Analytical Solution of Fick's Equations in the Case of Foreign Atom Diffusion in a Metallic Sample
In this work we develop an analytical method for resolution of the reaction-diffusion equations which govern impurity diffusion by the dissociative mechanism in a finite-thickness sample and from a deposit of solute atoms on the surface. This method is based upon the perturbation of basic solutions corresponding to limiting cases and the choice of suitable small parameters. The solutions obtained and their comparison to those of numerical studies are also presented in this paper.
David J. Fisher
A. Benmakhlouf "Analytical Solution of Fick's Equations in the Case of Foreign Atom Diffusion in a Metallic Sample", Defect and Diffusion Forum, Vols. 233-234, pp. 1-14, 2004