Calculation of Grain-Boundary Diffusion Parameters and Comparison with Experiment

Abstract

Calculations of C_p (the solute concentration at the grain‐boundary edge) vs the reduced penetration η have been carried out for β values of 5.0, 1.0, 0.5, and 0.1, and η values from 2.0 to 7.0 in increments of 0.5. The small increments in η for the calculations were taken in order to better resolve the slopes of ``lnC_p vs penetration'' curves for small η values. It is just this region of η values that is of interest in electron‐probe analysis when the β's are small and the signal‐to‐noise ratio of the diffusing species is at low levels. Grain‐boundary diffusion permeabilities‐derivable from electron‐probe analysis of thallium diffusion in nineteen bicrystals of potassium chloride‐were determined both by comparison of the slopes of the isoconcentration contours at the grain‐boundary edge, and, from the slopes of the grain‐boundary penetration curves, using the results of the present numerical calculations. The agreement between the two methods was erratic. The values of η differed by as much as a factor of 4 in some cases and agreed to within 5% in others. This is attributed to the inability of the probe to resolve within 1 μ of the grain boundary, and to the poor signal‐to‐noise ratio of the electron‐probe detector system for thallium.