On the range of validity of the continuum approach for nonlinear diffusional mixing of multilayers

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Abstract
Using finite difference calculations in continuum equations and using deterministic kinetic equations for calculations in a discrete lattice, the problem of the asymmetry, related to the strong concentration dependence of the diffusion coefficient in the diffusional mixing of binary multilayers, was investigated assuming that the stress effects are negligible and the binary system is ideal. Assuming exponential concentration dependence, it was obtained that the nonlinearity is manifested not only in the change of the range of the validity of the continuum approach (the validity limit was shifted to higher modulation length by about a factor of 10 in the range investigated), but also in peculiar concentration distribution and its time evolution. A fast homogenization took place in both models on the side where the diffusion is faster, and here the distribution remained practically flat and only the amplitude of the composition modulation decreased with time. The shift of a sharp boundary between the slow component and the newly formed (homogeneous) alloy was observed and when the slab of the slow component was eliminated the homogenization process was considerably accelerated. The details of the results obtained from the continuum and discrete models were different: the shape of the above moving boundary changed with time in the discrete model and showed a layer by layer dissolution kinetics, while in the continuum model the interface remained atomic sharp. Furthermore, the continuum model always gives a faster homogenization than the discrete model.