Polaronic transport in iron phosphate glasses containing HfO₂ and CeO₂

The electrical and dielectric properties of three series of glasses, xHfO₂-(40 - x)Fe₂O₃-60P₂O₅, 0 ≤ x ≤ 8 mol%, xCeO₂-(40 - x)Fe₂O₃-60P₂O₅, 0 ≤ x ≤ 8 mol%, and xHfO₂-(38 - x)Fe₂O₃-2B₂O₃-60P₂O₅ 2 ≤ x ≤ 6 mol%, have been investigated by impedance spectroscopy over a wide frequency and temperature range. As expected, these glasses exhibit polaronic conductivity which strongly depends on the fraction of ferrous ions, Fe²⁺/Fe_tot. Following a detailed discussion on the DC conductivity, we use the MIGRATION concept to model their conductivity spectra. It is found that in each series of glasses, the shape of the conductivity isotherms remains the same indicating that the time-temperature superposition principle is satisfied and that the mechanism of conductivity is the same. Returning to a model-free scaling procedure, namely Summerfield scaling, it is found that while conductivity isotherms for each composition yield a master curve, we need to suitably shift individual master curves on the frequency axis to generate a super-master curve. We examine the dependence of the DC conductivity and the shift factors on the number density of charge carriers. Next, using the fact that the dielectric strength of relaxation for each isotherm is well-defined in these systems, we scale the conductivity isotherms using the Sidebottom scaling procedure. This procedure yields a super-master curve, implying that length scales for polaronic transport also change with composition. Further, using the scaling features of permittivity spectra, we extract in a straightforward way the characteristic spatial extent of localized hopping of polarons and find that it decreases with increasing number density of charge carriers. The magnitude of these values obtained from permittivity spectra lies in the same range as those for the polaron radius calculated using the equation proposed by Bogomolov and Mirilin.