New nearly constant loss feature detected in glass at low temperatures

At sufficiently low temperatures, disordered ionic materials display the well-known Nearly Constant Loss (NCL) effect, with ionic conductivities becoming approximately proportional to frequency and virtually independent of temperature. There is a broad consensus that the effect is a collective phenomenon, with many interacting ions participating, each of them performing some non-vibrational motion that remains strictly localised. The underlying many-particle dynamics have been analysed in Monte Carlo simulations and also by straightforward modelling. Both kinds of treatment predict that, with decreasing frequency, a frequency squared behaviour should become visible. Here, we report on the experimental detection of the squared to linear crossover in an NCL component of conductivity spectra of sodium borate glasses, xNa2O·(1 − x) B2O3 with x = 0.05 and x = 0.1, at temperatures below 100 K. From the composition dependence of the effect it is obvious that it is caused by the sodium ions. We demonstrate that this behaviour corresponds to an almost trivial property of the mean square displacement of the confined, but locally mobile ions, which approaches a temperature-independent long-time value, reflecting the finite size of the accessible volume. In the log–log plot of measured conductivity versus frequency, the transition from slope two to slope one is rather gradual, reflecting the existence of different local neighbourhoods of the sodium ions.