Many materials science phenomena, such as growth and self-organisation, aredominated by activated diffusion processes and occur on timescales that arewell beyond the reach of standard-molecular dynamics simulations. Kinetic MonteCarlo (KMC) schemes make it possible to overcome this limitation and achieveexperimental timescales. However, most KMC approaches proceed by discretizingthe problem in space in order to identify, from the outset, a fixed set ofbarriers that are used throughout the simulations, limiting the range ofproblems that can be addressed. Here, we propose a more flexible approach --the kinetic activation-relaxation technique (k-ART) -- which lifts theseconstraints. Our method is based on an off-lattice, self-learning, on-the-flyidentification and evaluation of activation barriers using ART and atopological description of events. The validity and power of the method aredemonstrated through the study of vacancy diffusion in crystalline silicon.
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