Bulk Diffusion Measurements to Study the Effectiveness of Barrier Layers: I. Mathematical Treatment
Lei Tian, Michael O. Thompson and Rüdiger Dieckmann
Department of Materials Science and Engineering, Cornell University, Bard Hall,
Ithaca, NY 14853-1501, U.S.A.
Chung-Yuen Hui and Yu-Yun Lin
Department of Theoretical and Applied Mechanics, Cornell University, Thurston
Hall, Ithaca, NY 14853-1501, U.S.A.
Abstract
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 too 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.
J. Appl. Phys., 90 (8) [2001] 3799-3809.