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

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 Ea(σ) or by linear fitting of the characteristic frequency fmax obtained from the large Debye peak in M’’-logf spectroscopic plots against T-1 which gives an activation energy Ea(fmax). We report an analysis of Ea(σ) and Ea(fmax) 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 logfmax – T-1 relationship and Ea(fmax). Results show the logfmax – T-1 relationship and Ea(fmax) are strongly dependent on the permittivity-temperature profile and the temperature range measured relative to Tm (temperature of the permittivity maximum). Ferroelectric materials with a sharp permittivity peak can result in non-linear logfmax – T-1 plots in the vicinity of Tm. In cases where data are obtained either well above or below Tm, linear logfmax – T-1 plots can be obtained but overestimate or underestimate the activation energy for conduction, respectively. It is therefore not recommended to use Ea(fmax) to obtain the activation energy for bulk conduction in ferroelectric materials, instead Ea(σ) should be used.