Layer-Resolved Decomposition of the Van Hove Function Reveals Non-Gaussian Proton Transport in a Layered Oxide

Abstract

Understanding non-Gaussian ion transport in crystalline solids is essential for linking local atomic environments with long-range conductivity. Here, we investigate proton diffusion in the layered oxide Ba2ScAlO5·0.125H2O using nanosecond-scale molecular dynamics simulations based on the M3GNet machine-learning potential. Under conditions where the structural layering of protons is well preserved, the system exhibits a clear separation between low-mobility layers (Layers 2 and 6) and high-mobility layers (Layers 4 and 8). This enables a physically grounded decomposition of the self-part of the Van Hove function into ions that remain persistently confined within low-mobility layers and ions in high-mobility layers that show only transient early time localization before following percolating in-plane pathways that support long-range transport. This distinction removes the arbitrariness inherent in mobility-based classifications and clarifies the microscopic origin of heterogeneous ion dynamics in layered crystalline materials. In the fast layer, the fast population develops a broad, weakly confined early time distribution that evolves into a Lévy-like algebraic tail whose envelope remains nearly time-invariant. A hybrid Tsallis–exponential model accurately captures both the non-Gaussian central peak and the truncated power-law tail. The cutoff length of the tail grows superdiffusively with time, revealing a hierarchy of rare, long-range jumps that dominate the mean-squared displacement even after the system enters an apparently diffusive region. These results establish a general framework for resolving heterogeneous transport in ordered ionic materials and provide new insight into the microscopic origins of non-Gaussian proton dynamics.