Interface Sharpening instead of Broadening by Diffusion in Ideal Binary Alloys

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 $A/B$ interface—if 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.

Figure 1

Composition distribution of $A$ during the dissolution of ten atomic layers of $A$ into $B(111)$ calculated using deterministic kinetic equations. The initially eight atomic layers width interface becomes abrupt and then remains sharp during the whole process due to the asymmetric diffusion (concentration dependent diffusivity). (Time units shown in the figure must be multiplied by 1000.)

Figure 2

Interface sharpening in an $A/B$ multilayer system. Only a half-bilayer is shown in the figure because of an $A$ or $B$ monolayer is symmetric to its center. (Time units shown in the figure must be multiplied by ${10}^6$.)

Figure 3

Schematic drawing of the flux distribution in the initial state ($t=0$—solid circles) in the case of concentration dependent diffusion coefficients. The arrows represent the atomic flux and its lengths are proportional to the absolute value of the flux.

Figure 4

Dissolution of 15 atomic layers of $A$ into $B(111)$ calculated using the Monte Carlo method. Qualitatively the same phenomenon can be observed as in Fig. 1. (Compositions are calculated by averaging the composition of each atomic layer perpendicular to the direction of diffusion.)