The mixed-alkali effect discussed within the context of percolative transport

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Maas et al. have discussed the mixed-alkali as a relaxation process whereby structures of amorphous systems adjust differently to different cations (dynamic structure model). In its original form, the dynamic structure model did not account for the strong frequency dependence of the conductivity observed in the presence of a single species of cation as it incorporates no other disorder into the amorphous structure. The percolation model has been able to predict the frequency dependence of the ac conductivity, but has not yet incorporated the influence of any effective interaction between cations (actually between individual cations and the structure) which would disfavor occupation of a site with a type A cation, if a type B cation has recently vacated the site. Such an interaction effectively decreases the number of sites available to a given cation species when a second type of cation is also present. In a statistical interpretation it leads to a reduction in the total energy when both cations are present, an effective attractive interaction. Within the percolation framework the additional physical constraint regarding site compatibility is now approximately taken into account (assuming that the time required for the adjustment of a given site to a new cation is very long, i.e., involves structural relaxation). Such an assumption is a natural extension of this model; incorporation of effects of a random potential into the dynamic structure model should make the treatments more nearly compatible.