Conductivity thresholds and glass structure in (K$_{2}$O)$_{x}$(GeO$_{2}$)$_{1-x}$ glasses

There are reports of conductivity thresholds with glass composition in solid electrolyte glasses. In the titled glass system, a seven order of magnitude increase in conductivity\footnote{Jain et al JNCS 222, 361 (1997).} occurs at x $>$ 0.10. The origin of the observation remains an open question. In titled glasses, we show that glass structure probed by the elastic behavior of its backbone shows two thresholds, a stress transition near x = 0.04 and a rigidity transition near x = 0.09. These elastic thresholds emerge from the reversibility window\footnote{S. Chakravarty et al. J.C.M.P 17,L1-7 (2005).} observed in calorimetric measurements, and in Raman scattering experiments that show scattering strength of the 520 cm$^{-1}$ mode of 3-member rings to show a global maximum in the reversibility window. The pronounced increase of conductivity apparently occurs when backbones become flexible at x $>$ 0.09, permitting K$^{+}$ ions to freely diffuse. The correlation between the electrical, thermal and optical properties of the present solid electrolyte glasses may well be a generic feature of these materials.