Determining the Burgers vectors and elastic strain energies of interface dislocation arrays using anisotropic elasticity theory

Abstract

A formalism for describing interface dislocation arrays linking the Frank–Bilby equation and anisotropic elasticity theory under the condition of vanishing far-field stresses is developed. The present approach enables the determination of a unique reference state for interface misfit dislocations, within which the Burgers vectors of individual dislocations are defined and allows for the unequal partitioning of elastic fields between neighboring crystals. The elastic strain energies of interface dislocation arrays are computed using solutions for short-range elastic fields. Examples of applications to simple interfaces are given, namely symmetric tilt and twist grain boundaries, as well as a pure misfit heterophase interface.