Introducing ab initio based neural networks for transition-rate prediction in kinetic Monte Carlo simulations

Abstract

The quality of kinetic Monte Carlo (KMC) simulations of microstructure evolution in alloys relies on the parametrization of point-defect migration rates, which are complex functions of the local chemical composition and can be calculated accurately with ab initio methods. However, constructing reliable models that ensure the best possible transfer of physical information from ab initio to KMC is a challenging task. This work presents an innovative approach, where the transition rates are predicted by artificial neural networks trained on a database of 2000 migration barriers, obtained with density functional theory (DFT) in place of interatomic potentials. The method is tested on copper precipitation in thermally aged iron alloys, by means of a hybrid atomistic-object KMC model. For the object part of the model, the stability and mobility properties of copper-vacancy clusters are analyzed by means of independent atomistic KMC simulations, driven by the same neural networks. The cluster diffusion coefficients and mean free paths are found to increase with size, confirming the dominant role of coarsening of medium-and large-sized clusters in the precipitation kinetics. The evolution under thermal aging is in better agreement with experiments with respect to a previous interatomic-potential model, especially concerning the experiment time scales. However, the model underestimates the solubility of copper in iron due to the excessively high solution energy predicted by the chosen DFT method. Nevertheless, this work proves the capability of neural networks to transfer complex ab initio physical properties to higher-scale models, and facilitates the extension to systems with increasing chemical complexity, setting the ground for reliable microstructure evolution simulations in a wide range of alloys and applications.

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“…11), the DFT-based parametrization maximized the agreement with experimental evidence. As argued in [4], the solubility limit as predicted by DFT did not match the experimental one, with a consequent overestimation of the clusters density. Nevertheless, the model significantly improved from the point of view of time rescaling, necessary to convert the time in the MC simulation into a physical time comparable to the experiment, that resulted more consistent.…”

“…In Ref. [11,4], the model predictions based on IAP or DFT were compared with experimental data for Fe-1.34%Cu, Fe-1.1%Cu and Fe-0.6%Cu alloys, annealed at 500-700°C. The simulations for these systems are more demanding than in the FeCr case, because of the high binding energy between the vacancy and the solute Cu atoms that slows down the simulation.…”

“…5000 atoms), see Ref. [11,61,4] for more details. In these works, the mechanism for the coherent stages of Cu precipitation in Fe was clearly highlighted, further stressing the importance of Cu clusters mobility [52]: classical Ostwald ripening is not sufficient to explain the rapid kinetics of Cu precipitation.…”

“…Unfortunately, a blind use of DFT may, in some cases, provide imperfect predictions (see e.g. [3,4]). Secondly, even with state-of-the-art computing facilities, using DFT still implies a huge cost in CPU resources which is often unaffordable and, sometimes, unwarranted.…”

“…[5] was fitted to faithfully reproduce the experimentally observed Cu solubility limit in Fe, whereas DFT is known to underestimate it (see discussions in Ref. [4]). The affordable computing time allows large and complex systems, containing up to several million atoms, to be studied.…”