Exact Solution for a Model of Dislocation Pipe Diffusion

Abstract

The dislocations are treated as an ideal array of parallel pipes of radius $a$ and diffusivity $D_p$ embedded in the bulk material of the diffusivity $D_b$. The exact solution of this problem of diffusion along semi-infinite edge dislocations is presented for cubic, tetragonal, and hexagonal crystals. The solution makes it possible to evaluate the dislocation pipe radius $a$ and the ratio of diffusivities $\Delta$ from one experiment. It is applied to experimental data for self-diffusion in tellurium available in the literature. The results of the calculations are a dislocation pipe radius $a=(1.5\mathrm{}\pm 0.5)\times {10}^{-4\mathrm{}}$ cm and an activation energy for the pipe diffusion along edge dislocations in tellurium $E_p=0.80\mathrm{}\pm 0.05$ eV.