Development of a fragment kinetic Monte Carlo method for efficient prediction of ionic diffusion in perovskite crystals

A massively parallel kinetic Monte Carlo (kMC) approach is proposed for simulating ionic migration in a crystal system by introducing the atomic fragmentation scheme (fragment kMC). The fragment kMC method achieved a reasonable parallel efficiency with 1728 central processing unit (CPU) cores, and the method enables the simulation of ionic diffusion in $\mu$m-scale perovskite crystals. To demonstrate the feasibility of the proposed approach, the fragment kMC method was applied to predict the diffusion coefficients of hydrogen and oxygen in SrTiO$_{(3-x)}$H$_x$ and BaTiO$_{(3-x)}$H$_x$ system. Finally, the fragment kMC method was customized for $\mu$-scale BaTiO$_3$ simulation under an applied bias voltage, and oxygen diffusion in BaTiO$_3$ model was evaluated. The respective grain sizes are sub-nanometre, and we conclude that the proposed fragment kMC method can be applied to calculate the extent of ionic migration in $\mu$-scale materials with fully atomistic simulation models at a reasonable computational cost.