Diffusion in Wide Grain Boundaries

Abstract

The rigorous solution of the grain‐boundary diffusion problem has been approximated by a series expansion method. The calculations show that higher‐order terms may be neglected in the bulk adjacent to the grain boundary. Thus, in this region Whipple's and Suzuoka's solutions represent a close approximation to the problem. Inside the grain boundary, however, higher‐order approximations have to be taken into account. These approximations gain importance in the case of wide grain boundaries. The solutions obtained for an instantaneous source have been fitted to available grain‐boundary diffusion data of Ni²⁺ in MgO at 1200°C. Numerical calculations give for the bulk diffusion coefficient D=2.9×10⁻¹² cm² sec⁻¹, the ratio of diffusion coefficient Δ=1.5 and for the grain‐boundary width a=75 μ.