The Rayleigh law in piezoelectric ceramics

Abstract

The direct longitudinal piezoelectric effect in lead zirconate titanate, barium titanate, bismuth titanate and strontium bismuth titanate ceramics was investigated with respect to the dependence on the amplitude of an alternating pressure. At low alternating pressure amplitudes, the behaviour of the piezoelectric charge and the piezoelectric coefficient may be explained in terms of the Rayleigh law originally discovered for magnetization and magnetic permeability in ferromagnetic materials. The charge versus pressure hysteresis loops measured for piezeoelectric ceramics may similarly be described as the Rayleigh loops. The results presented show that the Rayleigh law can be applied to irreversible displacement of several types of non- ferroelectric domain walls and imply universal validity of the Rayleigh law for displacement of ferromagnetic, ferroelastic and ferroelectric domain walls.

Temperature dependence of the direct piezoelectric effect in relaxor-ferroelectric single crystals: Intrinsic and extrinsic contributions

“…8,19 For all measurements, pressure is applied to the sample between two flat, well-aligned steel plates. Dynamic ͓ dy = 0 sin͑2 ft͔͒ and static ͑ st ͒ pressures are applied to the sample by a PZT actuator and the resultant force on the sample is measured with a quartz sensor.…”

“…On the other hand, d 33 − d 0 = ␣ 0 describes the irreversible part and is a purely extrinsic contribution. 8 Secondly, Eq. ͑2͒ describes a hysteretic, and therefore lossy, charge-stress loop with a finite width ͑at dy =0͒ of ⌬D = ␣ 0 2 .…”

“…͑2͒ describes a hysteretic, and therefore lossy, charge-stress loop with a finite width ͑at dy =0͒ of ⌬D = ␣ 0 2 . Finally, the dependence of the piezoelectric coefficient upon the frequency f of the applied dynamic stress can be written as 5,8 …”

“…Rayleigh-law behavior is characteristic of pinned interface motion; again, it is commonly observed in the direct piezoelectric response of polycrystalline ferroelectrics where ferroelastic switching is expected and these interfaces can be identified as non-180°d omain walls. 7,8 However, at least in ͓001͔ C -poled, domainengineered rhombohedral crystals, ferroelastic switching is not expected when stress is applied along the poling direction. 4,9 The origins of the hysteresis in the direct longitudinal piezoelectric response remain unclear.…”

The Effect of Antinotches on Domain Wall Mobility in Single Crystal Ferroelectric Nanowires

“…Although originally formulated for ferromagnetic materials, 24 Rayleigh's law can be analogously expressed for ferroelectrics and used to probe the role of domain wall contributions to both the dielectric 25 and extrinsic piezoelectric responses. 26 In the Rayleigh description of the dielectric response, the permittivity ε can be described by a linear relation in field amplitude E 0 25 under the influence of a weak (subcoercive) ac exciting field (E ) E 0 sin ωt)…”