Interface stress for nonequilibrium microstructures in the phase field approach: Exact analytical results

An exact expression for the temperature-dependent interface stress tensor (tension) and energy is derived within a phase field approach. The key problem, of which part of the thermal energy should contribute to the surface tension, is resolved with the help of an analytical solution for a nonequilibrium interface. Thus, for a propagating interface at any temperature, the interface stress tensor represents biaxial tension with magnitude equal to the temperature-dependent interface energy. Explicit expressions for the distributions of interface stresses are obtained for a nonequilibrium interface and a critical nucleus. The results obtained are applicable for various phase transformations (solid-solid, melting-solidification, sublimation, etc.) and structural changes (twinning, grain evolution), and can be generalized for anisotropic interface energy, for dislocations, fracture, and diffusive phase transformations described by Cahn-Hilliard theory. DOI: 10.1103/PhysRevB.87.054112