Elastodiffusion And Cluster Mobilities Using Kinetic Monte Carlo Simulations: Fast First-Passage Algorithms For Reversible Diffusion Processes

The microstructural evolution of metals and alloys is governed by the diffusion of defects over complex energy landscapes. Whenever metastability occurs in atomistic simulations, well-separated timescales emerge making it necessary to implement event-based kinetic models at larger scales. The crucial task then involves characterizing the important events contributing to mass transport. We herein describe fast first-passage algorithms based on the theory of absorbing Markov chains assuming that defects undergo reversible diffusion. We show that the absorbing transition rate matrix can be transformed into a symmetric definite-positive matrix enabling us to implement direct and iterative sparse solvers. The efficiency of the approach is demonstrated with direct computations of elastodiffusion properties around a cavity in aluminum andMonte Carlo computations of cluster diffusivity in low-alloyed manganese steels.