Title: Heterogeneity in Point Defect Distribution and Mobility in Solid Ion Conductors

Abstract: Alkali metal anodes paired with solid ion conductors offer promising avenues for enhancing battery energy density and safety. To facilitate rapid ion transport crucial for fast charging and discharging, it is essential to understand point defects within these conductors. In this study, we investigate the heterogeneity of defect distribution in Li$_3$OCl solid ion conductor, quantifying the defect formation energy (DFE) of lithium vacancies and interstitials as a function of distance from the surface through first-principles simulations. Our results reveal that the surface DFE is consistently lower than bulk except for one surface termination, indicating significant defect aggregation at surfaces. This difference can cause the defect density to be up to 14 orders of magnitude higher at surfaces compared to the bulk. Moreover, we unveil the transition in DFE when moving from the surface to the bulk through the DFE function, which exhibits an exponentially decaying relationship. Incorporating this exponential trend, we develop a revised model for the average behavior of defects that offers a more accurate description of the influence of grain size. Surface effects dominate for grain sizes $\lesssim$ 1 $\mu$m, highlighting the importance of surface defect engineering and the DFE function for accurately capturing ion transport in devices. We further explore the kinetics of defect redistribution by calculating the migration barriers for defect movement between bulk and surfaces. We find a highly asymmetric energy landscape for the lithium vacancies, exhibiting lower migration barriers for movement towards the surface compared to the bulk, while interstitial defects exhibit comparable kinetics between surface and bulk regions. These insights underscore the importance of considering both thermodynamic and kinetic factors in the design of solid ion conductors.