Anomalous-diffusion model of ionic transport in oxide glasses

The power-law frequency dependence of both the conductivity, σ(ω), and permittivity, ɛ(ω), of ion-conducting materials suggests that self-similar or scale-invariant behavior influences the transport of ions at high frequencies. Using an anomalous-diffusion model, we derive relevant power-law expressions for σ(ω) and ɛ(ω) and compare these with measurements performed on ${\mathrm{LiPO}}_3$ glass. Superior fits to the measured data are obtained compared to the commonly used Kohlrausch-Williams-Watts (KWW) description of the electrical modulus, most particularly in the notorious high-frequency regime. Evaluation of our results in terms of an anomalous-diffusion model suggests the dominance of interaction-based constraints to diffusion.