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.

A Mechanistic Analysis of Ruthenium Transport in UO2

“…This situation is analogous to that encountered in fission gas mobility in uo 2 where the trapping-diffusion 1Jlodel (2, 3) provides a much better description of the phenomenon than does s:bnple diffusion .. Similarly, analysis of diffusion in polycrystalline bodies JllUSt consider grain bormdary as well as volume di:f;fusion (4). Diffusion of carbon in steel is often treated as a s:imple diffusion process (S), but detailed under .. standing of carburization can be achieved only by an analysis which involves carbide precipitation along with dif.fusion(6).…”

Microstructure dependence of diffusional transport

“…For an idealized grain boundary geometry, analytical solutions are available for the concentration pro®les [9±11]. These solutions can be employed to analyze the grain boundary di usion coe cients from experimental measurements [12]. In recent years, some numerical models were developed to overcome the simple geometry and topology restrictions.…”

“…However, at short times t 2000 there is a little di erence between the simulated hCi and the calculated hCi because the condition d ( D v t 1a2 is not well satis®ed at short times. The plot of the logarithm of the average concentration versus y 6a5 was the basis for experimental measurements of grain boundary di usion coe cients [12].…”

Desorption Process by Grain Boundary Diffusion in Thin Plate

“…and for (4) where Dc and DB are the diffusivity in the grain boundary and that in the bulk, respectively. Since the element diffuses out from both surfaces, the flow along Y axis becomes zero at the center of the specimen thickness.…”

“…An extended model or calculation was given by Suzuoka(3), Levine et al. (4) and Claire (5). The first treatment of grain boundary diffusion for a finite system was done by Gilmer et al (6).…”