Kinetic Monte Carlo modeling of Y₂O₃ nano-cluster formation in radiation resistant matrices

As known, Y₂O₃ nano-clusters considerably increase radiation resistance of reactor construction materials. To model the nano-cluster formation kinetics, we propose the simplest possible mathematical model and perform kinetic Monte Carlo (KMC) simulations. We extended the KMC simulated results to the experimentally relevant times using autoregressive integrated moving average forecasting. Within the model, we have studied prototypical attractive interaction energies and particle concentrations, and compared the simulations with experiments. We have observed the standard Lifshitz-Slyozov-Wagner (LSW) theory, predicting the average cluster radius growth with time, R‾∼t^1/p, with p=3 in the long-time limit, for weak (0.1 eV) mutual particle attraction. However, the respective cluster growth rates in these KMC simulations are overestimated compared to the experiments. The best agreement with experiment is obtained for a medium (0.3 eV) and strong (0.5 eV) attractions, when nano-cluster formation occurs during intermediate asymptotic time scale, where power order p ranges from 5 to 7.6 depending on interaction, without reaching actually the LSW long-time limit. Such a stronger interaction leads also to a more compact {110}–faceted nano-clusters.