Scaling relations of domain reversal dynamics in rhombohedral and tetragonal PIN–PMN–PT ferroelectric single crystals

Abstract

The domain reversal dynamics of rhombohedral and tetragonal PIN–PMN–PT ferroelectric single crystals has been investigated by analyzing the variation of hysteresis loops under various electric fields and frequencies. As the electric field amplitude E0 continuously increases, the hysteresis area ⟨A⟩ clearly reflects three stages of polarization reversal. The complete scaling relations of domain reversal dynamics were determined. For rhombohedral PIN–47PMN–29PT crystals, the dynamic hysteresis area follows the law of ⟨A⟩ ∝ f −0.38816E05.21244 in the first E0-stage and ⟨A⟩ ∝ f 0.03553E00.37126 in the third E0-stage. For tetragonal PIN–37PMN–39PT crystals, the dynamic hysteresis area follows the law of ⟨A⟩ ∝ f −0.09054E02.74854 in the first E0-stage and ⟨A⟩ ∝ f −0.15504E02.06936 in the third E0-stage. The negative α indicates that with the alternating velocity of the increasing periodic electric field, more and more domain reversals fail to follow with the alternating electric field. However, rhombohedral PIN–47PMN–29PT crystals possess a positive α in the third E0-stage, indicating that 71° and 109° domains can keep pace with varying E0 more easily. The positive β indicates that when the electric field frequency is fixed, more and more domains begin to reverse with the intensity of the increasing electric field. In addition, the function of ⟨A⟩ ∝ f αE0β cannot be applied to the second E0-stage, where the non-180° domain rotation starts occurring but 180° domain rotation has not finished yet.

Composition dependent phase structure, dielectric and electrostrain properties in (Sr0.7Bi0.2□0.1)TiO3–PbTiO3–Bi(Mg0.5Ti0.5)O3 systems

“…The corresponding relationship between ln<A> and lnE 0 is shown in figure 8(e). Obviously, ln<A> with lnE 0 exhibits a linear relationship in stage I and stage III, which indicates stages I and III conforms to a scaling behavior [55][56][57]. The polarization mechanism of stage I is mainly ascribed to 180 • domain wall motion and stage III is considered to be polarization extension.…”

Establishing a Relationship between the Piezoelectric Response and Oxygen Vacancies in Lead-Free Piezoelectrics

“…The dynamic hysteresis and scaling behavior of the two ceramics are researched in this part, to further clarify the process of the polarization reversal. The hysteresis area ⟨ A ⟩ representing the energy dissipation in one cycle of polarization is described as a scaling function of frequency f and electric field amplitude E as follows: ⟨ A ⟩ ∝ f α E β . − The relationship between ⟨ A ⟩ and E , f can reflect the key dynamics of domain nucleation, growth, and motion and the corresponding polarization reversal process by quantifying the values of exponents α and β . For talking in a targeted way, the effect of E is only discussed in this section.…”

“…Figure a,d shows the evolution of the P – E loops of the two samples with increasing E at fixed f = 2 Hz, illustrating the strong E -dependence of the loop profile. Similar to other material systems, − the P – E loops can be divided into three regions (liner, minor, and saturated loops) with increasing E , referring to the calculated ln⟨ A ⟩ and its differentials d (ln⟨ A ⟩)/d (ln E ) as a function of ln E of the two samples [Figure b,e]. The β value of 7BF-BT-Cu is bigger than that of 7B 1.05 F-BT in the first region and smaller than that of 7B 1.05 F-BT in the third region, illustrating that the presence of Cu 2+ can enhance the response of domains to the external electric field, supported by the significant improvement of P r [Figure c] and the faster saturation of the P–E loops of the 7BF-BT-Cu sample [marked by the arrow in Figure b,e].…”

Dissolution of four-stage to three-stage dynamic scaling behavior with stabilization of relaxor character in K0.5Bi0.5TiO3 based binary system

“…Each ferroelectric material has a characteristic P-E loop under different electric field and frequency. The energy dissipated per cycle of electric field application, that reflects the growth, nucleation process and motions of domains, can be deduced from the area of the ferroelectric hysteresis loop (P-E loop) [1,2]. Hence the study of P-E loops at different electric fields and different frequencies is essential for the better understanding of domain dynamics hidden in each material.…”