Mixed alkali effects in beta-alumina and related solid electrolytes
The mixed alkali effects in the d.c. conductivity and other electrical properties of various ?-alumina systems have been studied, and by referring to the data obtained from X-ray measurements, these effects have been assigned to different cations exhibiting distinct but different site preferences. Cations which have a large ionic radius with respect to the conduction slot width (e.g. K+, Tl+) occupy BR sites because of the consequent reduction in steric and electrostatic repulsion energies. These then act to "block" the conduction pathways to the mobile species ("pathway blocking effect"). At higher "foreign" ion concentrations, the m0 sites will be filled after all the BR sites have been "used-up", resulting in the conductivity rising again. Typically, for this pattern of behaviour the minimum is found at 70% "foreign" ion content. The more polarizable Ag+ ion on the other hand shows a greater preference for interstitial sites than the Na+ ion does. This however is manifested in two ways: on initial replacement of Na+ by Ag+, mixed alkali interstitial pairs are formed which apparently are more mobile than (Na2)+ interstitial pairs; this results in a conductivity increase. The formation of Ag+ - 02- complexes immobilises the Ag+ ions, resulting in a conductivity decrease. Eventually this leads to a conductivity minimum at a composition close to that at which the formation of bound Ag+ triplets is optimised. In the T? system there is no conductivity minimum, the continuous decrease in conductivity being assigned to the decrease in the number of mobile ions (i.e. the Na+ ion). The T?+ ion is too large to participate in the conduction process. The Na - Li system is even more unusual in that it seems to show no set pattern of behaviour. X-ray experiments (in progress) seem to indicate that the system is influenced by a "site inversion" process which may have occurred in this work at two different compositions in different samples. We believe that Li+ ions initially go into m0 sites, giving rise to a conductivity minimum due to the "immobilisation effect" (as in Na - Ag). However the site inversion may also take place before this point has been reached, causing the MA effect now to be governed by the "blocking effect" giving a conductivity minimum at a higher Li+ ion content, (see also published work of Briant and Farrington). Work was also done on the glass system 0.40M20. 0.10B203. 0.50Si02' where M is Na, or a mixture of Na - Li or Na - K. The conductivities followed the general pattern observed before in MA glass systems, that is a continuous drop to a conductivity minimum at a composition around the middle of the isotherm. Overall, the K system produced a larger MA effect than the Li system. However on closer inspection of the dilute foreign alkali regions (i.e. small concentrations of K and Li) the behaviour of both systems was very similar. Using Moynihan and Lesikar's model of the weak electrolyte theory, it was possible to generate theoretical isotherms which coincided well with the experimental data. From this treatment, consistent values for the mobile ion concentration in the Na borosilicate glass were calculated. These seemed to indicate that the high conductivity of this Na borosilicate glass with respect to many other Na+ ion conducting glasses was due, not to a greater number of mobile ions (as Ravaine and Souquet have suggested), but rather to the ions being more mobile. A.c. effects in both types of system (vitreous and crystalline) were studied, in particular the broadening/narrowing of the modulus spectrum. These were assigned to the same factors which caused the MA effects in the d.c. conductivity i.e. "modulus narrowing" to immobilisation effects which restrict the motions of the "mobile" ions, and "modulus broadening" to partial blocking effects, which produce a distribution of path lengths. These crystals seem to provide the first opportunity for looking at "microscopic" theories of a.c. dispersions which have for many years attracted attention with regard to dielectric behaviour in glass.