Papers by Author: A. Benmakhlouf

Abstract: The analytical treatment of dissociative diffusion by using the matched perturbation method given in the literature deals with a virtually infinite foreign-atom source producing a constant^concentration at the boundary. In this paper, a new mathematical model is developed for analysing the dissociative diffusion of the solute atoms in the case of finite-source conditions. The mathematical model combines the reaction-diffusion equations which govern solute atom diffusion by the dissociative mechanism and the boundary condition expressing the fact that the rate at which solute leaves the source is always equal to that at which it enters the sheet over the surface x=0. Solutions obtained by applying the matched perturbation method and their comparison with those of the numerical study are also presented in this paper.

Abstract: 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.