The effect of diffusivity gradients on diffusion to dislocations

Abstract

The kinetic theory developed by Cottrell and Bilby (1949) and by Ham (1959) to describe the stress-assisted migration of point defects to dislocations is extended to take into account the gradient in diffusivity that exists in the stress field of dislocations. This diffusivity gradient arises from the interaction between the activation volume of diffusion of the point defects and the stress field of the dislocations. The partial differential equation defining the rate of loss of point defects due to diffusion, drift and diffusivity gradient is presented. The results of numerical integrations of this equation for the case of the dislocation acting as a perfect sink are also reported. It is shown that while the diffusivity gradient influences the rate of defect migration to the dislocation it has no effect on the form of the kinetics. In this respect the results are in substantial agreement with those obtained by Ham in showing t2/3 kinetics only at early times. An important qualitative conclusion to emerge from the results is that for a positive activation volume of diffusion the diffusivity gradient enhances the flow due to drift and diffusion in the case of interstitial type defects and retards it in the case of vacancy-type defects.