A continuum description of partially coherent interfaces (Q1805329)

A continuum model for a two-phase crystal-crystal system is constructed which takes into account the interfacial structure. Following \textit{J. W. Cahn} and \textit{F. C. Larché} [J. Res. Natl. Bur. Standards 89, 467-500 (1984)], such a structure is parameterized by an ``interfacial structure tensor'' which is identically zero when the interface is coherent and different from zero in presence of misfit dislocations which break the local continuity of the lattice. A particular feature of the present paper is that it assumes a nonconvex interfacial energy density (with a sharp minimum associated with coherence) and combines it with a convex bulk energy density. The authors study a model system consisting of an elastic film on a rigid substrate and find a minimizing sequence of coherent and incoherent regions on the interface which accomodate both the misfit and the tendency of the interface to remain coherent. Such a sequence only appears after the system has reached a certain critical size.