Diffusion Along Dislocations

The Smoluchowski pipe model for diffusion along dislocations is modified so as to allow an exact solution of the two-dimensional diffusion equation. Using the continuously variable diffusion coefficient: D=D0/r2, where r is the radial coordinate perpendicular to the dislocation, rather than a step function, yields a diffusion profile proportional to: (D0t)−¼ exp[−2z/a(D0t)¼], a=Γ(¼)(2π)−½≃1.45 for large z, where z is the coordinate perpendicular to the surface from which diffusion occurs. Near the surface, where the Smoluchowski theory fails, the penetration is predicted to be anomalously high. A characteristic diffusion coefficient for a grain boundary composed of parallel dislocations was calculated on the present model and found to be inversely proportional to the spacing of the dislocations.