Mid- And far-infrared absorption of alkali borate glasses and the limit of superionic conductivity

Transmission spectra of alkali borate glass films of known thickness have been studied as a function of film thickness in the frequency range 50-2000 cm^-1, and the composition range 0-70 mol % Na₂O. The apparent absorption coefficient of the Na⁺ "rattling" mode at ≈200 cm^-1 becomes almost independent of film thickness for d > 5 μ, implying that the absorption coefficient α of the bulk glass can be determined with reasonable accuracy, α proves to be a linear function of alkali oxide content. We use the value of α to estimate the ionic conductivity at infrared frequencies, and argue that this value establishes the theoretical maximum for superionic conductivity - it lies some 10 orders of magnitude above the ambient temperature conductivity of the high alkali glass. It is suggested that the peak value of the IR conductivity is connected to the ac conductivity of glass by a log σ(f) vs log/regime of unit slope [specifically σ/(S cm^-1) = 10^-12.3f] up to 100 GHz, followed by a short f² regime. The mid-IR spectra indicate the presence of four coordinated borons with maximum concentration at 40 mol % Na₂ O, and confirm that B₂O^{5 4-} and BO₃^3- moities dominate the structure at the high alkali extreme.