Scaling behavior of dynamic hysteresis in soft lead zirconate titanate bulk ceramics

Abstract

The scaling behavior of the dynamic hysteresis of ferroelectric bulk system was investigated. The scaling relation of hysteresis area ⟨A⟩ against frequency f and field amplitude E0 for the saturated loops of the soft lead zirconate titanate bulk ceramic takes the form of ⟨A⟩∝f−1∕4E0, which differs significantly from that of the theoretical prediction and that of the thin film. This indicates that the scaling relation is dimension dependent and that depolarizing effects in the interior must be taken into account to model bulk materials. Additionally, the scaling relation for the minor loops takes the form of ⟨A⟩∝f−1∕3E03, which is identical to that of the thin film as both cases contain similar 180° domain-reversal mechanism.

A finite element formulation for piezoelectric shell structures considering geometrical and material non‐linearities

“…The influence of the temperature on the saturation parameter of the polarization P sat and the electric coercitive field E c has been experimentally studied by Reference [37] for P b(Zn 1/3 Nb 2/3 )O 3 − P bT iO 3 single crystals and by Reference [38] for PZT ceramics. With increasing temperature, the domain walls start moving earlier and the hysteresis area decreases.…”

“…Following the experimental investigations in Reference [39] we assume a linear relation between the natural logarithms of the temperature and the saturation polarization. With the experimental data from [38] for the material PZT we include the phenomenological saturation parameter…”

“…As there do not exist sufficient test results, this influence has been neglected. Based on Reference [38] we include the relation…”

“…A thin piezoelectric PZT ceramic disc is introduced by Yimnirun et al [38] who gives experimental results for the temperature-dependent polarization behavior, see Figure 19. The disc with an outer diameter d 1 and the thickness t is subjected to an electric field in thickness direction for different temperatures in the range of 298 to 453 Kelvin.…”

“…proposed by Reference [34]. The influence of the temperature on piezoelectric material behavior has been studied experimentally in References [36,37,38,39]. [39] shows that the ferroelectric hysteresis curves become smaller with increasing temperature.…”