Ferroelectric hysteresis loop

Crystals with one of the ten polar point-group symmetries (Ci, C2, Cs, C2V, C4, C4V, C3, C3v, C(, Cgv) are called polar crystals. They display spontaneous polarization and form a family of ferroelectric materials. The main properties of ferroelectric materials include relatively high dielectric permittivity, ferroelectric-paraelectric phase transition that occurs at a certain temperature called the Curie temperature, piezoelectric effect, pyroelectric effect, nonlinear optic property - the ability to multiply frequencies, ferroelectric hysteresis loop, and electrostrictive, electro-optic and other properties [16, 388],... 

The crystals grown in this manner are in the form of clear sheets. The symmetry of the crystals is pseudotetragonal with a cell size of a0 = 3.841 A. and c0 = 32.83 A. Electrodes can be evaporated, or indium amalgam can be applied to the flat surfaces of the crystals, to produce samples for measurements. The d.c. resistance of the crystals is about 1012 fi-cm. They exhibit ferroelectric hysteresis loops up to the Curie temperature of 643°C. 

Figure 15.14 (a) Ferroelectric hysteresis loop for a single-crystal, (b) Polycrystalline sample. 

Perovskites Structure-Property Relationships 6.33 Ferroelectric Hysteresis Loops... 

Figure 6,9 Ferroelectric hysteresis loops, schematic (a) typical loop indicating P P and Ej (b) single crystal ABO (c) medium-grained ceramic ABO (d) fine-grained ceramic ABO,...

The existence of ferroelectric phase in sufficiently thin antiferroelectric films had been revealed experimentally in several works [64-66]. In Ref. [64], the switchable ferroelectric polarization has been observed in PbZrOs antiferroelectric thin film on Si substrate. It has been revealed, that both in the latter film and in one more antiferroelectric BiNb04 one, the ferroelectric phase appears only if the film thickness is smaller then certain threshold value, which depends on material parameters. For instance, the ferroelectric hysteresis loop has been observed [65] in 100 nm thick PbZrOs/Si Alms, while those thicker than 400-500 nm revealed antiferroelectric behavior. Note, that the other primary ferroic demonstrates the same behavior. Namely, the films of antiferromagnetic BiFeOs on SrTiOs substrate reveal the emergence of ferromagnetism at the thicknesses less than 100 nm [67]. 

Ferroelectric hysteresis loop and remnant polarization appear at temperatures T< Tf(R). This behavior can be called frozen superparaelectric phase. 

Figure 18.11 Ferroelectric hysteresis loops for hard and soft Pbo.5gZro,42Ti03 ceramics modified by various amounts of Nb and Fe dopants (a) on linear scales (b) on semi-logarithmic scale (the first quadrant).

Figure 18.16 Relaxation of the ferroelectric hysteresis loops in hard (doped with 1.0atom% Fe) PZT (58/42) ceramics, (a) For different cooling rates from the paraelectric state (b) The...

Figure 18.17 Comparison of ferroelectric hysteresis loops. Soft (1.0atom% Nb-doped) PZT (58/42) ceramics and hard (1.0atom% Fe-doped) PZT (58/42) ceramics relaxed by ac-field cycling at 125 °C. The measurements are carried out under the same conditions.

The FMR field of the Fe304/PZT and Fe304/PMN-PT muitiferroic composites exhibited the characteristic butterfly shape in their FMR field vs. electric field curves as shown in Fig. 7, which coincided with the ferroelectric hysteresis loops of the PZT and PMN-PT respectively and were similar... 

Figure 7. Butterfly curves of resonance fields vs. electric fields and ferroelectric hysteresis loops of muitiferroic composite Fe304/PZT (a) and FesOVPMN-PT (b).

Rg.4.5 -1 Ferroelectric hysteresis loop. Ps, spontaneous polarization Pj, remanent polarization Ec, coercive field... 

CH2 CF2)x(Cp2 CHF)-i x)n,Vinylidene fluoride-trifluoro-ethylene Copolymer, ((VDF)x(TrFE)]-x)n (LB Number 72-2) (Polymer). Random polymers (CH2CF2) t (CF2CHF)i j exhibit a ferroelectric hysteresis loop for... 

An AC field with a period of 100 s and an amplitude of 100 V, applied to polyurea films 1 tm thick, was capable of aligning the urea dipoles. A ferroelectric hysteresis loop as observed in Fig. 3 was observed for the poly urea thin films [47,48]. A remanent polarization of 1 /aC/cm and a coercive field strength ( ,.) of 100 MV/m were observed for such polyurea films [9]. The tensile piezoelectric... 

Fig. 5.6 Ferroelectric hysteresis loop. Ps is spontaneous polarization, Pr is remanent polarization and Eic is the coercive field...

Figure 22-9. Ferroelectric P-E hysteresis loops ofLiNbOs thin films (170 nm). (a) Symmetric ferroelectric hysteresis loop of the Pt-eletrode/LiNbOs film/Au-electrode sample, having of 60 pbC/cm and Ecof23 k V/mm (Cheng etal., 1991) (b) Au-electrode/LiNbOs film/n-Si substrate sample, with the scale of X-axis is 27 kV/cm/div. And Y-axis 3.0 fxC/cm /div. (Xu and Mackenzie, 1992, with permission).

The ferroelectric hysteresis loop for the PbTiOs ceramic sintered at 11(X)°C is shown in Figure 6-14. The remanent polarization (P ) was 1.73 /rC/cm that is similar to the reported values of PbTiOs ceramics. However, instead of a rectangular hysteresis loop, a circular loop was obtained due to the low resistivity developed from the fine grained structure. A decrease in the Curie temperature Tc was also noticed this was again attributed to the effect of fine grain size. Because of the chemical homogeneity and the low... 

Figure 1.14 Ferroelectric hysteresis loop (polarization vs applied voltage). Reprinted with permission from Ok et ah, Chem. Soc. Rev., 35, 710 (2006). Copyright (2006) Royal Society of Chemistry...

Fig. 30.16. The ferroelectric hysteresis loop relating applied electric held and polarization, both along (001] for 0 -R2(MoO4)j.

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