Visualizing Concerted Ion Migration of Superionic Conductors via Directed Graphs

A directed-graph model is proposed to describe the concerted ion migration in superionic conductors. Here, each ion hopping during the molecular dynamics simulation is represented as a displacement vector. One hopping event is then temporally and spatially connected to another based on a cutoff distance determined from the short-range part of the van Hove correlation function (i.e., closer than the first peak of the pair distribution function), thereby reconstructing the concerted ion migration. This enables the quantitative visualization of concerted migration within short time intervals. The parameters of this model are derived from physically meaningful quantities such as jump distances, diffusion coefficients, and pair distribution functions, reducing the reliance on arbitrary hyperparameters. We applied the model to Li10GeP2S12, Na2Ni2TeO6, and AgI, demonstrating its general applicability and robustness. The model quantitatively bridges microscopic ion trajectories with macroscopic ionic conductivity. It accurately reproduces the ion conductivity obtained via the Green–Kubo formalism with ion–ion correlations, corresponding to conductivities measured by electrochemical methods such as impedance spectroscopy. This consistency validates the concerted migration picture from our directed-graph model, where more than five ions are frequently involved in each concerted migration event. Our analysis further reveals that enhanced conductivity is linked to a local “correlation distance” between hopping ions. This suggests that controlling local interactions such as ion-lattice coupling offers a pathway to optimize the concerted ion migration in superionic conductors.