Relaxation dynamics of the conductive processes for PbNb₂O₆ferroelectric ceramics in the frequency and time domain

Abstract

The relaxation dynamics of the conductive process present in PbNb 2 O 6 piezoelectric ceramics was investigated. A relaxation function in the time domain, (t), was found from the frequency dependence of the dielectric modulus (imaginary component, M ) by using a relaxation function in the frequency domain, F * (ω). The best relaxation function, F * (ω), was found to be a Cole-Cole distribution function, in which relaxation characteristic parameters, such as α and τ CC , are involved. On the other hand, the relaxation function, (t), obtained by the time domain method, was found to be a Kohlrausch-Williams-Watts (KWW) function type. The thermal evolution of the characteristics parameters of the KWW function (β and τ * ) was analysed. The values of the activation energy (E a ), obtained in the whole investigated temperature interval, suggest the existence of a relaxation mechanism (a conductive process), which may be interpreted by an ion hopping between neighbouring sites within the crystalline lattice. The results are corroborated with the formalism of the AC conductivity.

Relaxation dynamics of the conductive processes in BaTiO3 ceramics at high temperature

“…The evidence of the relaxation process, characterized by a frequency shift towards higher values with the increase of the temperature, is shown in this figure. Moreover, the maximum value of M remains practically constant as the working temperature increase, similar to the observed in some ionic conductors [16,17].…”

“…In order to describe the temporal response of these distribution functions, it is common to use an analytical distribution function of relaxation times [17][18][19], which can be obtained using the relaxation parameters ( ,˛and ) in the frequency domain [17].…”

“…In the first region (220-440 • C), characterized by a CC distribution function, the Fourier transform for CC distribution function has been not establishments yet, being common to describe the temporal response using the analytical distribution function of the relaxation time [17][18][19], which can be expressed in the following form:…”

“…In the second region (460-620 • C) (where the distribution function corresponds to a DC-type function) the analytical distribution function in the frequency domain is given by [17]:…”

“…In order to analyze the resulting behavior, it is necessary to investigate the thermal evolution of the parameters of the relaxation distribution function, which can be obtained from the fitting of the distribution functions, as reported in the literature [17,18]. Among them, the Kohlrausch-Williams-Watts (KWW) function, expressed by the Eq.…”