Incoherence at heterogeneous interfaces

To describe the small scale defect structure of incoherent interfaces in an elastic bi-crystal, we consider a multiscale variational model composed of two parts: a bulk energy density W and a nonconvex interfacial energy dens ity psi that depends on the microscopic lattice mismatch at the grain bound ary and the relative crystallographic normal. Mismatch is described using a referential coherence tensor that measures the relative misfit at the grai n boundary and serves to couple the bulk elastic deformation of the grains to small scale defect structures at the interface. Minimizing this energy y ields predictions for the distribution of defect microstructures at the int erface as a function of grain size, elastic: stiffness, and lattice mismatc h. Calculations for a heterophase (01)/(01) interface in a two-dimensional bi-crystal system are presented. (C) 1999 Elsevier Science Ltd. All rights reserved.