The effect of capillarity on the chemical potential in interfaces

A theory of the effect of curvature on the chemical potential of atoms inside an interface, e.g. a grain boundary, is developed under the assumption that the interface is an ideal source or sink for vacancies. Three simple geometries are considered to illustrate the theory. Corrections to the chemical potential appear already in the first order in curvature. The magnitude of the correction term depends on the elastic properties of the phases forming the interface, its intrinsic structure and the relative size of the grains it separates. For migrating interfaces between dissimilar phases, the correction depends on the diffusivities and the molar volumes of the two phases, rather than on their elastic moduli. The implications of the theory for fine-grained materials are discussed.