Diffusion in an ensemble of intersecting grain boundaries forming a triple junction

Grain boundary diffusion in an ensemble of three intersecting grain boundaries forming a triple junction is described in the framework of quasi-steady Fisher’s model. Two configurations, which differ in the number of grain boundaries adjacent to the surface with a diffusant source and in the tilt angle to the surface, are considered. Analytical expressions for the diffusant concentration distribution along each grain boundary that constitutes the triple junction and for the point of the triple junction are derived with the proviso of equal diffusion fluxes at the triple point. The expressions for the diffusant concentration distribution along the grain boundaries include not only diffusion constants (grain-boundary and bulk diffusion coefficients) but also structural characteristics of the ensemble of grain boundaries (the depth of the triple junction point and the angle between the grains forming the triple junction). It is shown that, if the coefficients of grain boundary diffusion are equal for all boundaries making the ensemble and for an equilibrium angle of 120° in a polycrystal, the diffusive mass transport rate in the triple junction zone is lower than that in a single grain boundary irrespective of the configuration of grain boundaries.