Defect structures at thin film-substrate interfaces

We consider the loss of lattice coherence at a planar interface between a thin film and substrate. Coherence is determined locally at the interface by a relative deformation gradient at the interface. We construct an interfacial free energy density f^αs such that a fully coherent interface is a global minimizer of f^αs, and there are symmetry related local minima of f^αs corresponding to line defects at the interface. By considering both the interfacial energy and the elastic energy of the film, we calculate equilibrium states as a function of film thickness to predict both the loss of coherence and the geometric pattern of interfacial detects.