Scaling Behavior in the Conductivity of Alkali Oxide Glasses, Polymers, and Doped Crystals

Although the frequency dependent conductivity, σ(ω), of ion-containing glasses displays power law dispersion (σ(ω) ≈ ωn) that can usually be described by a master curve, several findings have suggested that this scaling fails at low temperatures as indicated by a temperature dependence of the scaling exponent, n. This behavior is investigated in the frequency range between 1 Hz and 106 Hz for different materials including alkali metaphophate glasses and a polymer. Two distinct regimes of conductive behavior, σI and σII, are identified. The first, σI, is strongly temperature dependent and appears to obey a master curve representation. The second, σII, exhibits only a weak temperature dependence with a roughly linear frequency dependence. A strong depression of σI occurs for the mixed alkali case, but σII is unaffected and occurs at roughly the same location in all the alkali compositions studied. It is proposed that σII does not arise from cation motion, but rather originates from a second mechanism likely involving small distortions of the underlying glassy matrix. This assignment of σII is further supported by the approximately universal location of σII, to within an order of magnitude, of a variety of materials, including a polymer electrolyte and doped crystal. Since σI(T) and σII(T ≈ const.) are viewed as separate phenomena, the temperature dependence of the scaling exponent is shown to result merely from a superposition of these two contributions and does not indicate any intrinsic failure of the scaling property of σI