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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
L.P. Kadanoff in: Phase Transitions and Critical Phenomena, C. Domb, M.S. Green eds. (Academic Press, London 1976) p.1.
P. Pfeuty and G. Toulouse, Introduction to the Renormalization Group and Critical Phenomena, (Wiley, London 1977).
L.D. Landau and E.M. Lifshitz, Statistical Physics (Addison-Wesley, Reading MA 1958), chapter XIV.
J.W. Cahn, Acta Metall. 10, 907 (1962).
U. Wurz, Ber. Bunsenges, Phys. Chem. 76, 360 (1972).
N.B. Chanh and J.P. Bastide, Bull. Soc. Chim. Fr., 1911 (1968).
C.B. Walker and D.T. Keating, Phys. Rev. 130, 1726 (1963).
R.B. Griffiths, “Critical and Multicritical Transformations”, to be published in Proceedings, International Conference on Solid-Solid Phase Transformations, (TMS-AIME, Warrendale, PA, 1983) p.15.
G. Inden, Bull. Alloy Phase Diagrams 2, 412 (1982).
P.R. Swann, W.R. Duff, and R.M. Fisher, Trans. Metall. Soc. AIME 245, 851 (1969).
S.M. Allen and J.W. Cahn, Acta Metall. 23, 1017 (1975).
J.S. Langer, Acta Metall. 21, 1649 (1973).
H.E. Cook and J.E. Hilliard, Trans. Metall. Soc. AIME 233, 142 (1965).
D.S. Gaunt and G.A. Baker, Phys. Rev. B1, 1184 (1970).
S.M. Allen and J.W. Cahn, Acta Metall. 24, 425 (1976).
D. Goodman, J.W. Cahn and L.H. Bennett, Bull. Alloy Phase Diagrams 2, 29 (1981).
W.L. Rragg and E.J. Williams, Proc. Roy. Soc. London A145, 699 (1934); A151, 540 (1935).
G. Inden and W. Pitsch, Z. Metallk. 62, 627 (1971).
S.M. Allen and J.W. Cahn, Acta Metall. 20, 423 (1972)
G. Inden, Acta Metall. 22, 945 (1974).
When Fηηη is not required to be identically zero by symmetry, a second order transition 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 except 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 order-disorder in face centered cubic crystals gave such a point with four coexisting phases [22].
W. Shockley, J. Chem. Phys. 6, 130 (1938).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Allen, S.M., Cahn, J.W. Phase Diagram Features Associated with Multicritical Points in Alloy Systems. MRS Online Proceedings Library 19, 195–210 (1982). https://doi.org/10.1557/PROC-19-195
Published:
Issue Date:
DOI: https://doi.org/10.1557/PROC-19-195