https://doi.org/10.1051/epjn/2025064
Regular Article
Overview of kinetic Monte Carlo methods used to simulate microstructural evolution of materials under irradiation
1
EDF Lab les Renardières, Moret-sur-Loing, 77818, France
2
Université Paris-Saclay, CEA, Service de recherche en Corrosion et Comportement des Matériaux, SRMP, F-91191, Gif-sur-Yvette, France
3
Département de physique, Institut Courtois and Regroupement québécois sur les matériaux de pointe, Université de Montréal, Montréal, H3C 3J7 Québec, Canada
4
Département de génie physique, Institut Courtois and Regroupement québécois sur les matériaux de pointe, École Polytechnique de Montréal, C.P. 6079, Succ. centre-ville, Montréal, Québec, H3C3A7, Canada
* e-mail: gilles.adjanor@edf.fr
Received:
12
June
2025
Received in final form:
3
September
2025
Accepted:
4
September
2025
Published online: 20 October 2025
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 factorization 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 homogenized 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 or other concentrated alloys such as austenitic stainless steels. A new activation-relaxation technique combining barriers and prefactors on-the-fly calculations can be used for this purpose in kinetic Monte Carlo studies of slow diffusion processes.
© G. Adjanor et al., Published by EDP Sciences, 2025
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
