Diffusion in an Ensemble of Intersecting Grain Boundaries

Abstract

Grain boundary (GB) diffusion in an ensemble of three grain boundaries intersecting in the point of GB triple junction is described on the basis of quasi-steady Fisher’s model. Two versions of the configuration of the ensemble are considered, namely, with different number of GBs adjacent to the surface covered with a diffuser source and with different angle between GB and surface. Analytical expressions for the distribution of diffuser concentration along each GB of an ensemble are derived supposing that the GB diffusion fluxes are equal in the GB triple junction. The expressions for the diffuser concentration distribution along GBs in both ensembles include not only diffusion constants (like GB and bulk diffusion coefficients) but also structural characteristics of the ensemble of grain boundaries (i.e. the depth of the triple junction point under the surface and the angle between GBs in the triple junction point). The specific features of diffusion kinetics in the ensembles of different configuration with an angle of 120o(the equilibrium angle in a polycrystal) were revealed by comparing the diffuser concentration distributions in the ensembles and in the single GB.