AC impedance studies on Li0.5+0.5xGexFe2.5−1.5xO4 system

The AC impedance properties of Ge4+ ion-substituted Li ferrites with the general chemical formula Li0.5+0.5xGexFe2.5−1.5xO4 (where x = 0.0, 0.1, 0.2, 0.3 and 0.4) have been analyzed in the frequency range 50–1 MHz at different temperatures between 50 and 250 °C. Nyquist plots recorded at different temperatures indicate a decrease in the impedance of the compositions with increasing the temperature. One semicircle has been observed for all samples, which reveals that the conduction in these samples is through the grain boundaries. It has been observed that the magnitudes of real (Z′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Z^{{\prime }}$$\end{document}) and imaginary (Z″\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Z^{{\prime \prime }}$$\end{document}) components of the impedance decrease with increasing temperature. It is attractive to note that the relaxation time (τz) varies linearly with temperature. The AC electrical conductivity has been studied at room temperature at different frequencies from 50 Hz up to 1 MHz. The frequency exponential factor (s) was estimated, and it was found to be composition dependent.