Measurement of grain-boundary diffusion at low temperatures by the surface accumulation method. I. Method and analysis

Abstract

An analysis of the measurement of grain‐boundary diffusion at low temperatures by the surface‐accumulation mehod was carried out. In this method atoms are allowed to diffuse along grain boundaries from a source to a free surface where they spread out, accumulate, and are measured. The diffusion is carried out at low temperatures so that only the grain boundary and surface ’’short‐circuit paths’’ are active, and lattice diffusion is frozen out. This method is generally more sensitive than the depth profiling method for measuring grain‐boundary diffusion at low temperatures. However, the kinetics of the surface accumulation are strongly dependent on the nature of the source and sink. Treating the surface as a sink of finite capacity with a finite diffusion coefficient, diffusion analyses were developed for either a constant or an instantaneous source. Two dimensionless parameters, G and H, play important roles in determining the form of the solutions. H involves the ratio of grain‐boundary capacity to surface capacity. G is proportional to the ratio of the grain‐boundary diffusivity to that of the surface. When G⩽1 and H⩽1, conditions for uniform concentration on the surface and quasi‐steady‐state diffusion in the grain boundary are met, and the general solution becomes relatively simple. For a constant source, the surface concentration then obeys the relation c_s=1−exp(−st), where s is a parameter proportional to the boundary diffusivity and t is the time. The application of the analyses to a variety of diffusion systems was discussed. It was concluded that the conditions for the simple solutions to apply are not particularly stringent.