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 inter acting defects or impurities in a solid matrix. Local models are used to ap proximate the interactions among particles and a specific application of th e algorithms to the study of vacancy agglomeration is presented. It is show n that an extension of the Ising model, including an effective second neigh bour interaction, gives a vacancy clusters energetics in good agreement wit h some recent quantum mechanical calculations. The accelerate algorithms im plemented 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 rapi d fluctuations between quasi-degenerate configurations. We demonstrate the equivalence between the results obtained using standard and accelerated alg orithms. Moreover we discuss in detail the gain in terms of CPU time when t he algorithms are applied to two different vacancy interaction models. In t he case of a simple Ising model (SIM) an optimised code similar to 10(5) ti mes faster than the standard Metropolis can be implemented; on the other ha nd, when the extended interaction is considered, the gain reduces to simila r to 10(3). Therefore the gain in speed, achievable with accelerate codes, is strongly dependent on the kinetic features of the interaction models. In deed a relevant consequence of the second neighbor interaction is the migra tion of the aggregates which boosts the agglomeration process. This faster agglomeration reduces the effects of bottlenecks during the ripening proces s thus reducing the difference in efficiency between accelerated and conven tional codes. (C) 2000 Elsevier Science B.V. All rights reserved.