Interfacial Energy and Fine Defect Structures for Incoherent Films

This note summarizes recent results in which modern techniques of the calculus of variations are used to obtain qualitative features of film-substrate interfaces for a broad class of interfacial energies. In particular, we show that the existence of a critical thickness for incoherency and the formation of interfacial dislocations depend strongly on the convexity and smoothness of the interfacial energy function.