The temperature and frequency dependence of conductivity, dielectric properties, infrared absorption, and electron-paramagnetic-resonance data are presented for semiconducting phosphate glasses based on oxides of Ti, V, Mn, Fe, Co, Ni, Cu, Mo, and W. The vanadate system is examined in a range of compositions, most of the others in the composition 50 mol% oxide. A polaronic model is shown to be generally applicable, and the variation of activation energy for conduction with type of glass and transition-metal-ion (TMI) spacing is found to dominate the magnitude of the conductivity. In particular, a strong preexponential factor containing a term of the form $e^{-2\mathrm{}\alpha a}$ arising from electron tunneling is not observed. The results suggest that the theory of small polaron hopping in the adiabatic approximation may be most appropriate for phosphate glasses. Measurements of the static dielectric constant show no effects of disorder at high temperatures. Characteristic differences are noted between the infrared spectra of glasses such as V, Mo, W, and Ti and Ni, Co, Cu, and Mn, respectively, which are attributed to different structures within the glass matrix. These differences are suggested to lead to larger phonon dispersion in the latter glasses. It is found that the dependence of the properties of vanadate glasses upon composition can be described only if effects of polaron interactions are considered leading to a hopping probability of the form $c{\mathrm{}(1-c)\mathrm{}}^{n+1\mathrm{}}$, where $c$ is the proportion of TMIs in a reduced state and $n$ is the number of sites surrounding the polaron at which strong interactions occur. Reasonable agreement with experiment is obtained on this basis for the change in electrical properties with the value of $c$.

• Received 9 November 1971

DOI:https://doi.org/10.1103/PhysRevB.6.4629