Introduction

In Chapter 10, the force multipole and small inhomogeneous models for point defects in infinite homogeneous regions were described. The interaction of inhomogeneous inclusions with various types of stresses has been treated in Chapters 7 and 8. Consequently, there is no need in this chapter to devote further attention to interactions between point defects and stress in terms of the small inhomogeneous inclusion model. Attention is therefore focused on these interactions in terms of the force multipole model.

Section 11.2 includes a treatment of the interaction between a single point defect (represented by a force multipole) and a general internal or applied stress. In Section 11.3, the force multipole model is used to investigate the volume change due to a single point defect in a finite body possessing a traction-free surface, where the defect image stress can play an important role. Then, with Section 11.3 in hand, Section 11.4 takes up the particularly interesting problem of the behavior of a finite traction-free body filled with a statistically uniform distribution of point defects, which may, for example, be vacancies in thermal equilibrium or solute atoms dispersed throughout a solid solution. Analyses are given of the volume changes, macroscopic shape changes and lattice parameter changes (as measured by X-ray diffraction) produced by the defects. A demonstration is given of the intuitive result that a uniform concentration of point defects in a finite body with a traction-free surface produces a uniform average strain throughout the body. If the centers are spherically symmetric and act as centers of pure dilatation, the macroscopic body either expands or contracts uniformly throughout the body (depending upon whether the centers possess positive or negative strengths) with no change in body shape. If the centers possess lower symmetry, the body again expands or contracts uniformly but undergoes a macroscopic shape change, reflecting the symmetry of the defects.