On the isotropy of continuized dislocated crystals. II. The isotropy of diffusive properties

Abstract

The classical theory of the influence of single immobile dislocations on the diffusion of point defects cannot be applied to the description of the influence of a finite but very large number of dislocations on this diffusion, because in this case dissipative effects (due to dislocations) cannot be neglected. In this paper these dissipative effects are described by means of a generalized gauge procedure taking advantage of the existence of the short-range order in continuized dislocated crystals. It is shown that, for uniformly dense distributions of dislocations, the existence of dissipative effects means the existence of a (nonvanishing) scalar curvature of a conformally flat configurational space of a single diffusing point defect. Equations describing the interaction energy between dislocations and a diffusing point defect are proposed, and the contribution to this energy of elastic as well as inelastic interactions is discussed.