Introduction

The fundamentals necessary to analyze the interaction energies and forces thatcan occur between the various defects treated in this book are now in place. Theelastic fields produced by the defects, and the interactions between the defectsand various elastic fields, have been formulated in previous chapters.

The general procedure for determining the interaction between two defects is toobtain the elastic field due to one defect at the location of the other and thento determine the interaction of the latter defect with this field. Since thenumber of possible defect–defect interactions is far too large toconsider comprehensively, this final chapter is restricted to a limited numberof representative interactions, which serve to demonstrate basic methods.

Point defect–point defect interactions

First, a general formulation is given of the interaction energy between two pointdefects that are represented by force multipoles, as in Chapters 10 and 11.Following this, the interaction between two point defects, each possessing cubicdefect symmetry, is analyzed for the case of an isotropic system.

General formulation

The interaction energy between a single point defect and a general elastic fieldhas been formulated in Chapter 11 (see Eqs. (11.1)–(11.4)), and the displacementfield due to a force multipole is given by Eq. (10.10). The interaction energybetween two point defects, i.e., D1 and D2, can therefore be obtained byimagining that D2 is created at the origin in the presence of D1 at theposition, x, and using the above results for the interaction energy and requiredelastic field.