Understanding transport properties of conducting solids: Meyer-Neldel rule revisited

Fundamental understanding of mass transport in solids as a function of temperature is crucial to applications in various all-solid-state ionic devices, including fuel cells, sensors, and batteries. Commonly, electrical properties have been investigated at various temperatures and the activation energy computed from the slope of the Arrhenius plot. Changes in the activation energy as a function of chemical composition induced by chemical substitution/doping are used as a tool to understand defects and transport phenomena in solids. Meyer and Neldel found that the energy of activation can appear in the pre-exponential factor, A, in a manner that cancels the traditional activation energy factor in the Arrhenius equation at a certain transition temperature. This pre-exponential activation energy is manifested as an entropy and designated as the entropy of activation and the phenomenon is called as the Meyer-Neldel rule (MNR). Entropy of activation has been associated with the stochastic nature of the barrier heights, which is then reflected in the randomness of the jump frequency of the charge carriers. Many of the theoretical approaches developed to study this phenomenon utilize a Boltzmann distribution of the barrier heights; we have used a classical Bose-Einstein (BE) distribution in which, at the transition temperature, a large number of very low-energy barriers appear as a “condensate” minimizing the role of the activation energy. The advantage of using the BE statistics over the Boltzmann statistics lies in the fact that the former naturally contains a transition temperature. Using this model, we have further analyzed the entropy of several Li-stuffed garnet-type solid electrolytes, which are being considered for all-solid-state Li batteries and as well as several other fast ion-conducting solids.