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Phase Diagram Features Associated with Multicritical Points in Alloy Systems

Published online by Cambridge University Press:  15 February 2011

Samuel M. Allen  and
John W. Cahn
Samuel M. Allen
Affiliation:
Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
John W. Cahn
Affiliation:
Center for Materials Science, National Bureau of Standards, Washington, D.C. 20234
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Abstract

Many features in the vicinity of critical points in phase diagrams can be illustrated using a Landau type free energy expansion as a power series in one or more order parameters and composition. This simple approach can be used with any solution model. It also predicts limits to metastability, and is useful for understanding mechanisms of phase change. The theory is applied to all the critical points that can occur in binary systems according to a Landau theory: critical consolute points, order-disorder transitions, tricritical points, critical end points, as well as to systems in which two transitions such as chemical and magnetic ordering occur.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 19: Symposium E – Alloy Phase Diagrams , 1982 , 195
Copyright
Copyright © Materials Research Society 1983

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References

REFERENCES

1. Kadanoff, L.P. in: Phase Transitions and Critical Phenomena, Domb, C., Green, M.S. eds. (Academic Press, London 1976) p.1.Google Scholar
2. Pfeuty, P. and Toulouse, G., Introduction to the Renormalization Group and Critical Phenomena, (Wiley, London 1977).Google Scholar
3. Landau, L.D. and Lifshitz, E.M., Statistical Physics (Addison-Wesley, Reading MA 1958), chapter XIV.Google Scholar
4. Cahn, J.W., Acta Metall. 10, 907 (1962).CrossRefGoogle Scholar
5. Wurz, U., Ber. Bunsenges, Phys. Chem. 76, 360 (1972).CrossRefGoogle Scholar
6. Chanh, N.B. and Bastide, J.P., Bull. Soc. Chim. Fr., 1911 (1968).Google Scholar
7. Walker, C.B. and Keating, D.T., Phys. Rev. 130, 1726 (1963).CrossRefGoogle Scholar
8. Griffiths, R.B., “Critical and Multicritical Transformations”, to be published in Proceedings, International Conference on Solid-Solid Phase Transformations, (TMS-AIME, Warrendale, PA, 1983) p. 15.Google Scholar
9. Inden, G., Bull. Alloy Phase Diagrams 2, 412 (1982).Google Scholar
10. Swann, P.R., Duff, W.R., and Fisher, R.M., Trans. Metall. Soc. AIME 245, 851 (1969).Google Scholar
11. Allen, S.M. and Cahn, J.W., Acta Metall. 23, 1017 (1975).Google Scholar
12. Langer, J.S., Acta Metall. 21, 1649 (1973).CrossRefGoogle Scholar
13. Cook, H.E. and Hilliard, J.E., Trans. Metall. Soc. AIME 233, 142 (1965).Google Scholar
14. Gaunt, D.S. and Baker, G.A., Phys. Rev. B 1, 1184 (1970).CrossRefGoogle Scholar
15. Allen, S.M. and Cahn, J.W., Acta Metall. 24, 425 (1976).Google Scholar
16. Goodman, D., Cahn, J.W. and Bennett, L.H., Bull. Alloy Phase Diagrams 2, 29 (1981).CrossRefGoogle Scholar
17. Bragg, W.L. and Williams, E.J., Proc. Roy. Soc. London A145, 699 (1934); A151, 540 (1935).Google Scholar
18. Inden, G. and Pitsch, W., Z. Metallk. 62, 627 (1971).Google Scholar
19. Allen, S.M. and Cahn, J.W., Acta Metall. 20, 423 (1972)Google Scholar
20. Inden, G., Acta Metall. 22, 945 (1974).CrossRefGoogle Scholar
21. When Fηηη is not required to be identically zero by symmetry, a second order Mansition can nonetheless occur [3] at the point of intersection if any of the curves Fηη = 0 and Fηηη = 0. This critical point is topologically analogous to a eutectic ecept that all three phases have become identical. Three two-phase coexistence fields radiate from this point. Each is similar to the two-phase field of Fig. 2. One of the phases is disordered, the other two differ in the sign of η, which in this case gives phases no longer identical by symmetry. Under some conditions more than three phases can meet at such a point. To the best of our knowledge no such critical point has ever been reported. An early theory of orderdisorder in face centered cubic crystals gave such a point with four coexisting phases [22].Google Scholar
22. Shockley, W., J. Chem. Phys. 6, 130 (1938).Google Scholar