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Oxyhydrides have drawn attention because of their fast ion conductivity andstrong reducing properties. Recently, hydride ion migration inSrTiO$_{3-x}$H$_{x}$ oxyhydride crystals has been investigated, showing thathydride ion migration is blocked by slow oxygen diffusion. In this study, weinvestigate the hydride-ion migration mechanism using a kinetic Monte Carloapproach to understanding the relationship between the hydride and oxygen ions.The difficulties in applying the method to hydride and oxygen ion migrationinvolve complex changes in the ionic migration barrier, which shiftsdynamically depending on the characteristics of the surrounding hydride andoxygen ions. We can predict these complex changes using a machine-learningneural network model. The simulation can then be performed using this model topredict the temperature-dependent ionic-migration behavior. We found that oursimulation results with respect to the activation barrier for hydride iondiffusion accorded well with those obtained by experiment. We also found thathydride ion migration is affected by slow oxygen diffusion and that oxygendiffusion is accelerated by changes in the ionic migration barriers. Theparallel-processing efficiency of our proposed method was 84.92 \% for our1,000-CPU implementation, suggesting that the approach should be widelyapplicable to simulations of ionic migration in crystals at a reasonablecomputational cost.

Predicting highly correlated hydride-ion diffusion in SrTiO$_3$ crystals  based on the fragment kinetic Monte Carlo method with machine-learning  potential