Overview of kinetic Monte Carlo methods used to simulate microstructural evolution of materials under irradiation

Kinetic Monte Carlo (KMC) methods are commonly used to simulate the microstructure evolution of metals under irradiation due to their ability to generate the random walks underlying defect-mediated diffusion processes at the atomic scale. However, the range of applicability of KMC methods is severely limited by the kinetic trapping of the simulated trajectories within low energy basins presenting small intra-basin barriers. This results in dramatically reducing the efficiency of the classical KMC algorithm. Kinetic trapping can be alleviated by implementing non-local jumps relying on the theory of absorbing Markov chains. A factorisation of an auxiliary absorbing transition matrix then allows to generate escaping paths and first-passage times out of trapping basins. Although, the speed-up can be of several orders of magnitudes, this is sometimes not enough for very long-term prediction. We must then turn to homogenised rate-equation formulation of the problem. Usually solved deterministically, the corresponding large ordinary differential equation system often suffers from the curse of dimensionality. Dedicated Monte Carlo schemes can simulate the coarse-grained rate equations based on a chemical master equation. Finally, we show the relevance of relaxing the rigid-lattice assumption in the calculation of the free energy barriers and attempt frequencies to capture elastic effects that are important for certain systems, such as high entropy alloys. The activation-relaxation technique can be used for this purpose in kinetic Monte Carlo studies of slow diffusion processes.