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

Abstract

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 (10–10⁷ Hz) down to cryogenic temperatures (∼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., σ′(ω) = σ _dc + A(T)ω*, 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 σ _dc region decreases gradually and that of the JPL region increases. Eventually, the σ _dc region disappears and the JPL region alone dominates the spectrum. However, at the lowest temperatures, both the σ _dc and JPL regions disappear and σ′(ω) obeys a super-linear power law (SPL) (σ′ ∝ ω^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, ε″(ω), spectra. It is therefore proposed that the entire low-temperature/low-frequency spectra can be described by a modified Jonscher power law, σ′(ω) = σ _dc(T) + A(T) ωⁿ  + B(T)ω^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.