Variable range hopping and modulus relaxation in NiFe2O4 ceramics

Abstract

Nickel ferrite ceramics prepared from combustion derived powders have been investigated using dielectric, impedance, and modulus spectroscopy over a wide frequency (0.1 Hz–1 MHz) and temperature range (173–473 K). Step-like dielectric response ε'T,f is related to the surface barrier layer capacitor (SBLC) effect. Dielectric relaxation peaks in ε″(f) masked by the huge dielectric loss are revealed by εder″(f) derived from the ε′(f) data following Kramers – Kronig transformations. Multiple relaxations are evidenced from the asymmetric nature of εder″(f) peaks. Impedance Cole-Cole analysis reveals two relaxation processes corresponding to grain and grain-boundary effects. A maximum in the grain capacitance (Cg) at 293 K is attributed to the collective influence of electron and hole charge carriers on dielectric polarization. The modulus analysis reveals distinctly three relaxations occurring at temperatures T ≥ 323 K, and only two relaxations for T < 323 K. The variation of modulus relaxation frequencies ln(fmax) with (1/T) suggests different conduction mechanisms for temperature above and below 323 K. The two relaxations observed in the entire temperature range originate due to hopping of holes and electrons at equivalent B-sites of NiFe2O4, while the third relaxation seen only at temperatures T > 323 K is attributed to defect hopping. The present analysis based on modulus relaxation, dc conductivity, and power law exponent sT indicates two different conduction mechanisms for Nickel ferrite NiFe2O4 with variable range hopping dominating at lower temperatures, and thermally activated hopping at higher temperatures.