Modeling the first stages of Cu precipitation in α-Fe using a hybrid atomistic kinetic Monte Carlo approach

We simulate the coherent stage of Cu precipitation in α-Fe with an atomistic kinetic Monte Carlo (AKMC) model. The vacancy migration energy as a function of the local chemical environment is provided on-the-fly by a neural network, trained with high precision on values calculated with the nudged elastic band method, using a suitable interatomic potential. To speed up the simulation, however, we modify the standard AKMC algorithm by treating large Cu clusters as objects, similarly to object kinetic Monte Carlo approaches. Seamless matching between the fully atomistic and the coarse-grained approach is achieved again by using a neural network, that provides all stability and mobility parameters for large Cu clusters, after training on atomistically informed results. The resulting hybrid algorithm allows long thermal annealing experiments to be simulated, within a reasonable CPU time. The results obtained are in very good agreement with several series of experimental data available from the literature, spanning over different conditions of temperature and alloy composition. We deduce from these results and relevant parametric studies that the mobility of Cu clusters containing one vacancy plays a central role in the precipitation mechanism.