E5 Diffusion and Ionic Mobility (Mixed Alkaline Effect)

Topic

In its mathematical form, ionic transport within this glass follows the same framework used for the same purpose by another model in this set—specifically, the one describing ionic transport in a ceramic. This framework comprises the Nernst-Einstein relation, which links the diffusion coefficient of each mobile ion to the ionic conductivity produced by that ion, and the Arrhenius dependence, which describes how that ionic conductivity increases with temperature. Because this glass shares this mathematical form with the ceramic, an increase in temperature results in a comparable increase in ionic conductivity for both materials, in accordance with the Arrhenius dependence.

When this glass contains a single alkali oxide as the mobile ionic charge carrier, its ionic conductivity is determined solely by the concentration and mobility of that alkali ion within the network; this "pure" ionic conductivity serves as a reference point against which other compositions of the same glass are compared. The presence of only one type of alkali ion, rather than a mixture of several, ensures that the ionic conductivity remains close to that pure value, free from additional anomalies.

Conversely, when the glass contains a mixture of two different alkali oxides instead of just one, the ionic conductivity no longer falls along the linear interpolation one would expect between the pure ionic conductivities of the individual alkali oxides; instead, it drops well below that line. This anomalous, markedly non-linear reduction in ionic conductivity is precisely the "mixed-alkali effect." As the ratio of the two alkali oxides approaches an equal mixture—rather than being dominated by one—this mixed-alkali effect typically becomes more pronounced, causing the ionic conductivity to fall even further below the expected linear interpolation. Thus, this model—with the ionic transport and mixed-alkali effect that initially defined it—highlights an anomaly characteristic and distinctive of this glass when compared to a crystalline ceramic: the fact that this glass lacks the structural periodicity found in the ceramic means that the mixture of two different alkali oxides moving within the same disordered network creates mutual interference—a phenomenon not replicated by an equivalent mixture within a periodic crystalline network—and that this interference is, ultimately, what produces the mixed-alkali effect itself, which has no counterpart in the crystalline ceramic.

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