Superficial stress and strain at coherent interfaces

Abstract The thermodynamics of a coherent interface separating two non-hydrostatically stressed crystals is examined using the Gibbsian paradigm of a dividing surface and associated superficial quantities. Cahn–Hilliard diffuse interface theory is used to derive equations governing the equilibrium composition, stress, and strain profiles through a planar surface of discontinuity. Expressions are then obtained for the superficial stress and strain (excess volume) assuming the isotropic elastic constants are independent of composition and the lattice parameter is a quadratic function of the composition. Materials parameters are identified for which the superficial stress becomes independent of the position of the dividing surface, and the dependence of the superficial stress on the application of a stress normal to the interface, as well as the strain components in the plane of the interface, is calculated for various compositional strains. The superficial stress is estimated to be of the order 1–10 3 dynes/cm and can be either positive or negative in sign.