Bulk diffusion measurements to study the effectiveness of barrier layers: I. Mathematical treatment

The exchange of a tracer material, e.g., a radioactive isotope, between two samples forming a diffusion couple depends on the rate of the diffusion of the tracer in each of the two samples and also on the rate of the transfer of the tracer across the interface between these samples which may or may not contain a barrier layer with a different chemical composition and/or structure. Diffusion couples with three different initial tracer distributions are considered. In order to extract from experimental data values for tracer diffusion coefficients and for the rate constant for the tracer transport across the interface, a detailed analysis of the required mathematics is given. This analysis is of interest as well for obtaining true values for bulk diffusivities and also to characterize quantitatively the resistance of interfaces (=barriers) to the exchange of certain species. Some examples of experimental results are presented and briefly discussed.