Lattice-geometry effects in garnet solid electrolytes: a lattice-gas Monte Carlo simulation study

Abstract

Ionic transport in solid electrolytes can often be approximated as ions performing a sequence of hops between distinct lattice sites. If these hops are uncorrelated, quantitative relationships can be derived that connect microscopic hopping rates to macroscopic transport coefficients; i.e. tracer diffusion coefficients and ionic conductivities. In real materials, hops are uncorrelated only in the dilute limit. At non-dilute concentrations, the relationships between hopping frequency, diffusion coefficient and ionic conductivity deviate from the random walk case, with this deviation quantified by single-particle and collective correlation factors, f and fI, respectively. These factors vary between materials, and depend on the concentration of mobile particles, the nature of the interactions, and the host lattice geometry. Here, we study these correlation effects for the garnet lattice using lattice-gas Monte Carlo simulations. We find that, for non-interacting particles (volume exclusion only), single-particle correlation effects are more significant than for any previously studied three-dimensional lattice. This is attributed to the presence of two-coordinate lattice sites, which causes correlation effects intermediate between typical three-dimensional and one-dimensional lattices. Including nearest-neighbour repulsion and on-site energies produces more complex single-particle correlations and introduces collective correlations. We predict particularly strong correlation effects at xLi=3 (from site energies) and xLi=6 (from nearest-neighbour repulsion), where xLi=9 corresponds to a fully occupied lithium sublattice. Both effects are consequences of ordering of the mobile particles. Using these simulation data, we consider tuning the mobile-ion stoichiometry to maximize the ionic conductivity, and show that the ‘optimal’ composition is highly sensitive to the precise nature and strength of the microscopic interactions. Finally, we discuss the practical implications of these results in the context of lithium garnets and other solid electrolytes.

Dynamic Ion Correlations in Solid and Liquid Electrolytes: How Do They Affect Charge and Mass Transport?

“…From what we have discussed so far we can conclude that, although has been correctly used as a figure of merit to establish the presence of correlated ion transport in solid electrolytes, it provides minimal insight on the origin of these correlation effects. Indeed, for all the conditions simulated in the cubic garnet structure, the Haven ratio decreases monotonically as a function of lithium content, mimicking what one observes for the correlation factor in the simple hard‐core interactions scenario . For a fundamental understanding of the ionic transport, the correlation factor and the collective correlation factor are more insightful parameters as they are both strongly influenced by ion‐ion and ion‐lattice effects.…”

“…In the case of unequal site energies and hard‐core interactions combined (Figure c), the lithium ions preferentially fill the tetrahedral sites first. This is due to the fact that in the cubic garnet structure, the tetrahedral site is always lower in energy than the octahedral one . Similar to the nearest‐neighbor case, both and exhibit minima, here however, at a lithium content of x Li =3 when all Td sites are occupied.…”

“…Recently, Morgan reported a systematic study of the influence of correlated ion motion on the ionic conductivity of garnet solid electrolytes using lattice‐gas Monte Carlo simulations . In these simulations, a lattice of interconnected tetrahedral sites (Td, 1/3 of all sites) and octahedral sites (Oh, 2/3 of all sites) was considered.…”

“…Moreover, the collective correlation factor is , which means that both outcomes (S) and (D) described in Figure are equally probable at all x Li . Therefore, when only hard‐core interactions are considered, equals and we are looking at a simple vacancy‐mediated ion transport mechanism in the LLZO structure …”

“…Turning back to a real system, we would expect all of these interactions to play a role in the overall transport of the ions. As an exemplary scenario, we show the results for the conditions in which Δ E nn =Δ E site =3 k B T and the hard‐core interactions are also included (Figure d) . At Li contents x Li →3, the more energetically‐favorable tetrahedral sites are fully occupied and leads to an ordered state in the structure.…”