It was recalled that so-called anomalous fast diffusion was often analyzed in terms of an interstitial-substitutional model. The equations which were used for modelling these mechanisms were of reaction-diffusion type, and analytical solution was possible only after making large simplifications. The dissociative version of this model was simulated by using finite difference and Monte Carlo methods. In the latter case, the diffusion of various species (interstitial impurities, substitutional impurities, vacancies), and reaction jumps, occurred according to probabilities which were jump-frequency dependent. In the case of the finite difference method, an implicit scheme was used to solve the system of non-linear partial differential equations. In both cases, finite source conditions were assumed. Good agreement between the results obtained using the 2 methods was found. The double-stages of the simulated profiles were found to have similar shapes to those observed experimentally in Nb-Co. The first stage was well-described by a Gaussian function, whereas the second was satisfactorily represented by an erfc-type function. A detailed study of the 2 stages led to a qualitative agreement with Stolwijk’s analysis in 2 limiting cases; where diffusion was vacancy- or foreign-interstitial controlled. On the other hand, the effective diffusion coefficients diverged from those which were obtained by using Stolwijk’s expressions.

Numerical Studies of Anomalous Fast Diffusion in Metallic Alloys and Semiconductors. A.Hasnaoui, A.Benmakhlouf, A.Hoummada, J.K.Naciri, A.Menai: Applied Surface Science, 2000, 162-163, 100-10