1994 Volume 102 Issue 1190 Pages 897-901
The grain-boundary diffusion equation, Eq. (1.11), was derived for the small-grain deep-penetration diffusion, and solved for the instantaneous source condition. The obtained solution, Eq. (2.9), consists of two terms, one is the simple diffusion solution for the grain-boundary diffusion only, and the other is the factor which expresses the effect of the flux from the grain boundary toward the interior of the grains.
Equation (3.4), which gives the average concentration at given distance and time, should be useful for determination of the diffusion parameters for the grain boundary and the bulk by tracer technique, and also for the analysis of kinetics in the formation of a grain-boundary phase by preferential diffusion in dielectric ceramics.
