On the theory of diffusion relaxation in polycrystals

Abstract

The presence of impurities in a crystal lattice is one of the causes of anelasticity of solids. Impurities in single crystals may lead to relaxation of the Snoek [1] and Zener [2] type, and affect the level of dislocation internal friction [3]. In polycrystals there is yet another mechanism of relaxation, i.e., the “uphill” diffusion of impurity atoms in a random elastic stress field produced by the deformation of randomly oriented crystals. This mechanism may contribute to the internal friction, elastic aftereffect and transient creep. Diffusion relaxation of this kind was first analyzed by Zener [4] who, having concluded that the difference between the relaxation and nonrelaxation moduli cannot be accurately calculated, estimated the order of magnitude of this difference; he based this estimation on the calculation of a second-order moment function from the reciprocal of the Young's modulus. An implicit assumption in Zener's model is that the elastic strain of a crystal is determined only by the orientation of its crystallographic axes and on the external applied force field, being independent of the strains of adjacent crystals. The inadequacy of such a model for a polycrystal is evident. Moreover, this approach does not allow to obtain the distribution function of relaxation times. An accurate computation of the intensity of relaxation in polycrystals of an arbitrary crystal symmetry, which takes into account pair correlations between the separate grains, is presented in this article.