Coherent phase equilibria of systems with large lattice mismatch

In many metallurgical applications, an accurate knowledge of miscibility gaps and spinodal decompositions is highly desirable. Some binary systems where the main constituents of the same crystal structures have similar lattice parameters (less than 15% difference) reveal a composition, temperature shift of the miscibility gap due to lattice coherency. So far, the well-known Cahn's approach is the only available calculation method to estimate the coherent solid state phase equilibria. Nevertheless, this approach shows some limitations, in particular it fails to predict accurately the evolution of phase equilibria for large deformation, i.e. the large lattice parameter difference (more than 5%). The aim of this study is to propose an alternative approach to overcome the limits of Cahn's method. The elastic contribution to the Gibbs energy, representing the elastic energy stored in the coherent boundary, is formulated based on the linear elasticity theory. The expression of the molar elastic energy corresponding to the coherency along both directions [100] and [111] has been formulated in the small and large deformation regimes. Several case studies have been examined in cubic systems, and the proposed formalism is showing an appropriate predictive capability, making it a serious alternative to the Cahn's method. The present formulation is applied to predict phase equilibria evolution of systems under other stresses rather than only those induced by the lattice mismatch. The elastic contribution to the Gibbs energy, representing the elastic energy stored in the coherent boundary, is formulated based on the linear elasticity theory in both the small and large deformation regimes. Several case studies have been examined in cubic systems, and the proposed formalism is showing an appropriate predictive capability.