Beyond the Fisher model of grain boundary diffusion: effect of structural inhomogeneity in the bulk

Abstract

An extension of the Fisher model of grain boundary diffusion is suggested, in which the diffusion along the short-circuit paths in the bulk of the crystalline grains (dislocations, subgrain boundaries, interphase boundaries in the lamellar structures) is taken into account. In the framework of the suggested model the bulk is treated as a stochastic mixture of defect-free crystalline regions and regions of bad material inside the short-circuit paths. The Harrison classification of the diffusion regimes is extended to the new D-regime, in which the kinetics of the penetration of the diffusing element along the grain boundaries is dominated by diffusion along these short-circuit paths. Three different kinetic modes during the grain boundary diffusion in the D-regime are uncovered: for the short annealing times the penetration kinetics follows the Whipple law, but with the bulk diffusion coefficient substituted by g 2 D d, for the intermediate annealing times the penetration distance along the grain boundary is a weak function of time and for the long times the Whipple law is valid again, but with the bulk diffusion coefficient substituted by gD d, where g and D d are the volume fraction of the material inside the short-circuit paths and the diffusion coefficient along them, respectively. The applications of the suggested model to the analysis of experimental data are discussed.