As we have shown in Appendix A, lattice imperfec­tions, such as a self-interstitials, a small precipitate, or small dislocation loops can also be modeled as an inclusion. These can be created by transforming a region O in the perfect crystal to a different crystal structure. If the transformation strain is emn(R), then the displacement field outside this region is given by

d3 RG, y.k'(r, r’ + R)emn(R) [B20] where G is now the elastic Green’s function.

Again, far from the defect region where |r — r’| >> |R|, we may employ a Taylor series expansion for the Green’s function, and we end up with the multipole expansion of eqn [B9]. The mul­tipole tensors are now given by

Pjk Cjkmn d R emn(R)

Pjkl Cjkmn d RR1 emn(R)

d3RR/ Rp emn(R) tensors then encompasses their description by either Kanzaki forces or by transformation strains. These tensors, in particular the dipole tensor Pjk, serve as more general parameter for their properties.