Quantifying Continuous Configurational Entropies in Solid Electrolytes from Molecular Dynamics Simulations

Within structurally related families of solid electrolytes, increasing disorder of some form is often associated with increased ionic conductivity. One such form of disorder that is often invoked to explain trends in ionic conductivity is the spatial or "configurational" disorder of the mobile ions. As a general rule, materials in which the mobile ions occupy identical regularly arranged sites are poor solid electrolytes, while materials with mobile ions that are disordered over crystallographically inequivalent sites often have much higher ionic conductivities. Providing the mobile ions occupy well-defined crystallographic sites, the degree of site disorder can be quantified from molecular dynamics simulation data using Shannon-like discrete configurational entropies, which are calculated as a function of the probabilities of each site being occupied [1].<br/><br/>While this approach yields semi-quantitative "configurational entropies" for the mobile ion species, the resulting values depend on the choice of discrete sites within each structure and on the approach used to assign mobile ions to individual sites. In addition, it necessarily gives a "coarse-grained" description of the mobile-ion configurational entropy and may discard useful information.<br/><br/>In this talk, we will present an alternative approach, wherein we calculate a continuous configurational entropy using methods drawn from the field of solution chemistry [2], using as input the time-average density of the mobile ion species calculated from molecular dynamics simulation. Obtaining well-converged results for the continuous single-particle entropy requires well-converged low-variance mobile ion densities, which we calculate using advanced statistical mechanical sampling techniques [3, 4].<br/><br/>While full thermodynamic calculations require accounting for many-body contributions to the configurational entropy, the single-particle configurational entropy is a useful descriptor for quantifying the degree of disorder for the mobile ion species in solid electrolytes. As an illustrative example, we apply our method to the lithium-ion solid electrolyte Li₇La₃Zr₂O₁₂ (LLZO) and compare results for the low-temperature poorly-conducting tetragonal phase versus high-temperature highly-conducting cubic phase. Our results predict that the change in configurational entropy for the transition from tetragonal to cubic LLZO includes a non-trivial contribution from the host-framework configurational entropy, which would be considered to be zero using a discrete-site-projection scheme. This result provides a quantitative link between host-framework flexibility, mobile-ion disorder, and ionic conductivity in this archetypical lithium-ion solid electrolyte.<br/><br/>[1] Kweon et al. Chem. Mater. 29, 9142 (2017)<br/>[2] Lazaridis. J Phys. Chem. B 102, 3541 (1998)<br/>[3] Coles et al. J. Chem. Phys. 151, 064124 (2019)<br/>[4] Coles et al. J. Chem. Phys. 154, 191101 (2021).