Reconciling ionic-transport properties with atomic structure in oxide glasses

Structural evidence for the microsegregation of alkalis in oxide glasses is reviewed and the implications for ionic transport, viz., nearest-neighbor hopping, cooperative and correlation effects, are considered. Distinctions are drawn between the hopping of alkalis in silicate glasses, where changes in the configurations of neighboring bridging and nonbridging oxygens are expected, and alkali hopping in fully compensated aluminosilicate glasses where nonbridging oxygens are absent and conformational changes in the network are minimized. A simple expression is introduced for the microscopic energy barrier facing a migrating alkali ${\mathit{E}}_{\mathit{a}}$, and this is corrected to account for the cooperative effects of the other ions involved by dividing by the Kohlrausch exponent β, which defines the conductivity relaxation function exp[-(t/${\mathrm{\tau }}^{\mathrm{*}}$)β]. Structural parameters determined by x-ray and NMR spectroscopy enable us to calculate ${\mathit{E}}_{\mathit{a}}$. Conductivity relaxation experiments give a measure of β. The macroscopic diffusion enthalpy that is measured, W, is given by the ratio ${\mathit{E}}_{\mathit{a}}$/β. Thus we are able to show how the local structure of an alkali in a silicate glass can be used to predict the measured diffusion enthalpy. The smaller values of W reported for aluminosilicate glasses are rationalized structurally in terms of the removal of nonbridging oxygens from the modified network. In considering silicate glasses containing small concentrations x of alkali, as this necessarily leads to reductions in alkali microsegregation, decreased cooperative effects and increased hopping distances are expected.

Taken together with the attendant fall in the high-frequency dielectric constant and the rise in β, this combination of changes naturally explains the increased enthalpies observed in low alkali glasses and the rise in alkali diffusion frequency factors. Increased hopping distances are also invoked to explain the crossover dependences of the diffusion coefficients and enthalpies of the separate alkalis in mixed alkali glasses. In particular, the increase in W for a given alkali, as its proportion γ drops for a fixed alkali concentration x, is attributed to an increase in the hopping distance and can again be predicted from the local structure, providing allowance is made for an associated reduction in cooperative effects. From the separate local structures of the two alkalis, the observed fall in the diffusion coefficients of the two alkalis and the minima in the isothermal dc electrical conductivity resulting from the increase in the respective diffusion enthalpies are well reproduced. In addition, the maxima in the measured dc electrical conductivity enthalpy W in the Kohlrausch exponent β and also in the Haven ratio f, all characteristic of alkali mixing, are closely predicted. Finally the increase in magnitude of the mixed alkali effect reported in aluminosilicate glasses is explained in terms of increased cooperativity associated with the reduced energy barriers ${\mathit{E}}_{\mathit{a}}$ for the two alkalis resulting from there being fewer nonbridging oxygens present in the glass structure.