Grain boundary diffusion in polycrystalline solids with an arbitrary grain size

Common Levine and McCallum's approach to the grain boundary diffusion in polycrystalline solids is analyzed in dependence on the grain size and the type of diffusion kinetics in a range from a single boundary to nanocrystals. Both "instantaneous" and "constant" diffusion sources are treated. As a rule, the logarithm of concentration averaged over a section of polycrystal is found to be proportional to y(m), where y is the depth. It was shown that there exists a smooth transition from m = 1 regime for a single boundary (the Fisher's solution; epsilon congruent to 0), m = 6/5 for a common polycrystal (Levine & McCallum's solution, epsilon congruent to 10(-5)) to m = 3/2 for nanocrystals (epsilon = 0.1 divided by 0.5) and m = 2 For a homogeneous grain boundary material (epsilon --> infinity). First two solutions are referred to the B type regime and the later characterizes the C type regime. The 3/2-solution represents an intermediate regime. Expressions have been developed to calculate the diffusivity of grain boundaries in this regime by experimental data.