Misfit dislocations arranged in a hexagonal network in anisotropic elasticity. Related displacement field and stored elastic energy

Abstract

A method presented in a previous paper to determine any biperiodic elastic displacement field (Bonnet, 1981) is developed analytically for a hexagonal network of misfit dislocations lying along a plane separating two different anisotropic crystals. The network is possibly non-regular. The three components of the displacement field are expressed, in both the crystals, as double Fourier series. Each harmonic term depends on coefficients calculated from the roots of a sextic polynomial whose coefficients generalize those established by Eshelby et al. (1953). For the particular case of a regular hexagonal network, analytical expressions are obtained for the stored elastic energy E s when (i) the Burgers vectors are parallel to the interface and (ii) each crystal has an elastic symmetry axis perpendicular to the interface. Applications to low angle twist boundaries parallel to (111) planes in f.c.c. materials (Al, Cu) and the heterotwin (111)Si‖(111)CoSi 2 interface show in fact small effects of the anisotropy of these crystals on the values of E s.