Diffusion and Ion Conduction in Cation-Conducting Oxide Glasses
Authors: Mehrer Helmut 
Published: February 2016

In this Chapter we review knowledge about diffusion and cation conduction in oxide glasses. We first remind the reader in Section 1 of major aspects of the glassy state and recall in Section 2 the more common glass families. The diffusive motion in ion-conducting oxide glasses can be studied by several techniques – measurements of radiotracer diffusion, studies of the ionic conductivity by impedance spectroscopy, viscosity studies and pressure dependent studies of tracer diffusion and ion conduction. These methods are briefly reviewed in Section 3. Radiotracer diffusion is element-specific, whereas ionic conduction is not. A comparison of both types of experiments can throw considerable light on the question which type of ions are carriers of ionic conduction. For ionic conductors Haven ratios can be obtained from the tracer diffusivity and the ionic conductivity for those ions which dominate the conductivity.In the following sections we review the diffusive motion of cations in soda-lime silicate glass and in several alkali-oxide glasses based mainly on results from our laboratory published in detail elsewhere, but we also take into account literature data.Section 4 is devoted to two soda-lime silicate glasses, materials which are commonly used for window glass and glass containers. A comparison between ionic conductivity and tracer diffusion of Na and Ca isotopes, using the Nernst-Einstein relation to deduce charge diffusivities, reveals that sodium ions are the carriers of ionic conduction in soda-lime glasses. A comparison with viscosity data on the basis of the Stokes-Einstein relation shows that the SiO2 network is many orders of magnitude less mobile than the relatively fast diffusing modifier cations Na. The Ca ions are less mobile than the Na ions but nevertheless Ca is considerably more mobile than the network.Section 5 summarizes results of ion conduction and tracer diffusion for single Na and single Rb borate glasses. Tracer diffusion and ionic conduction have been studied in single alkali-borate glasses as functions of temperature and pressure. The smaller ion is the faster diffusing species in its own glass. This is a common feature of all alkali oxide glasses. The Haven ratio of Na in Na borate glass is temperature independent whereas the Haven ratio of Rb diffusion in Rb borate glass decreases with decreasing temperature.Section 6 reviews major facts of alkali-oxide glasses with two different alkali ions. Such glasses reveal the so-called mixed-alkali effect. Its major feature is a deep minimum of the conductivity near some middle composition for the ratio of the two alkali ions. Tracer diffusion shows a crossover of the two tracer diffusivities as functions of the relative alkali content near the conductivity minimum. The values of the tracer diffusivities also reveal in which composition range which ions dominate ionic conduction. Tracer diffusion is faster for those alkali ions which dominate the composition of the mixed glass.Section 7 considers the pressure dependence of tracer diffusion and ionic conduction. Activation volumes of tracer diffusion and of charge diffusion are reviewed. By comparison of tracer and charge diffusion the so-called Haven ratios are obtained as functions of temperature, pressure and composition. The Haven ratio of Rb in Rb borate glass decreases with temperature and pressure whereas that of Na in Na borate glass is almost constant.Section 8 summarizes additional common features of alkali-oxide glasses. Activation enthalpies of charge diffusion decrease with decreasing average ion-ion distance. The Haven ratio is unity for large ion-ion distances and decreases with increasing alkali content and hence with decreasing ion-ion distance.Conclusions about the mechanism of diffusion are discussed in Section 9. The Haven ratio near unity at low alkali concentrations can be attributed to interstitial-like diffusion similar to interstitial diffusion in crystals. At higher alkali contents collective, chain-like motions of several ions prevail and lead to a decrease of the Haven ratio. The tracer diffusivities have a pressure dependence which is stronger than that of ionic conductivity. This entails a pressure-dependent Haven ratio, which can be attributed to an increasing degree of collectivity of the ionic jump process with increasing pressure. Monte Carlo simulations showed that the number of ions which participate in collective jump events increases with increasing ion content – i.e. with decreasing average ion-ion distance. For the highest alkali contents up to four ions can be involved in collective motion. Common aspects of the motion process of ions in glasses and of atoms in glassy metals are pointed out. Diffusion in glassy metals also occurs by collective motion of several atoms.Section 10 summarizes the major features of ionic conduction and tracer diffusion and its temperature and pressure dependence of oxide glasses.