Parameter of dielectric loss distribution in the new model for complex conductivity based on Havriliak–Negami formula

Abstract

This paper is focused on the comparison of the results of various approximation models describing the frequency dependences of the dielectric constant ε′∕ε0(f) and ε′′∕ε0(f), the tangent of the loss angle tgδ(f) and the electrical conductivity γ′(f) and γ′′(f) of nonlinear dielectrics. The classic ferroelectric material of the PZT system with x=0.50 was chosen as the object of study. Based on the analysis of temperature-frequency dependences of the “empirical” parameters α and β, a regularity has been revealed that allows them to be calculated. A new relationship has been established through the parameter α, which allows to relate the temperature and frequency dependences of the complex electrical conductivity as ω→∞ and as ω→0 in the Havriliak–Negami approximation models and in the new model for the description of the complex electrical conductivity γ∗. It is shown that α is a parameter of the temperature-frequency distribution of dielectric losses. Using the obtained expressions, a new theoretical description of experimental spectra having a relaxation character was proposed. It has been proven that the use of the new model makes it possible to accurately describe the set of studied spectra, including the high and low frequencies, in the frequency range from 10−3 to 108Hz.

Keywords

• nonlinear dielectrics
• reach-through conductivity
• relaxation
• havriliak–negami model
• complex conductivity