Calculation of proper energy barriers for atomistic kinetic Monte Carlo simulations on rigid lattice with chemical and strain field long-range effects using artificial neural networks.

In this paper we take a few steps further in the development of an approach based on the use of an artificial neural network (ANN) to introduce long-range chemical effects and zero temperature relaxation (elastic strain) effects in a rigid lattice atomistic kinetic Monte Carlo (AKMC) model. The ANN is trained to predict the vacancy migration energies as calculated given an interatomic potential with the nudged elastic band method, as functions of the local atomic environment. The kinetics of a single-vacancy migration is thus predicted as accurately as possible, within the limits of the given interatomic potential. The detailed procedure to apply this method is described and analyzed in detail. A novel ANN training algorithm is proposed to deal with the necessarily large number of input variables to be taken into account in the mathematical regression of the migration energies. The application of the ANN-based AKMC method to the simulation of a thermal annealing experiment in Fe-20%Cr alloy is reported. The results obtained are found to be in better agreement with experiments, as compared to already published simulations, where no atomic relaxation was taken into account and chemical effects were only heuristically allowed for.