Introduction

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

The general procedure for determining the interaction between two defects is to obtain the elastic field due to one defect at the location of the other and then to determine the interaction of the latter defect with this field. Since the number of possible defect–defect interactions is far too large to consider comprehensively, this final chapter is restricted to a limited number of 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 point defects that are represented by force multipoles, as in Chapters 10 and 11. Following this, the interaction between two point defects, each possessing cubic defect symmetry, is analyzed for the case of an isotropic system.

General formulation

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