Accurate meso-scale dynamics by kinetic Monte Carlo simulation via free energy multicanonical sampling: oxygen vacancy diffusion in BaTiO₃

Abstract

A conceptually accurate method to connect the free energy multicanonical sampling to mesoscale kinetic Monte Carlo (kMC) dynamics is proposed. The required input parameters for kMC simulation are the attempt frequency and activation energy for each event, and the free energy multicanonical sampling enables to obtain the kinetic parameters as a function of temperature, which is the most significant difference from a conventional kMC approach that is based on fixed attempt frequency and activation energy. The present approach is applied to oxygen diffusion in single crystal BaTiO 3 including Zn dopant (160 ppm) where an anomaly in the oxygen diffusion is experimentally confirmed; the oxygen diffusion coefficient is slightly dropped at around 1080 K. We carried out 1 μs kMC dynamics in the temperature range of 1020 to 1120 K, and obtained a diffusion anomaly at around 1060 K, which is not obtained in conventional kMC calculations. In addition, the calculated diffusion coefficients using the present approach are in the same order as those of experimental ones, whereas the calculated diffusion coefficients using the conventional method are larger than those of experiment by one order of magnitude at least. The results indicate the advantages of the present approach in comparison with the conventional ones because any assumption and fixation of kinetic parameters are not required in the dynamics simulation.