Entropy factor in the hopping frequency for ionic conduction in oxide glasses induced by energetic clustering

The contribution of configurational entropy to the effective hopping frequency of ionic transport in amorphous systems is discussed. The effective rate of ion hopping has been extracted from the onset frequency of the ac conductivity measured in ionically conducting silicate glasses. Both the onset frequency and the dc conductivity exhibit Arrhenius-type thermal activation with similar values for the activation energy, DeltaEa=0.65+/-0.3 eV. The prefactor of the onset frequency results in nu0'=(1.05+/-0.05)x10(11) Hz, which is much lower than characteristic vibrational frequencies (10(13) Hz). Following standard hopping percolation theory, the long-range motion is dominated by a fraction of high-energy barriers that connect clusters of faster sites. The multiplicity of equivalent sites for ion hop entails a retardation of the effective jumping time with respect to the elementary hop. This effect can be assimilated into a negative activation entropy term in the frequency prefactor of the ion hopping rate, which depends on the features of energy clustering and accounts for the wide dispersion of nu0' reported for many conducting glasses. The model implies an effective percolation length of Lc approximately 7 nm, in good agreement with previous works.