Large scale application of kinetic ART, a near order-1 topologically- based off-lattice kinetic Monte-Carlo algorithm with on-the-fly calculation of events

Using a topological classification of events\footnote{B. D. McKay, Congressus Numerantium 30, 45 (1981).} combined with the Activation-Relaxation Technique (ART nouveau) for the generation of diffusion pathways, the kinetic ART (k-ART)\footnote{F. El-Mellouhi, N. Mousseau and L. J. Lewis, Phys Rev B, 78,15 (2008).} lifts many restrictions generally associated with standard kinetic Monte Carlo algorithms. In particular, it can treat on and off-lattice atomic positions and handles exactly long-range elastic deformation. Here we introduce a set of modifications to k-ART that reduce the computational cost of the algorithm to near order 1 and show applications of the algorithm to the diffusion of vacancy and interstitial complexes in large models of crystalline Si (100 000 atoms).