Non-Arrhenius ionic conductivities in glasses due to a distribution of activation energies

Previously observed non-Arrhenius behavior in fast ion conducting glasses [\textit{Phys.\ Rev.\ Lett.}\ \textbf{76}, 70 (1996)] occurs at temperatures near the glass transition temperature, $T_{g}$, and is attributed to changes in the ion mobility due to ion trapping mechanisms that diminish the conductivity and result in a decreasing conductivity with increasing temperature. It is intuitive that disorder in glass will also result in a distribution of the activation energies (DAE) for ion conduction, which should increase the conductivity with increasing temperature, yet this has not been identified in the literature. In this paper, a series of high precision ionic conductivity measurements are reported for $0.5{Na}_{2}{S}+0.5[x{GeS}_{2}+(1-x){PS}_{5/2}]$ glasses with compositions ranging from $0 \leq x \leq 1$. The impact of the cation site disorder on the activation energy is identified and explained using a DAE model. The absence of the non-Arrhenius behavior in other glasses is explained and it is predicted which glasses are expected to accentuate the DAE effect on the ionic conductivity.