Percolation in alloys with thermally activated diffusion

Abstract

For diffusion in a real alloy, some concepts of formal percolation theory may need to be reconsidered because the "immobile" atoms are not truly immobile. Our Monte Carlo simulations of vacancy diffusion on bcc lattices show the existence of a relationship between the activation barrier heights for the vacancy-atom exchanges and the effective percolation threshold concentration. In the language of formal percolation theory, we have modeled this problem by varying the immobile species' barrier height from infinity to some finite value and calculating the resulting percolation threshold. When both species of atoms have a finite mobility, however, our results can be interpreted in terms of probabilities for vacancies to escape local clusters in a fixed amount of time. We find that the dynamical behavior undergoes a marked change above and below the formal percolation threshold, but the strength of the percolating cluster is much less important than in formal percolation theory.