We report on ac conductivity measurements of oxide ion conductors with composition Gd 2 ͑Zr y Ti 1−y ͒ 2 O 7 , at temperatures between 170 and 500 K and in the frequency range 1 Hz-3 MHz, and show that a crossover from a sublinear power law to a linear frequency dependence ͑or nearly constant loss behavior͒ in the ac conductivity can be clearly observed in a wide temperature range. This crossover is found to be thermally activated, and its activation energy E NCL to be much lower than the activation energy E dc for the dc conductivity. We also found that the values of E NCL are almost independent of composition, and therefore of the concentration of mobile oxygen vacancies, unlike those of E dc . Moreover, for each composition, the values of E NCL = 0.67Ϯ 0.04 are very similar to those estimated for the energy barrier for the ions to leave their cages, E a = 0.69Ϯ 0.05. These results support that the nearly constant loss behavior, ubiquitous in ionic conductors, is originated from caged ion dynamics.
͑1͒where A is a constant with weak temperature dependence 3,4 and 0 the permittivity of vacuum. The term "nearly constant loss" is due to the corresponding nearly frequency independent behavior of the dielectric loss NCL Љ ͑ ͒ = NCL Ј ͑ ͒ / 0 Ϸ A. Despite the great interest in ionically conducting materials during the last decades, most experimental and theoretical work has been devoted to understand the dynamics of mobile ions at much higher temperatures, when the ions eventually give rise to a long-range charge transport characterized by a frequency-independent conductivity dc , and an NCL contribution to the ac conductivity is usually absent from experimental data. Therefore, until recently, conductivity data showing an NCL behavior were scarce in the literature. [5][6][7][8][9] It was in 1999 that Ngai first pointed out the correlation existing between the high values of the dc conductivity dc and the high values of the NCL magnitude A found in superionic conductors with technological interest for their application as electrolytes in solid-state batteries and fuel cells. 4,10 Based on this fact and on several other properties of the NCL experimentally observed in ionic conductors, Ngai proposed its physical origin might be due to the displacement of the mobile ions in their local vibrational motion at low temperature and/or high frequency. León et al. [11][12][13] later found experimental evidence, in two different lithium ionic conductors, consistent with such an origin for the NCL contribution to the ac conductivity. From the measurement of the crossover temperature ͑frequency͒ at which the NCL behavior terminates at different fixed frequencies ͑temperatures͒, they were able to determine an activation energy E NCL for the crossover which was found to be much lower than the activation energy E dc for the dc conductivity, governed by ion hopping dynamics, and in fact E NCL was found to be similar to the value estimated for the energy barrier for the ions to leave their cages, E a . Different models for ionic co...