Formulation of a Statistical Mechanical Theory to Understand the Li Ion Conduction in Crystalline Electrolytes: A Case Study on Li-Stuffed Garnets

Ionic conductivity in solids is being computed using a wide range of computational methods such as molecular dynamics simulations and is measured using experimental methods, including electrochemical impedance spectroscopy and dc methods, and solid-state nuclear magnetic resonance spectroscopy. We report for the first time a statistical mechanical approach to estimate Li ion conductivity in the crystalline Li-stuffed garnet-type structure Li₅La₃Ta₂O₁₂, Li_5.5La_2.5Ba_0.5Ta₂O₁₂, and Li₆La₂BaTa₂O₁₂. The estimated conductivity and activation energy for ionic conduction were found to be very consistent with experimental values for all three investigated garnets. The ionic conductivity was computed from the electrostatic friction coefficient of the Li ion using a combination of nonequilibrium statistical mechanics and electrostatics. The developed theory is derived from the fundamental transport equations that can be adapted to a wide range of crystalline ceramics electrolytes where crystallographic information is available, and sophisticated computational software and equipment may not be needed.