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.