Lattice-adaptive kinetic Monte Carlo (LA-KMC) for simulating solute segregation/depletion at interfaces

¹ Consejo Nacional de Investigaciones Científicasy Técnicas (CONICET). Avda. Rivadavia 1917 - CP C1033AAJ - Ciudad Autonoma de Buenos Aires – Argentina.
² Belgian nuclear research centre (SCK•CEN), Nuclear Materials Institute (NMS), Structural Material Multiscale Modelling group (SMM), Boeretang 200, B-2400 Mol, Belgium.

^* Corresponding Author, E-mail: nicolas.m.b.castin@gmail.com

Abstract

We propose a novel approach for simulating, with atomistic kinetic Monte Carlo, the segregation or depletion of solute atoms at interfaces, via transport by vacancies. Differently from classical lattice KMC, no assumption is made regarding the crystallographic structure. The model can thus potentially be applied to any type of interfaces, e.g. grain boundaries. Fully off-lattice KMC models were already proposed in the literature, but are rather demanding in CPU time, mainly because of the necessity to perform static relaxation several times at every step of the simulation, and to calculate migration energies between different metastable states. In our LA-KMC model, we aim at performing static relaxation only once per step at the most, and define possible transitions to other metastable states following a generic predefined procedure. The corresponding migration energies can then be calculated using artificial neural networks, trained to predict them as a function of a full description of the local atomic environment, in term of both the exact location in space of atoms and in term of their chemical nature. Our model is thus a compromise between fully off-lattice and fully on-lattice models: (a) The description of the system is not bound to strict assumptions, but is readapted automatically performing the minimum required amount of static relaxation; (b) The procedure to define transition events is not guaranteed to find all important transitions, and is thereby potentially disregarding some mechanisms of system evolution. This shortcoming is in fact classical to non-fully off-lattice models, but is in our case limited thanks to the application of relaxation at every step; (c) Computing time is largely reduced thanks to the use of neural network to calculate the migration energies. In this presentation, we show the premises of this novel approach, in the case of grain-boundaries for bcc Fe-Cr alloys.