Coherent phase equilibrium in alloys with congruent points

The effects of elastic stress on phase equilibrium are examined for an alloy system possessing a congruent point in the absence of stress. The stress-free molar free energies of each of the phases are represented by a Taylor series expansion in temperature and composition about the stress-free congruent point temperature and composition. This representation has enabled us to derive an analytical description of the stable and metastable coherent phase diagrams which are valid in the vicinity of the congruent point regardless of the detailed solution thermodynamics of the alloy. We find the following for stable coherent phase equilibrium: the exponents describing the power law temperature dependence of certain field lines can be altered due to elastic stress; phase compositions for alloy compositions along certain field lines can be independent of both temperature and alloy composition; and a jump in volume fraction of magnitude less than one is possible with a smooth change in temperature or composition. We find the following for metastable coherent phase equilibrium: regardless of the degree of elastic inhomogeneity, there can be at most one jump in the volume fraction with a smooth change in temperature or composition; two-phase equilibrium in single-phase regions of the stress-free phase diagram is possible; and the equilibrium state of the system can depend on the processing path used to reach a given temperature and alloy composition. We have employed the theory and known thermophysical data to estimate the importance of elastic stress on phase equilibrium in the Ni-V system.