Percolation of diffusionally evolved two-phase systems

Abstract

Percolation thresholds and critical exponents for universal scaling laws are computed for microstructures that derive from phase-transformation processes in two dimensions. The computed percolation threshold for nucleation and growth processes, p[subscript c] ≈0.6612, is similar to those obtained by random placement of disks and greater than that of spinodal decomposition, p[subscript c] ≈0.4987. Three critical exponents for scaling behavior were computed and do not differ significantly from universal values. The time evolution of a characteristic microstructural length was also computed: For spinodal decomposition, this length grows according to a power law after a short incubation period; for nucleation and growth, there are several transitions in the nature of the growth law. We speculate that the transitions in nucleation and growth derive from competing effects of coalescence at short times and then subsequent coarsening. Short-range order is present, but different, for both classes of microstructural evolution. © 2011 American Physical Society.