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A massively parallel kinetic Monte Carlo (kMC) approach is proposed forsimulating ionic migration in a crystal system by introducing the atomicfragmentation scheme (fragment kMC). The fragment kMC method achieved areasonable parallel efficiency with 1728 central processing unit (CPU) cores,and the method enables the simulation of ionic diffusion in $\mu$m-scaleperovskite crystals. To demonstrate the feasibility of the proposed approach,the fragment kMC method was applied to predict the diffusion coefficients ofhydrogen 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 weconclude that the proposed fragment kMC method can be applied to calculate theextent of ionic migration in $\mu$-scale materials with fully atomisticsimulation models at a reasonable computational cost.

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