Fast ionic conduction in ${\mathrm{Na}}_2$S+${\mathrm{B}}_2$${\mathrm{S}}_3$ glasses: Compositional contributions to nonexponentiality in conductivity relaxation in the extreme low-alkali-metal limit

The conductivity relaxation phenomenon in glassy and crystalline ionic conductors has been known for many years to be a highly nonexponential process. The stretched exponential function exp-(t/τ${)}^{\mathrm{\beta }}$ has been used with varying levels of success to describe this relaxation. Whether the nonexponentiality is due to parallel conducting processes acting independently of each other and having a distribution of relaxation times or to serial processes strongly coupling the ionically conducting species and constraining each other’s relaxation, the exact nature of this process is still unknown. If coupling is the active mechanism responsible for the nonexponentiality, then there should be a relationship between the extent of the nonexponentiality and the average ion separation distance; the greater the ion-ion separation, the smaller the coupling between the ions. To test this hypothesis, wide composition, frequency, and temperature range conductivity measurements have been performed on the fast-ion-conducting glass series, ${\mathrm{Na}}_2$S+${\mathrm{B}}_2$ ${\mathrm{S}}_3$. For x(${\mathrm{Na}}_2$S)=0.001, the relaxation is nearly exponential. As the ${\mathrm{Na}}_2$S concentration increases, the estimated ion-ion separation distance decreases; so do both the dc conductivity activation energy and the β parameter in the stretched exponential. The β parameter, however, shows a much stronger dependence to the ion-ion separation distance. It is also found that for nearly all of the glasses studied to date, the composition dependencies of the β parameter can be cast onto a master plot of β versus average ion-ion separation distance. In this way, we provide a universal trend for the compositional dependence of the nonexponentiality in glass.