Fast kinetic Monte Carlo simulations using hash table based caching with applications to nanowire growth and sintering

We describe an implementation of a rate cache designed to eliminate redundant calculations in kinetic Monte Carlo (KMC) simulations. The cache is a hash table of rates, indexed by local neighborhoods of an atom configuration. We present numerical evidence suggesting that the set of such local neighborhoods seen during KMC is small and repeating, implying that the utilization of such a cache is advantageous. We present a simulated annealing technique to search for effective, system-specific hash functions. In tandem with an optimized hash function, the implementation of the rate cache results in significant performance gains. Equipped with an efficient implementation, we are able to simulate nanowire growth by the vapor-liquid-solid (VLS) method as an example. An energy parameter study is presented. We show that the KMC model captures a wide range of observed phenomena, including faceting at the liquid-solid interface and nanowire kinking. Simulation results illustrating the role of faceting on nanowire kinking are also presented. As a second example of the implementation we study sintering, the evolution of porous granular material by surface diffusion and atomistic changes in species, representing an atom's orientation or spin. We provide coarsening statistics and show that the mean disc-equivalent radius of the grains grows according to a power law, consistent with previous analysis and experiments.