Late-stage coarsening dynamics in phase separating systems: simulation results

Abstract

Simulations of diffusional interactions among precipitate particles with a given instantaneous size distribution and volume fraction are referred to as snapshot simulations. Dynamic (time-dependent) and snapshot simulations of large ensembles of coarsening particles with monopolar and dipolar interactions are presented. The snapshot simulations show that the deviation of coarsening rates from that of the infinite dilution limit of TLS varies as 3√V v or √V v (Debye screening) depending on the range of volume fraction and number of particles in the system. Dynamic simulation results of the same system confirm the cubic growth law of particles showing that they are in the asymptotic regime. The deviation of coarsening rates from TLS from dynamic simulations is larger than that predicted by the snapshot simulations at V v = 0.10 and higher. The results of the snapshot and dynamic simulations however agree at volume fractions ≤0.01. Structure factor calculations indicate that the scaled structure factor S(q) ~ q −4 (Porod's law) at large values of wave number q, consistent with the presence of sharp interfaces between the droplet and matrix phases.