Hopping conduction mechanism and impedance spectroscopy analyses of the half-doped perovsikte Nd${}_{0.5}$Ba${}_{0.5}$FeO${}_3$ prepared by sol-gel method

Polycrystalline Nd${}_{0.5}$Ba${}_{0.5}$FeO${}_3$ (NBFO) perovskite was prepared with sol-gel method, calcined at a temperature of 900 °C. Here, we study the influence of the Barium ion Ba${}^{2+}$ introduced in the Nd site on the structural, electrical, dielectric and thermodynamic properties of our NBFO sample. The electrical conductivity obeying the Jonscher's power law indicates that the prepared material shows a semiconducting behavior, and that the conduction process is presented by charge carriers performing an abrupt translational motion (NSPT model). The behavior of dielectric constants such as permittivity and loss coefficient has been interpreted based on the Maxwell-Wagner's theory of interfacial polarization. The curves of imaginary parts of impedance (Zʹʹ) and modulus (Mʹʹ) show a dielectric relaxation phenomenon in the sample with activation energy near to that determined from the dc conductivity study. TheNyquist diagram (Zʹʹ vs. Zʹ) tells us that the grain resistance (R${}_g$) and the grain boundary resistance (R${}_{gb}$) decrease monotonically with an increase in temperature. The latter result confirms that the charge carrier motion is related to the abrupt jump displacement. This result indicates that the transport mechanism for NBFO compound is governed by the grain boundaries effect. In addition, thermodynamic factors including enthalpy ΔH, entropy ΔS, and free energy of activation ΔF were identified.