Mechanistic Origin of Superionic Lithium Diffusion in Anion-Disordered Li6PS5X Argyrodites

The rational development of fast-ion-conducting solid electrolytes for all-solid-state lithium-ion batteries requires understanding the key structural and chemical principles that give some materials their exceptional ionic conductivities. For the lithium argyrodites Li6PS5X (X = Cl, Br, or I), the choice of the halide, X, strongly affects the ionic conductivity, giving room-temperature ionic conductivities for X = {Cl,Br} that are ×103 higher than for X = I. This variation has been attributed to differing degrees of S/X anion disorder. For X = {Cl,Br}, the S/X anions are substitutionally disordered, while for X = I, the anion substructure is fully ordered. To better understand the role of substitutional anion disorder in enabling fast lithium-ion transport, we have performed a first-principles molecular dynamics study of Li6PS5I and Li6PS5Cl with varying amounts of S/X anion-site disorder. By considering the S/X anions as a tetrahedrally close-packed substructure, we identify three partially occupied lithium sites that define a contiguous three-dimensional network of face-sharing tetrahedra. The active lithium-ion diffusion pathways within this network are found to depend on the S/X anion configuration. For anion-disordered systems, the active site–site pathways give a percolating three-dimensional diffusion network; whereas for anion-ordered systems, critical site–site pathways are inactive, giving a disconnected diffusion network with lithium motion restricted to local orbits around S positions. Analysis of the lithium substructure and dynamics in terms of the lithium coordination around each sulfur site highlights a mechanistic link between substitutional anion disorder and lithium disorder. In anion-ordered systems, the lithium ions are pseudo-ordered, with preferential 6-fold coordination of sulfur sites. Long-ranged lithium diffusion would disrupt this SLi6 pseudo-ordering, and is, therefore, disfavored. In anion-disordered systems, the pseudo-ordered 6-fold S–Li coordination is frustrated because of Li–Li Coulombic repulsion. Lithium positions become disordered, giving a range of S–Li coordination environments. Long-ranged lithium diffusion is now possible with no net change in S–Li coordination numbers. This gives rise to superionic lithium transport in the anion-disordered systems, effected by a concerted string-like diffusion mechanism.

Our focus in this study is on the underlying diffusion mechanisms operating in each molecular dynamics simulation. To help identify these we post-process each simulation trajectory to obtain a set of "inherent structures" that capture the key diffusive motions of the lithium ions [1][2][3]. Each inherent structure is generated by taking a "snapshot" single configuration from the relevant molecular dynamics trajectory and performing a conjugategradient geometry optimisation, which relaxes the structure into a local potential energy minimum. By repeating this process for a sequence of configurations sampled at fixed time-intervals we obtain an "inherent-structure trajectory" that can then be analysed alongside the original unprocessed simulation trajectory.
These inherent-structure trajectories are useful because we are interested in identifying non-trivial displacements of lithium ions, i.e. those displacements that contribute to net lithium diffusion. These are different to vibrational motions, which produce short-lived lithium displacements that do not contribute to meaningful lithium diffusion. For a given starting configuration, performing a geometry optimisation to obtain the corresponding inherent structure has the effect of "quenching out" much of this high-frequency thermal motion, providing a clearer description of the underlying diffusion mechanisms. Figure S1 shows the unprocessed x, y, z coordinates for a single lithium ion from the 50 % site-inverted Li 6 PS 5 Cl siulation, and the corresponding inherent structure coordinates. The inherent structure trajectory tracks the unprocessed trajectory, but filters out much of the shorttimescale short-ranged vibrational motion. The larger scale diffusion motion that describes the movement of the lithium ion through the host framework, however, is preserved. * b.j.morgan@bath.ac.uk To help understand the different mechanisms of lithium diffusion in our simulations, part of our analysis of the simulation trajectories consists of an analysis of lithium positions and dynamics in terms of occupation of the set of tetrahedral holes formed by the closepacked S/X-anion substructure. Occupation of a specific tetrahedron broadly corresponds to a lithium ion being assigned as occupying the corresponding crystallographic site, and transitions between adjacent tetrahedra give a discretised "site-to-site" description of the lithium diffusion process.
Because the calculation of each inherent structure involves performing a geometry optimisation to relax the structure into a local potential energy minimum, the structures of any given molecular dynamics configuration and its corresponding inherent structure differ. For any single molecular dynamics timestep, this can lead to individual lithium ions being assigned to different sites depending on whether the coordinates from the raw trajectory or from the corresponding inherent structure are used when calculating the tetrahedral-site occupations.
This behaviour is illustrated in Figure S2, which shows  the indices of the sites assigned as "occupied" at each timestep for a single lithium ion from the 0 % siteinverted Li 6 PS 5 I simulation (upper panel) and from the 50 % site-inverted Li 6 PS 5 Cl simulation (lower panel). Both site-occupation trajectories follow the same general sequence of sites, and describe the same underlying diffusion behaviour. The site-occupation trajectory obtained from the unprocessed simulation coordinates, however, contains transient site-to-site transitions that are absent from the inherent structure trajectory. These additional transitions correspond to short-lived vibrational motions; in nearly every case the transition to a new site does not persist beyond a single analysis frame. Working with the inherent structure trajectory, therefore, has the benefit of filtering out these non-diffusive "vibrational" transitions between sites, while preserving the transitions that describe the time-evolution of the lithium-ion configuration that underpins the key lithium-diffusion processes.

DATA AVAILABILITY
A dataset containing inputs and outputs for all DFT calculations supporting this study is available under the CC-BY-4.0 licence from the University of Bath Research Data Archive [5]. All code used to analyse the simulation trajectories and to generate the corresponding figures is available as a series of Jupyter notebooks under the MIT licence as Ref. [4].