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

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< or =1 and H< or =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/sub 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