Fast-ion conduction and flexibility and rigidity of solid electrolyte glasses

Abstract

Electrical conductivity of dry, slow cooled ${({\text{AgPO}}_{3})}_{1\ensuremath{-}x}{(\text{AgI})}_{x}$ glasses is examined as a function of temperature, frequency, and glass composition. From these data compositional trends in activation energy for conductivity ${E}_{A}(x)$, Coulomb energy ${E}_{c}(x)$ for ${\text{Ag}}^{+}$ ion creation, Kohlrausch stretched exponent $\ensuremath{\beta}(x)$, low-frequency $[{\ensuremath{\epsilon}}_{s}(x)]$ and high-frequency $[{\ensuremath{\epsilon}}_{\ensuremath{\infty}}(x)]$ permittivity are deduced. All parameters except ${E}_{c}(x)$ display two compositional thresholds, one near the stress transition, $x={x}_{c}(1)=9%$, and the other near the rigidity transition, $x={x}_{c}(2)=38%$ of the alloyed glass network. These elastic phase transitions were identified in modulated differential scanning calorimetry, IR reflectance, and Raman-scattering experiments earlier. A self-organized ion-hopping model of a parent electrolyte system is developed that self-consistently incorporates mechanical constraints due to chemical bonding with carrier concentrations and mobility. The model predicts the observed compositional variation in $\ensuremath{\sigma}(x)$, including the observation of a steplike jump when glasses enter the intermediate phase (IP) at $x>{x}_{c}(1)$, and an exponential increase when glasses become flexible at $x>{x}_{c}(2)$. Since ${E}_{c}$ is found to be small compared to network strain energy $({E}_{s})$, we conclude that free carrier concentrations are close to nominal AgI concentrations, and that fast-ion conduction is driven largely by changes in carrier mobility induced by an elastic softening of network structure. Variation in the stretched exponent $\ensuremath{\beta}(x)$ is square-well like with walls localized near ${x}_{c}(1)$ and ${x}_{c}(2)$ that essentially coincide with those of the IP $({x}_{c}(1)<x<{x}_{c}(2))$, and suggest filamentary (quasi-one-dimensional) conduction in the IP, and conduction with a dimensionality greater than 1 outside the IP.