ABSTRACT
In low-viscosity liquids, diffusion is inversely related to viscosity via the Stokes-Einstein relation. However, the Stokes-Einstein relation breaks down near the glass transition as the supercooled liquid transitions into the non-ergodic glassy state. The nonequilibrium viscosity of glass is governed by the liquid-state viscous properties, namely, the glass transition temperature and the fragility. Here, a model is derived to predict the ionic diffusivity of a glass from its nonequilibrium viscosity, accounting for the compositional dependence of the glass. The free energy activation barrier for diffusion is related to the activation enthalpy for viscous flow using the Mauro-Allan-Potuzak model of nonequilibrium viscosity [Mauro, J. C.; Allan, D. C.; Potuzak, M. Nonequilibrium Viscosity of Glass. Phys. Rev. B 2009, 80, 094204]. These insights allow for accurate prediction of activation barriers for diffusion of alkali ions. The model is supported by experimental results and nudged-elastic band calculations applied to sodium silicate and borate glasses.
ABSTRACT
The mixed alkali effect, the deviation from expected linear property changes when alkali ions are mixed in a glass, remains a point of contention in the glass community. While several earlier models have been proposed to explain mixed alkali effects on ionic motion, models based on or containing discussion of structural aspects of mixed-alkali glasses remain rare by comparison. However, the transition-range viscosity depression effect is many orders in magnitude for mixed-alkali glasses, and the original observation of the effect (then known as the Thermometer Effect) concerned the highly anomalous temperature dependence of stress and structural relaxation time constants. With this in mind, a new structural model based on topological constraint theory is proposed herein which elucidates the origin of the mixed alkali effect as a consequence of network strain due to differing cation radii. Discussion of literature models and data alongside new molecular dynamics simulations and experimental data are presented in support of the model, with good agreement.
ABSTRACT
Conductivity data of the xAgI(1 - x)AgPO(3) system (0 ≤ x ≤ 0.5) were collected in the liquid and glassy states. The difference in the dependence of ionic conductivity on temperature below and above their glass transition temperatures (T(g)) is interpreted by a discontinuity in the charge carrier's mobility mechanisms. Charge carrier displacement occurs through an activated mechanism below T(g) and through a Vogel-Fulcher-Tammann-Hesse mechanism above this temperature. Fitting conductivity data with the proposed model allows one to determine separately the enthalpies of charge carrier formation and migration. For the five investigated compositions, the enthalpy of charge carrier formation is found to decrease, with x, from 0.86 to 0.2 eV, while the migration enthalpy remains constant at ≈0.14 eV. Based on these values, the charge carrier mobility and concentration in the glassy state can then be calculated. Mobility values at room temperature (≈10(-4) cm(2) V(-1) s(-1)) do not vary significantly with the AgI content and are in good agreement with those previously measured by the Hall-effect technique. The observed increase in ionic conductivity with x would thus only be due to an increase in the effective charge carrier concentration. Considering AgI as a weak electrolyte, the change in the effective charge carrier concentration is justified and is correlated to the partial free energy of silver iodide forming a regular solution with AgPO(3).
