Super-linear frequency dependence of ac conductivity of disordered Ag2S-Sb2S3 at cryogenic temperatures

The ac conductivity of a new class of disordered solids, i.e. mechanochemically synthesized amorphous fast ion conducting Ag2S-Sb2S3 materials, has been investigated in the audio frequency range (10-10(7) Hz) down to cryogenic temperatures (similar to 10 K). The conductivity spectra exhibit the usual signature of a disordered system at higher temperatures, well described by the Jonscher power law (JPL) i.e., sigma'(omega) = sigma(dc) + A(T)omega*, although the frequency exponent (n < 1) is found to be a weak function of temperature. However, as the temperature is lowered, the frequency width of the sigma(dc) region decreases gradually and that of the JPL region increases. Eventually, the sigma(dc) region disappears and the JPL region alone dominates the spectrum. However, at the lowest temperatures, both the sigma(dc) and JPL regions disappear and sigma'(omega) obeys a super-linear power law (SPL) (sigma' alpha omega(m), m >= 1). It is observed that the SPL has strikingly similar characteristics to the well-established nearly-constant-loss (NCL) behaviour corresponding to m = 1. Both SPL and NCL appear in the same time-temperature (low-temperature/low-frequency) domain. Furthermore, in both cases the conductivity is a distinctly weak function of temperature but quite sensitive to frequency, and the SPL/NCL -> JPL crossover frequency is thermally activated with almost the same energy as the ac activation energy. The presence of the SPL is further manifested in the form of a well-defined minimum in the dielectric loss, epsilon ''(omega), spectra. It is therefore proposed that the entire low-temperature/low-frequency spectra can be described by a modified Jonscher power law, omega(n) + B(T)omega(m), m = 1 (NCL), m >= 1 (SPL), where the second term with n < 1 accounts for the JPL and the third term with m >= 1 accounts for SPL/NCL. The results and some other low-temperature/ low-frequency conductivity data are consistent with an asymmetric double well potential (ADWP) model.