Noise in beta "-alumina solid electrolytes: Theory and experiment.

Abstract

Measurements of noise in \ensuremath{\beta}'' aluminas (Na, Pb, Ag, and Ca) showing diffusion noise spectra, with high-frequency asymptote ${\mathrm{\ensuremath{\omega}}}^{\mathrm{\ensuremath{-}}3/2}$, have been reported by Brophy and co-workers since 1985, both for ceramics and single crystals. Comparison with the standard formulas by Burgess, Lax and Mengert, and Van Vliet and Fassett, showed that the observed noise was 9 to 12 orders of magnitude too high. In the present paper this discrepancy is addressed and removed. A detailed analysis is presented based on the two-dimensional planar diffusive motion of ions and defects in the Beevers-Ross (BR) and anti-Beevers-Ross sites of the conduction plane. Coulomb interaction in the plane is shown to have little effect due to screening; however, the antiferroelectric coupling, which gives rise to superlattice ordering as observed by Collin et al., causes correlated jumps within a coherence area, involving ambipolar motion of vacancy anti-BR sites, cation BR sites, and cation anti-BR sites. In addition, electrostatic induction via the spinel blocks couples the fluctuations in adjacent conduction planes. For Na-\ensuremath{\beta}'' and Pb-\ensuremath{\beta}'' single crystals quantitative agreement is obtained and the essential features of x-ray- and neutron-scattering data are confirmed.