Accelerated Monte Carlo algorithms for defect diffusion and clustering

We present a hierarchy of accelerate Monte Carlo (MC) algorithms which can be used to investigate the kinetic evolution of systems consisting of interacting defects or impurities in a solid matrix. Local models are used to approximate the interactions among particles and a specific application of the algorithms to the study of vacancy agglomeration is presented. It is shown that an extension of the Ising model, including an effective second neighbour interaction, gives a vacancy clusters energetics in good agreement with some recent quantum mechanical calculations. The accelerate algorithms implemented allow to speed up the calculations avoiding the bottlenecks which occur when the standard Metropolis algorithm is applied. These bottlenecks are due to the huge amount of rejected transition attempts and to the rapid fluctuations between quasi-degenerate configurations. We demonstrate the equivalence between the results obtained using standard and accelerated algorithms. Moreover we discuss in detail the gain in terms of CPU time when the algorithms are applied to two different vacancy interaction models. In the case of a simple Ising model (SIM) an optimised code ~ 105 times faster than the standard Metropolis can be implemented; on the other hand, when the extended interaction is considered, the gain reduces to ~ 103. Therefore the gain in speed, achievable with accelerate codes, is strongly dependent on the kinetic features of the interaction models. Indeed a relevant consequence of the second neighbor interaction is the migration of the aggregates which boosts the agglomeration process. This faster agglomeration reduces the effects of bottlenecks during the ripening process thus reducing the difference in efficiency between accelerated and conventional codes.