Evaluation of interfacial excess contributions in different phase-field models for elastically inhomogeneous systems

In elastically inhomogeneous solid materials, the presence of strains causes changes in both morphology and phase equilibria, thereby changing the mechanical and chemical properties. For any given initial phase- and grain-structure, it is difficult to determine experimentally or analytically these changes in properties. Phase-field models coupled with micro elasticity theory can be used to predict the morphological and chemical evolution of such strained systems, but their accuracy with respect to interfacial excess contributions has not been tested extensively. In this study, we analyse three existing phase-field schemes for coherent two-phase model systems and a Cu6Sn5-Bct-Sn system. We compare the chemical composition and stress state obtained in the simulations with analytical values calculated from Johnson's (Johnson 1987 Metall. Trans. A 18 233-47) model. All schemes reproduce the shift in chemical composition, but not the strains. This deviation is due to excess interfacial energy, stresses, and strains not present in the analytical results, since all three schemes are based on assumptions different from the stress and strain relations at equilibrium. Based on this analysis, we introduce a new scheme which is consistent with the analytical calculations. We validate for the model system that this new scheme quantitatively predicts the morphological and chemical evolution, without any interfacial excess contributions and independent of the diffuse interface width.