The Continuum Theory of Lattice Defects

The chapter presents a discussion on the continuum theory of lattice defects. The continuum analog of a crystal containing imperfections is an elastic body in a state of stress not produced by surface and body forces. The appropriate tool for handling the “continuum theory of lattice defects” is thus the usual theory of elasticity modified to include internal stress. Unlike the residual stresses encountered in engineering practice, these internal stresses have to be considered as capable of moving about in the medium. Recent interest in solid state physics has stimulated further development. The discussion of this chapter emphasizes on some of the background principles and illustrates them by specific examples chosen to bring out the peculiar features involved. Naturally, the continuum theory can hardly be expected to answer questions of current interest about the more intimate behavior of lattice defects (for example, the binding energy of two adjacent point defects). On the other hand, the theory perhaps suffers from the disadvantage that its limitations are more immediately obvious than are those of other approximate methods that have to be used in dealing with the solid state, for it sometimes gives good results even in what appear to be extreme cases. The theory of elasticity is concerned with the relation between the deformation of a body and the energy content of itself and its surroundings. The chapter also discusses specification of internal stress, including the Somigliana dislocations and the incompatibility tensor.