Point defect interactions in harmonic cubic lattices

Publisher Website
Google Scholar
Abstract
If one applies continuum elasticity to the problem of the interaction between two similar point defects in a crystal then one finds that, to lowest order, the interaction energy , where R is the interdefect spacing, ξa(R) is the displacement field of the first defect evaluated at the position of the second, and each defect is simulated by a distribution of body force— a grad δ( r ). For an isotropic crystal div ξ a (R) vanishes and there is thus no interaction to this order. For this reason it is usually asserted that the lowest order interaction between two point defects is the induced interaction which is quadratic in the strains produced by one defect at the other and thus varies as |R| −6. In this paper we shall present a method of calculating the interaction E(R) on the basis of lattice theory. This method takes into account the discrete nature of the crystal throughout and can thus be applied when the interdefect spacing is comparable with the lattice parameter. We have chosen to apply the method to a lattice with cubic symmetry held together by nearest-neighbour forces which are such that the model crystal is elastically isotropic. We have then evaluated E for a number of close-pair separations. We find that E is both non-zero and anisotropic for such close pairs. Moreover, we can also determine the asymptotic form of E for large | R | and we find that the leading term is ∼ |R| −5, and anisotropic. We have then proceeded to treat close pairs of defects in an anisotropic cubic lattice.

This publication has 6 references indexed in Scilit: