A CONTINUUM DESCRIPTION OF PARTIALLY COHERENT INTERFACES

A continuum model of a two-phase crystal-crystal system is constructed in which the structure of the interface between the phases is determi ned by energy minimization, rather than by being specified a priori. T he interfacial structure is parameterized by a variable ($) over cap H corresponding to the jump in the surface deformation gradient (or str ain) at the interface, so that coherence is defined locally by the con dition ($) over cap H = 0. The energy of the system is taken to be the sum of the bulk and interfacial energies, where the interfacial energ y density f(xs) depends on ($) over cap H. In order to explore how the equilibrium interfacial structure depends on the function f(xs)(($) o ver cap H), a model system consisting of an elastic film on a rigid su bstrate is studied, and the interfacial energy density is taken to be nonconvex with a sharp minimum associated with coherence. In this case , it can be shown that the energy of the system is driven to its infim um by separating the interface into coherent and incoherent regions, w hich may be viewed as a continuum analog to a partially coherent inter face. Further, this solution only appears above a certain critical thi ckness of the film, in agreement with misfit dislocation models of par tially coherent interfaces.