Structure and energy of crystal interfaces I. formal development

A variational method is developed for calculating the energy of an interface between two crystals of arbitrary structures and relative orientations. The method takes account of details of the interaction potential between atoms and allows for all possible displacements of atoms near the interface but, by considering the Fourier transforms of all the quantities involved, the number of significant variational parameters is kept small. The form of the variational function is such that deductions can be made about the existence of cusped energy minima for certain simple matchings between the two crystal lattices. The formalism contains the dislocation model of a erystal boundary as a limiting case but also allows for calculations in more general situations