Mechanical interactions between semicoherent heterophase interfaces and free surfaces in crystalline bilayers

Abstract

A force formalism is proposed to investigate the interactions between a semicoherent heterophase interface and free surfaces in anisotropic finite-thickness bilayers. The present approach enables the estimation of the mechanical forces acting on interfaces, which arise from inhomogeneous elastic fields between the neighboring materials. These short-range fields are produced by the superposition of coherency strains and the elastic strain fields of dislocation patterns, where the individual Burgers vectors are defined by requiring the global force balance on any internal plane perpendicular to the interfaces. Predictions in heterogeneous free-standing bilayers are compared to results for the homogeneous elasticity problem (i.e., both materials having the same stiffness) and the limiting case of infinite bicrystals. Examples of applications to pure misfit interfaces are given with controlled misfit dislocation spacings by continuously varying the alloy composition. The effect of dislocation density on the stability of semicoherent interfaces interacting with free surfaces is discussed in terms of the change in elastic strain energy of Pt/Pd bilayer systems.