Dielectric Relaxation and Electrical Modulus Formalism in Solids

The dielectric relaxation effects give a very important understanding of the microscopic dynamics of dipoles and charge carriers in solids, especially those materials where disorder, conductivity and interfacial effects make the dielectric response difficult to understand. A single and pedagogic exposition of dielectric relaxation in this work is introduced, starting with the analogous time domain Debye polarization equation and moving stepwise to the frequency domain complex permittivity formulation. Real and complex values of the dielectric permittivity are obtained and their physical interpretation, loss peak performance and Cole Cole presentation are provided in details. Abnormal Debye behaviour in real solids is treated by the Cole-Cole, Cole-Davidson and Havriliak-Negami models, which are focused on the characteristics of describing distributed and asymmetric relaxation-time spectra. In order to by-pass the restrictions due to the conductivity of the dc and as polarization of the electrodes at low frequencies, electrical modulus formalism is presented and derived in the case of Debye and non-Debye relaxation model. The usefulness of this method is illustrated by the fact that the complex modulus spectra of Nd 2 FeTiO 6 ceramic were analyzed in the entire span of temperatures. The presence of depressed and asymmetric modulus arcs, scaled master-curve behavior also obviously signal non-Debye relaxation behavior best fitted by the HavriliakNegami model. The joint analysis of permittivity-modulus offers a powerful model of isolating the intrinsic bulk relaxation and extrinsic conductive sources, and can be used to obtain physically useful relaxation parameters. The work is not only an introduction on a tutorial level, but also a practical guide to researchers working on dielectric and impedance spectroscopy of solid materials.