A 'mixed' dielectric response in langasite Ba₃NbFe₃Si₂O₁₄

The temperature dependence of the structural and dielectric properties of polycrystalline Ba3NbFe3Si2O14 has been studied using high temperature X-ray diffraction and impedance spectroscopy. In situ X-ray diffraction with temperature (330-873 K) and subsequent Rietveld refinement shows that Fe-langasite crystallizes in a single phase P321 structure, in the measured temperature range. The dielectric constant ε' exhibits low frequency dispersion and large variation (25-104), with temperature and frequency. The real part of the ac conductivity (σ') also shows a change of seven orders of magnitude (10-6 to 10-13). The conductivity was observed to diverge from the 'universal dielectric response' (UDR), σ(ω,T) = σdc + A1ωn. Three frequency (10 Hz-10 MHz) and temperature (123-573 K) dependent regions were observed: (a) a low frequency, frequency independent region, (b) a mid frequency, dispersive region, and (c) a high frequency, dispersive region. This behaviour can be understood by a double power law: σ(ω,T) = σdc + A1ωn2 + A2ωn1, which is similar to the modified Jonscher's law and holds good for other complex dielectric materials as well. The 'sub-linear' variation with frequency for n2 at all temperatures and for n1 above 323 K is attributed to hopping polarization. Remarkably, a 'super-linear' ac conductivity was observed with n1 ≥ 1 below 323 K. This anomalous behaviour is attributed to hopping between non-uniform potential wells. The dielectric relaxation studies in combination with Seebeck measurements (300-573 K) reveal that the colossal dielectric permittivity and deviation from the UDR are predominantly due to the hopping polarization of positively charged species in a distributed potential. It is suggested that this model may be applicable to understand the conductivity mechanism in a broad range of complex materials.