Mixed Barrier Model for the Mixed Glass Former Effect in Ion Conducting Glasses

Mixing two types of glass formers in ion conducting glasses can be exploited to lower conductivity activation energy and thereby increasing the ionic conductivity, a phenomenon known as the mixed glass former effect (MGFE). We develop a model for this MGFE, where activation barriers for individual ion jumps get lowered in inhomogeneous environments containing both types of network forming units. Fits of the model to experimental data allow one to estimate the strength of the barrier reduction, and they indicate a spatial clustering of the two types of network formers. The model predicts a time-temperature superposition of conductivity spectra onto a common master curve independent of the mixing ratio.

Figure 1

Conductivity activation energy for $0.3{\mathrm{Li}}_2\mathrm{S}+0.7[(1-x){\mathrm{SiS}}_2+x{\mathrm{GeS}}_2]$ (▪) [5], ${\mathrm{Li}}_2\mathrm{S}+[(1-x){\mathrm{GeS}}_2+x{\mathrm{GeO}}_2]$ (▴) [9], and rapidly quenched $x{\mathrm{Li}}_4{\mathrm{SiO}}_4+(1-x){\mathrm{Li}}_3{\mathrm{BO}}_3$ (•) [2] glasses. The fits (solid lines) according to Eq. (1) yield $E_{AB}/E_B=0.69$, $z=2.8$ for the ${\mathrm{SiS}}_2\mathrm{\text{−}}{\mathrm{GeS}}_2$ system and $E_{AB}/E_B=0.67$, $z=2.0$ for the ${\mathrm{SiO}}_2\mathrm{\text{−}}{\mathrm{B}}_2{\mathrm{O}}_3$ system. Because of the missing value for $x=1$ in the ${\mathrm{GeS}}_2\mathrm{\text{−}}{\mathrm{GeO}}_2$ system, we fixed $z=2$ and fitted $E_{\sigma }(x)/E_{\sigma }(x=0.8)$, yielding $E_A/E_B=0.63$ and $E_{AB}/E_B=0.57$.

Figure 2

Normalized activation energy $E_{\sigma }(x)/E_{\sigma }(0)$ for different domain sizes $l=2.4$ (○), 4.3 (□), and 6.2 (▵). The solid line marks the solution Eq. (1) with $z=4$, and the dashed lines are fits to Eq. (1) with $z$ as fitting parameter ($E_{AB}/E_B=0.5$ fixed). Inset: Arrhenius plots of the conductivity (in units of ${\sigma }_0$, cf. caption of Fig. 3) calculated by using the velocity autocorrelation method [18] for $x=0.0$ (×), and for $x=0.4$ with $l=2.4$ (○), 4.3 (□), and 6.2 (▵); lines are least-square fits.

Figure 3

(a) Conductivity spectra $\sigma (\omega )$ (in units of ${\sigma }_0=n{e}^2\nu a^2/E_A$ with $n$ the number concentration of mobile ions) for fixed temperature, $k_{\mathrm{B}}T/E_A=0.01$, two domain sizes $l$, and various mixing ratios $x$. Inset: Conductivity spectra of ${\mathrm{LiS}}_2+(1-x){\mathrm{GeS}}_2+x{\mathrm{GeO}}_2$ glasses for $x=0.1$ (●), $x=0.2$ (×), and $x=0.4$ (▪) at $T=253\mathrm{K}$, as well as for $x=0.6$, $T=224\mathrm{K}$ (▴), and $x=0.8$, $T=231\mathrm{K}$ (◆). (b) Scaled conductivity spectra for the data shown in (a).