The results of parallel kinetic Monte Carlo (KMC) simulations of the room-temperaturecoarsening of Ag(111) islands carried out using a very large database obtained via self-learningKMC simulations are presented. Our results indicate that, while cluster diffusion andcoalescence play an important role for small clusters and at very early times, at late timethe coarsening proceeds via Ostwald ripening, i.e. large clusters grow while small clustersevaporate. In addition, an asymptotic analysis of our results for the average island sizeS(t) as a function oftime t leads to acoarsening exponent n = 1/3 (where S(t)∼t2n), in good agreement with theoretical predictions. However, by comparing with simulationswithout concerted (multi-atom) moves, we also find that the inclusion of such movessignificantly increases the average island size. Somewhat surprisingly we also find that,while the average island size increases during coarsening, the scaled island-sizedistribution does not change significantly. Our simulations were carried out both as atest of, and as an application of, a variety of different algorithms for parallelkinetic Monte Carlo including the recently developed optimistic synchronousrelaxation (OSR) algorithm as well as the semi-rigorous synchronous sublattice (SL)algorithm. A variation of the OSR algorithm corresponding to optimistic synchronousrelaxation with pseudo-rollback (OSRPR) is also proposed along with a method forimproving the parallel efficiency and reducing the number of boundary events viadynamic boundary allocation (DBA). A variety of other methods for enhancingthe efficiency of our simulations are also discussed. We note that, because ofthe relatively high temperature of our simulations, as well as the large range ofenergy barriers (ranging from 0.05 to 0.8 eV), developing an efficient algorithm forparallel KMC and/or SLKMC simulations is particularly challenging. However,by using DBA to minimize the number of boundary events, we have achievedsignificantly improved parallel efficiencies for the OSRPR and SL algorithms. Finally, wenote that, among the three parallel algorithms which we have tested here, thesemi-rigorous SL algorithm with DBA led to the highest parallel efficiencies. Asa result, we have obtained reasonable parallel efficiencies in our simulations ofroom-temperature Ag(111) island coarsening for a small number of processors(e.g. Np = 2 and 4). Since the SL algorithm scales with system size for fixed processor size, we expectthat comparable and/or even larger parallel efficiencies should be possible for parallel KMCand/or SLKMC simulations of larger systems with larger numbers of processors.
Read full abstract