Small Polaron as the Source of the Frequency-Dependent Conductivity in Glasses Containing Transition Metal Oxides

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Abstract
Studies of the ac conductivity in glasses containing transition metal oxides show that there are two mechanisms for conduction present in the glasses. That mechanism which is dominant at low temperatures is characterized by almost complete temperature independence, and it is proportional to the frequency, while the mechanism dominant at high temperatures is characterized by an activation energy‐type temperature dependence, and it is independent of the frequency. An explanation of these effects based on a random glass lattice and the identification of the charge carrier as the small polaron is presented. This model leads to a prediction of a time‐dependent carrier concentration for the mechanism dominant at low temperatures. A formula for the conductivity as a function of temperature and frequency, which agrees well with the experimental observations, is derived from this model, using probability arguments. The reason for the good fit is discussed and some of the predictions of the formula are pointed out.