Thermodynamics of coherent interfaces under mechanical stresses. I. Theory

We present a thermodynamic theory of plane coherent solid-solid interfaces in multicomponent systems subject to nonhydrostatic mechanical stresses. The interstitial and substitutional chemical components are treated separately using chemical potentials and diffusion potentials, respectively. All interface excess quantities are derived using Cahn's (1979) generalized excess method without resorting to geometric dividing surfaces. We present expressions for the interface free energy as an excess quantity and derive a generalized adsorption equation and an interface Gibbs-Helmholtz equation that does not contain the interface entropy. The interface stress tensor emerges naturally from the generalized adsorption equation as an appropriate excess over bulk stresses and is shown to be generally nonunique. Another interface property emerging from the generalized adsorption equation is the interface excess shear. This property is specific to coherent interfaces and represents the thermodynamic variable conjugate to the shear stress applied parallel to the interface. The theory reveals a number of Maxwell relations describing cross effects between thermal, chemical, and mechanical responses of coherent interfaces. In Part II of this work, this theory will be applied to atomistic computer simulations of grain boundaries.