Description of grain-boundary diffusion in nanostructured materials for thin-film diffusion source

Using asymptotic solution methods of differential equations, the grain-boundary diffusion at transition (between regimes C and B) stages of annealing has been described for nano- and submicrocrystalline materials characterized by nonequilibrium grain boundaries and, thus, by a strong coordinate dependence of the diffusion coefficient near them. As a continuation of [1], the solution of the diffusion problem has been obtained for the condition of thin-film (instantaneous) exhaustible diffusion source frequently used in experiments. Based on the performed numerical calculations and qualitative estimates, expressions have been suggested for the average layer concentration and the region of their applicability has been established. The features of grain-boundary diffusion connected with allowance for near-boundary regions and type of the diffusion source have been treated analytically. Using the literature data the depth of penetration of diffusant into the near-boundary zone has been estimated for some materials.