Polarization remnant

The room-temperature polarization-field hysteresis of the ceramics shows well-saturated loops. The values of remnant polarization, spontaneous polarization and coercive field determined are reported in Table 3. The data of single crystal previously reported are also list in Table 3. 

Upon removal of the applied field, P does not go to zero but remains at a finite value called the remnant polarization Pf. As in the ferromagnetic case, this remnant is due to the fact that the oriented domains do not return to their random state upon removal of the applied field. In order to do that, the field has to be reversed to a coercive field E. ... 

Amorphous LiNbOs films made by sol-gel processing were subjected to a series of characterizations [57]. It was found that an amorphous LiNbOs film obtained by heating the gel film at 100°C for 2 h showed P-E hysteresis with remnant polarization Pr = 10 pC/cm2 and coercive field Ec= 110 kV/cm. Electron diffraction of such film showed a diffuse ring pattern characteristic of an amorphous nature. These are shown in Fig. 6 in which the scale for E is 147 kV/cm division and that for P is 5.6 pC/cm2 division. Further measurement showed a pyroelectric coefficient of 8 pC/cm2 K at 28°C. Note that for singlecrystal LiNbOa, Pr = 50 pC/cm2 and the pyroelectric coefficient was reported to be 20 pC/cm2 K [1]. Further, a piezoelectric resonance was observed at similar frequency range for both amorphous and crystalline LiNbOa, characteristic of a ferroelectric material [57]. 

When the field is subsequently removed a remnant polarization Pj exists due to the coupling between adjacent dipoles. The material is permanently polarized in the... 

Subsequently due to specific chain conformation in crystal unit cell and providing the highest remnant polarization, p phase has attracted more attention than the others in pyro-and piezoelectric applications (J.Jungnickel, 1996). 

Fig. 3.7 The temperature dependence of remnant polarization (a) and hysteresis loop (b) for nanorods of RocheUe salt with radius 15 nm. Symbols are experimental data from Ref. [42] (a) remnant polarization at applied field = 30 kV/cm (b) hysteresis loop at applied...

The comparison of Figs. 3.23 and 3.24 shows that the films thickness decrease reveals the features similar to those at the increase of distribution function width. This means that the decrease of film thickness may be considered as equivalent to the disordering of the system. The reason for that is that the fluctuations due to film thickness decrease have the same nature as those at the system disordering. In other words, in thinner films of relaxor ferroelectrics, the part of long range order decreases so that dipole glass state may appear in free-standing films. The complement state in such situation may be the electret-like one with remnant polarization induced by built-in field. Latter state is more profitable in the thinnest possible films with thickness less than some critical value. 

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

To summarize the Sect. 4.3.10.4, Langevin-like law for field dependence of polarization has been predicted in the temperature range Tcr R) >T> Tf(R) at fixed radius Rfixed temperature T). Bistable remnant polarization appears at temperatures T < Tf(R) (or at radii R Rf(T)). For nanoparticle radius less than critical one both hysteresis and its precursor, Langevin-like behavior, are smeared. 

Electrochemical stability at over 4 V is key property high purity solution casting ability to cast thin electrodes from very high (>80%) carbon formulations Orientation under high electrical fields of the beta crystallites in thin films achieves high sensitivity to changes in shape because of pressure (piezo) or temperature (pyro). Considered a ferroelectric material because the remnant polarization is stable. Piezo film for active cancellation of noise in sound absorbing foam laminate... 

Overall, we have systematically studied PVDF-based co- and terpolymers to tune its polarization profile for capacitor applications. The desirable terpolymer (VDF/TrFE/CTFE = 65.6/26.7/7.7), exhibiting a high dielectric constant (e 60) at the Curie temperature (35°C), shows a high breakdown electric field >500 MV/m, high energy density (releasing >13 J/cm ), relatively small energy loss, and almost no remnant polarization at zero electric field. 

Ferroelectrics are an important group of piezoelectric materials because they exhibit a much higher piezoelectric response than nonferroelectric piezoelectrics. For instance, for ceramics, d is 10°-10 pC/N for nonferroelectric piezoelectrics and 10 -10 pC/N for ferroelectrics for polymers, d is 10 -10 pC/N for nonferroelectric piezoelectrics and 10°-10 pC/N for ferroelectrics. This ferroelectricity is defined by the appearance of a switchable spontaneous polarization and characterized by a characteristic P-E loop, as shown in Figure 16.3. Besides the spontaneous polarization, the remnant polarization (P,) and coercive field E are also critical parameters for a ferroelectric. Compared to ceramics, ferroelectric polymers exhibit a smaller and a much higher E. ... 

Figure 16.3 Polarization versus electric field (P-E) loop for a ferroelectric polymer - P(VDF-TrFE), where and Ec are the remnant polarization and coercive field.

According to the dielectric results in the previous section, decreasing the temperature at which these measurements were taken should increase the hysteresis gap (ferroelectric behaviour), and increasing the temperature should further decrease the hysteresis. This was observed by Carl et al. (Carl and Geisen 1973) for PLZT (9.0/65/35). The slim ferroelectric behaviour of these PLZT compositions makes them ideal for use as ptrecision sensors and actuators, since they have almost no remnant polarization when the field is removed. Hence, the risk of depoling is eliminated in this case. 

If all the coefficients of equation (2) are known, one can accurately predict the longitudinal strain under a varying electric field for a given piezoelectric or electrostrictive material, and even for a material exhibiting both piezoelectric and electrostrictive effects, such as irreversible electrostrictive materials. For ideal reversible electrostrictive materials, which possess no remnant polarization at zero electric field, the odd power term of the electric field in equation (2) vanishes. However, we will consider the relaxor PLZT ceramics studied in this chapter as irreversible electrostrictives, to account for any ferroelectric behaviour under dc bias fields, and we will therefore include both terms of the electric field in equation (2). 

The piezoelectric properties of semicrystalline polymers, such as PVDF and its copolymers, are determined by the remnant polarization in the materials and the... 

The remnant polarization of the ferroelectric odd-numbered nylons is a function of the number, which is decisive to the electric dipole density. The smaller the number, the higher the dipole density. This is because tire number represents the... 

Table 3 Dipole density and remnant polarization of odd-numbered nylons...

The mechanism resulting in the enhancement was found to be attributed to the interfacial space-charge accumulation and the asymmetric distribution of the accumulated space charges along the direction across the interface between the two constituents (Chen et al. 1994). The remnant polarization and piezoeleetrie eoeffi-cients of the bilaminates are a function of the fiaction of the two constituents. 

In 1999, Gao et al. reported the development of nylon 11-PVDF blends whieh also exhibit a signifieantly enhaneed remnant polarization, P The P of the blend with the 50-50 eomposition is 85 mC/m, whieh is more than 60 % higher than those of individual nylon 11 or PVDF with the P of 52 mC/m (Gao et al. 1999 and Gao and Seheinbehn 2000). The eurves of the eleetrie field displacement, D, versus the applied eleetrie field, E, are shown in Fig. 7. The same paper also reported that the dependenee of ffie ferroeleetrieity of ffie blends depends on the fiaction of the two eonstituents and that the enhaneement might also be attributed to the space-eharge aeeumulation and distribution (Su et al. 1995). The piezoeleetrie strain eoeffieient,... 

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