Interface Sharpening instead of Broadening by Diffusion in Ideal Binary Alloys

Abstract

We demonstrate, using computer simulations based on deterministic kinetic equations and Monte Carlo technique, that during intermixing in an ideal AB system with an initially wide A=B interfaceif the diffusion coefficient D strongly depends on concentration-the interface can become sharp on nanoscale. The sharp interface shifts proportionally with time (in contrast to the square root law). Furthermore, it is also shown that at the beginning of the intermixing in a finite bilayer or in multilayers, the diminution of the concentration gradient takes place by filling up one of the initially pure layers (layer B if D is large there) and by the shift of the sharpening interface. DOI: 10.1103/PhysRevLett.89.165901 PACS numbers: 66.30.Pa, 68.35.Fx Very recently, studying the dissolution of thin (3 and 8 monolayers thick) Ni films into Cu(111) substrate, it was shown (both by experiments and by computer simulations, based on deterministic kinetic equations) that the interface remains sharp and shifts proportionally with the time t (in contrast to a shift with t p ) even in ideal systems having complete mutual solubility [1]. This result is inherently related to the strong nonlinearity of the problem: the strong concentration dependence of the diffusion coefficient D shifts the validity limit of the continuum approach (see also [2]), from which a parabolic law would be expected, out of the nanometer range. It was also shown in [1] that the parabolic law is obeyed at longer times and thus this ''irregular'' behavior can be observed only on nanoscale. Furthermore, it was obtained from computer simulations in [2] that, at the beginning of the intermixing in a finite bilayer or in multilayers with initially sharp A=B interfaces, the diminution of the concentration gradient takes place by filling up one of the initially pure layers (layer B if D is large there) and by the shift of the sharp interface. Although the above simulations were carried out for a discrete lattice, this phenomenon was also observed experimentally in the amorphous Si-Ge multilayers [3] by Auger depth profiling technique [4], illustrating that the above effects are rather related to the nonlinearity than to the discrete character of the medium, where the diffusion takes place.In this Letter, using computer simulations based on deterministic kinetic equations (discrete, atomic approach) [5] and Monte Carlo technique (which contains the effects of fluctuations as well), we demonstrate that on nanoscale (short diffusion distances, short time) and again in the case of strongly concentration dependent D, an initially wide A=B interface can become sharp even in an ideal system. While such a process is obvious in an alloy with a large miscibility gap (the metastable solid solution in the smeared interface region decomposes and a sharp interface should be formed), it is surprising at first sight in systems with complete mutual solubility, because according to the macroscopic Fick I law the direction of the atomic flux is always opposite to the direction of t...

Application of a Stochastic Kinetic Mean Field (SKMF) Method to Ordering Substitutional Atoms in Macro- and Nanosize F.C.C. Lattices

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Simulation of the Tracer Diffusion, Bulk Ordering, and Surface Reordering in F.C.C. Structures by Kinetic Mean-Field Method

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