Ionic correlations and failure of Nernst-Einstein relation in solid-state electrolytes

A microscopic understanding of fast ionic transport is fundamental to design novel solid-state electrolytes. We address the role of correlations in these systems and study in detail the tracer and charge diffusion coefficients, deriving a novel inequality between these two quantities. We investigate the failure of the Nernst-Einstein and the physical consequences of a nontrivial Haven ratio with extensive first-principles molecular dynamics in the fast ion conductor ${\text{Li}}_{10}{\text{GeP}}_2{\text{S}}_{12}$. Last, we show that the approximate tracer diffusion still provides accurate activation free energies.

Figure 1

The lithium density distribution in $\text{LGPS}$ obtained from FPMD simulations is in agreement with the experimental lithium crystallographic positions [3], reported with a radius proportional to site occupancy. The arrows point in the direction of active diffusion mechanisms.

Figure 2

The computed static fluctuation of the center of mass of lithium and sulfur atoms in LGPS, along all three Cartesian directions. Superimposed the linear behavior predicted by Eq. (5).

Figure 3

The integrated autocorrelation functions defined in Eq. (7) with error bars. The associated diffusion coefficients, equal to their value at large times, differ qualitatively. In the insets the short-time behavior is magnified.

Figure 4

On the left, the Arrhenius plot showing the difference between the tracer and charge diffusion coefficients as a function of inverse temperature. For comparison, values of the tracer diffusion coefficients from Ref. [4] are reported. In the upper right panel the ratio between the two coefficients along different directions as a function of temperature is shown. The table on the lower right summarizes values obtained for the Haven ratio, according to direction. $H_c$ and $H$ stand for values obtained with and without velocity renormalization, respectively, as in Eq. (6).