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. Multiple hoppings are then timely and spatially connected to reconstruct 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 like 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 accurately reproduces the ion conductivity obtained via the Green–Kubo formalism, which incorporates ion–ion correlations and corresponds to values measured by electrochemical methods such as impedance spectroscopy. This consistency validates the concerted migration picture from our directed-graph model. 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 offer a pathway to optimize the concerted ion migration in superionic conductors.