Lattice and Grain Boundary Diffusion in Polycrystals

Tracer diffusion mechanism in a polycrystalline medium with a plane source is discussed by assuming both the high diffusivity along the grain boundaries as compared with that inside the grains and the conservation of diffusant. The following theoretical results are obtained from the analytical solution of the problem. (1) In a small penetration region the grain boundaries act as sinks, i.e. a negative contribution to the amount of diffusant arises from the grain boundaries. (2) At a large penetration depth they act as sources, and the resultant positive contribution of grain boundary diffusion is such that the logarithm of the average concentration of diffusant from the boundary into the inside depends linearly on the 6/5 power of penetration depth. (3) Considering the grain size the present theory predicts the penetration curve in which both the lattice and the grain boundary diffusion play an important role. (4) The theory also finds the condition that the contribution from the lattice diffusion becomes dominant as compared with that from the grain boundary. A relation usable for the determination of the grain boundary diffusion coefficient from experimental data is given. These theoretical results are found in agree well with the experimental data. The limit for the validity of the present model is also discussed.