. Chem. Phys. 60, 1071 (1974).Google Scholar
7. Kohn, W. and Sham, L. J., Phys. Rev. 140, A1133 (1965); Hohenberg, P. and Kohn, W., ibid. 136, B864 (1964).Google Scholar
8. Moruzzi, V.L., Janak, J. F. and Williams, A. R., "Calculated Electronic Properties of Metals" (Pergamon, New York 1978).Google Scholar
9. Andersen, O.K, Jepsen, O., and Glötzel, D., "Highlights of Condensed Mater Theory", Proceedings of the International School of Physics Enrico Fermi, North-Holland, Amsterdam, 1985.Google Scholar
10. Yin, M.T and Cohen, M.L., Phys. Rev. Lett 45, 1004 (1980).Google Scholar
11. Wiliams, A.R, Gelatt, C.D., and Moruzzi, V.L., Phys. Rev. Lett. 44, 429 (1980).Google Scholar
12. Gelatt, C.D, Wiliams, A.R., and Moruzzi, V.L., Phys. Rev. B 27, 2005 (1985).Google Scholar
13. Faulkner, J.S, Prog. Mater. Sci. 27, pp. 1–187, 1982 (Pergamon Press).Google Scholar
14. Winter, H. and Stocks, G.M., Phys. Rev. B 27, 882 (1982).Google Scholar
15. Winter, H., Durham, P.J., and Stocks, G.M., J. Phys. F 14, 1047 (1984).Google Scholar
16. Sanchez, J.M Ducastelle, F. and Gratias, D., Physica 128A, 334 (1984).Google Scholar
17. Connolly, J.W.D. and Williams, A.R., Phys. Rev. B 27, 5169 (1983).Google Scholar
18. Terakura, K., Oguchi, T., Mohri, T., and Watanabe, K., Phys. Rev. B 35, 2169 (1987).Google Scholar
19. Mbaye, A.A, Ferreira, L.G., and Zunger, A., Phys. Rev. Lett. 58, 49 (1987).Google Scholar
20. Carlsson, A.E and Sanchez, J.M., Solid State Comm. 65, 527 (1988).Google Scholar
21. Mohri, T., Terakura, K., Oguchi, T. and Watanabe, K., Acta Metall. 36, 547 (1988).Google Scholar
22. Zunger, A., Wei, S.-H., Mbaye, A.A. and Ferreira, G.L., Acta Metall. 36, 2239 (1988).Google Scholar
23. Takizawa, S., Terakura, K. and Mohri, T., Phys. Rev. B 39, 5792 (1989).Google Scholar
24. Ferreira, L.G, Wei, S.-H. and Zunger, A., Phys. Rev. B 40, 3197 (1989); ibid. 41, 8240 (1990).Google Scholar
25. Sluiter, M., Fontaine, D.de Guo, X.Q. Podloucky, R. and Freeman, A.J., Physical Rev. B 42, 10460 (1990).Google Scholar
26. Sanchez, J.M, Stark, J.P. and Moruzzi, V.L., Phys. Rev. B 44, 5411 (1991).Google Scholar
27. Moruzzi, V.L., Janak, J. F. and Schwarz, K.,Phys. Rev B 37, 790 (1988).Google Scholar
28. Sanchez, J.M and Fontaine, D. de, in “Structure and Bonding in Crystals”, O'Keeffe, M. and Navrotsky, A. (Editors), Vol. II, p. 117, Academic Press, 1981.Google Scholar
29. Abriata, J.P and Bolcich, J.C., Bull. Alloy Phase Diag. 3, 34 (1982).Google Scholar
30. Popova, S.V, Intl. Cong. Cryst., 10th, Amsterdam, 7 Aug. 1975 , S99, Int. Union Cryst.Google Scholar
31. Hurley, G.F and Brophy, J.H., J. Less Comm. Met. 7, 267 (1964)Google Scholar
32. Das, B.K, Schmerling, M.A., and Lieberman, D.S., Mat. Sci. Eng. 6, 248 (1970).Google Scholar
33. Topor, L. and Kleppa, O.J., Met. Trans. A 19A, 1061 (1988).Google Scholar