A ‘mixed’ dielectric response in langasite Ba3NbFe3Si2O14

Abstract

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) = σ_dc + 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) = σ_dc + 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.