Kinetic activation-relaxation technique: An off-lattice self-learning kinetic Monte Carlo algorithm

Many materials science phenomena are dominated by activated diffusion processes and occur on time scales that are well beyond the reach of standard molecular-dynamics simulations. Kinetic Monte Carlo (KMC) schemes make it possible to overcome this limitation and achieve experimental time scales. However, most KMC approaches proceed by discretizing the problem in space in order to identify, from the outset, a fixed set of barriers that are used throughout the simulations, limiting the range of problems that can be addressed. Here, we propose a flexible approach—the kinetic activation-relaxation technique ($k$-ART)—which lifts these constraints. Our method is based on an off-lattice, self-learning, on-the-fly identification and evaluation of activation barriers using ART and a topological description of events. Using this method, we demonstrate that elastic deformations are determinant to the diffusion kinetics of vacancies in Si and are responsible for their trapping.

Figure 1

(Color online) Local topology analysis in $k$-ART: A truncated graph (b) is extracted from the complete lattice around the highlighted central atom (a), and analyzed using NAUTY (c) which returns a unique key associated with the given topology (d).

Figure 2

(a) Total squared displacement as function of KMC steps (or time, in the inset). (b) Distance between the two vacancies as a function of KMC steps.

Figure 3

(Color online) Total squared displacement as function of KMC steps for the six-vacancy system.

Figure 4

(Color online) CPU time versus simulated time for the hexavacancy aggregation problems. The red arrows indicate extensive self-learning phases in $k$-ART.