Grain Boundary and Lattice Diffusion in Polycrystalline Bodies

Abstract

Diffusion in a polycrystalline body is discussed under the assumption that two interrelated mechanisms consisting of diffusion through the grains and in the boundaries around the grains are dominant in different penetration regions. The general behavior of the average concentration-distribution of diffusant is described for the separate action of each mechanism, and the effects of their combined action are inferred. A realistic diffusion model for a polycrystalline body and a suitable empirical function to describe the loss of diffusant from the boundaries to the grains form the basis for these computations. Results are specifically applied to the analysis of the usual sectioning technique for measuring the ratio of grain boundary to lattice diffusion constants in a polycrystalline body. It is shown that, in the penetration range most commonly covered in polycrystalline diffusion experiments, the log of the average concentration varies as the 6/5 power of penetration depth contrary to the linear law reported previously. Comparison is made between the present and previous methods for establishing the grain boundary diffusivity of silver. The results are found to differ by a factor of 3 or 4. Criteria for validity of the method associated with the relative magnitudes of reduced time, grain size, and the ratio of grain boundary to lattice diffusion constants are established. Some of the results reported for Zn and Cd do not satisfy these criteria.