Elastic energy of regular hexagonal networks of intrinsic dislocations at interfaces separating media with isotropic elasticities

Abstract

The stored elastic energy E _s, per unit surface area, related to a regular hexagonal network of dislocations lying on a planar interface separating two elastically isotropic media has not yet been formulated into analytical expressions, except in the simple case expression of identical media and pure screw dislocations. In this work, a general closed expression for E _s is obtained for intrinsic dislocations from an approach based on a Fourier series analysis proposed previously by one of the authors. This expression can take account of a twist angle ψ and of a misfit [sgrave] in the boundary plane. Numerical applications are presented, relative to two usual cases: firstly, twist boundaries with pure screw intrinsic dislocations, for which a comparison is made with a previous result in the literature; secondly an interphase boundary containing pure edge Shockley intrinsic dislocations, namely Si/CoSi₂.