Use of the time constant related parameter fmax to calculate the activation energy of bulk conduction in ferroelectrics

Abstract

The activation energy associated with bulk electrical conduction in functional materials is an important quantity which is often determined by impedance spectroscopy using an Arrhenius-type equation. This is achieved by linear fitting of bulk conductivity obtained from complex (Z*) impedance plots versus T⁻¹ which gives an activation energy E_a(σ) or by linear fitting of the characteristic frequency f_max obtained from the large Debye peak in M′′–log f spectroscopic plots against T⁻¹ which gives an activation energy E_a(f_max). We report an analysis of E_a(σ) and E_a(f_max) values for some typical non-ferroelectric and ferroelectric materials and employ numerical simulations to investigate combinations of different conductivity–temperature and permittivity–temperature profiles on the log f_max–T⁻¹ relationship and E_a(f_max). Results show the log f_max–T⁻¹ relationship and E_a(f_max) are strongly dependent on the permittivity–temperature profile and the temperature range measured relative to T_m (temperature of the permittivity maximum). Ferroelectric materials with a sharp permittivity peak can result in non-linear log f_max–T⁻¹ plots in the vicinity of T_m. In cases where data are obtained either well above or below T_m, linear log f_max–T⁻¹ plots can be obtained but overestimate or underestimate the activation energy for conduction, respectively. It is therefore not recommended to use E_a(f_max) to obtain the activation energy for bulk conduction in ferroelectric materials, instead E_a(σ) should be used.