Eutectic and Peritectic Equilibria in Coherent Binary Alloys

Abstract

Phase equilibria in a coherent binary alloy for the eutectic and peritectic systems are ana lyzed in this study to construct a theoretical model that will provide conditions for three-phase equilibrium in the presence of coherency stress between the solid phases. Our analysis employs simple quadratic functions for the Gibbs energy for individual phases, considering the solid phases to be temperature-independent. To facilitate an analytical solution, we used simplified assumptions about the system, explicitly considering an infinite volume occupied by three phases and the solid phases being isotropic and linearly elastic. We use a mathematical optimization method, Lagrange multiplier, to minimize the functions of Gibbs free energy subject to the constraints of volume fractions and phase compositions that satisfy the equilibrium conditions. This theoretical study demonstrates the effect of coherency stress on invariant points of phase diagrams, including a liquid leveraging the original Larche-Cahn formulation to evaluate the impact of coherency stress on eutectic and peritectic points in binary alloys. The common tangent construction is not applicable in the presence of strain energy between the solids, and the Gibbs phase rule no longer holds. Our findings demonstrated that coherency stress has distinct consequences on the eutectic and peritectic equilibria due to the difference in compositions between one solid and liquid phase and the difference in the melting points of the solid phases; therefore, instead of forming the three-phase region, usual to eutectic equilibria, a two-phase region with one solid and liquid becomes more dominant in the peritectic equilibria.