Penetration profiles for fast grain-boundary diffusion by the dissociative mechanism

Abstract

A modified variant of Fisher’s model is proposed to describe the recently discovered phenomenon of fast impurity diffusion along grain boundaries (GBs) in metals as follows, (i) The fast diffusion is assumed to occur by the dissociative mechanism. Depending on the lattice dislocation density ρ the bulk diffusion of the impurity around GBs is either vacancy controlled [if (Dt)1/2≪ρ−1/2] or interstitial controlled [if (DT)1/2≫ρ−1/2]. In the first case the effective bulk diffusivity D depends on the GB concentration whereas in the second case D=const. (ii) Fast diffusers strongly segregate to GBs. The GB saturation effect is taken into account by introducing McLean’s isotherm of GB segregation. The GB penetration profiles calculated from approximate analytical solutions of the model exhibit two parts: a near-surface part caused by the GB saturation effect and a more deeply penetrating linear segregation part with a much smaller slope. The second part of the profile either shows strong downward curvature (vacancy-controlled D) or demonstrates normal Fisher-like behavior (interstitial-controlled D). Methods of profile treatment for the determination of GB diffusion parameters are presented. Based on the present model the available experimental data are critically considered and ideas of future experiments are discussed.