The thermodynamics of a coherent interface

A Gibbsian thermodynamic description of a simple coherent interface in a nonhydrostatically stressed, N component, crystalline solid is developed. Interfacial excess properties are defined in a manner consistent with the thermodynamics of nonhydrostatically stressed crystalline solids. This formalism is then used to describe the relationship between the independent thermodynamic variables and the interfacial energy. A result of the crystalline nature of the solid is that the interfacial energy and the interfacial stress are distinct quantities. This difference, along with the presence of a nonhydrostatic stress, results in fundamentally different forms for the standard interfacial thermodynamic relationships. In particular, we show that the Gibbs adsorption isotherm for a coherent spherical misfitting particle in a matrix contains terms which are related to both interfacial and bulk stresses and that these terms can be dominant in certain cases.