STATISTICAL SIMULATIONS OF DIFFUSIONAL COARSENING IN FINITE CLUSTERS

The problem of diffusional interactions in a finite-sized cluster of s pherical particles is studied. Simulations of diffusional interactions with size distribution and volume fraction V-v, as input parameters, referred to as snapshot (static) simulations, are compared with dynami c (time-dependent) simulation results. The precise size distribution i nformation in the snapshot simulations is obtained on the basis of a p erturbation technique proposed recently by Fradkov et al. [Phys. Rev. E 53, 3925 (1996)]. Robust iterative solution schemes for the quasista tic diffusion equation facilitate investigations of coarsening systems comprised of one million particles at ultralow (10(-13)) to moderate (0.25) volume fractions. The objective of carrying out simulations at such low volume fractions is to analyze the first-order volume-fractio n-dependent correction to the effective coarsening rate predicted by t he Todes, Lifshitz, and Slyozov (TLS) theory at infinite dilution. Whe n volume fraction is considered as an input parameter, the deviation o f coarsening rates from that of the infinite dilution limit of TLS var ies as (3)root V-nu for a finite cluster and root V-nu (Debye screenin g) for an infinite system. Accurate numerical investigations of the ro llover volume fraction ( V-nu) above which the (3)root V-nu behavior changes to root V-nu showed that V-nu varies as n(-2),where n is the number of particles in the spherical cluster. The deviation of coarsen ing rates from TLS observed from dynamic simulations agrees with that predicted by snapshot simulations for V-nu <0.01. The dynamic results are higher than the snapshot results for V-nu>0.01. The coarsening rat e of the average particle can be calculated directly from dynamic simu lations and indirectly from snapshot simulations by a perturbation rel ation. A different type of snapshot-ensemble averaging is suggested on the basis of the functional nature of the individual particle monopol e source or sink strengths. Dynamic and snapshot simulations with dipo les were carried out up to a volume fraction of 0.25, and departure fr om Debye screening behavior was observed. The inclusion of dipole term s affects the deviations noticeably only above a volume fraction of 0. 1.