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Scaling behavior and variable-range-hopping conduction of localized polarons in percolative BaTiO3-Ni0.5Zn0.5Fe2O4 ceramic composite with colossal apparent permittivity

The percolative BaTiO3-Ni0.5Zn0.5Fe2O4 (BTO-NZFO) ceramic composite represents a family of multifunctional materials exhibiting multiferroic properties and colossal apparent permittivity. It is of fundamental interest to investigate the conduction mechanism in such percolative composites from both macroscopic and microscopic perspectives. Herein, three representative systems with the NZFO content locating below the percolation threshold fc, near fc, and above fc, respectively, were investigated, using pure NZFO ceramic as a comparison. The conductivity of the composite as a function of NZFO content agrees well with the McLachlan model, which takes percolation into consideration and essentially equivalent to the Kirkpatrick model. The electrical conductivity of the composite conforms to Mott's variable-range-hopping (VRH) model in the temperature range of 303–573 K, suggesting that VRH conduction of localized polarons dominates the electrical behavior microscopically. Parameters including the most probable hopping range (R); the density of localized states at the Fermi level [N(EF)]; and the activation energies of VRH (W), dc conductivity (Edc), hopping (Eon), and relaxation (Er) were obtained and analyzed. Scaling behaviors of the conductivity and the imaginary part of complex impedance of the composite have been observed, implying that the distribution of relaxation times is temperature independent. The impedance data measured at different temperatures exhibit typical semiconducting behavior, which can be well fitted by an equivalent circuit model considering both grain and grain boundary responses. The correlation between conductivity and colossal apparent permittivity has also been revealed. The discoveries deepen the understanding of the conduction mechanism in such multifunctional composites composed of an insulating phase and a semiconducting phase.