Dielectric hysteresis loop

BaTi03, which has a perovskite crystal lattice, is a ferroelectric material i.e. a material in which the change in polarization P with varying applied electric field E traces a dielectric hysteresis loop analogous to the hysteresis loop exhibited by ferromagnetic materials. 

The ferroelectric domain structure in the crystal is a reason of the non-linear behavior of the polarization as a function of an electric field. Dielectric hysteresis appears in the alternating electric fields. The dielectric hysteresis loop is one of the most important features of ferroelectric materials (Fig. 5.6). Hysteresis loop or domain structure observation could serve as a proof of ferroelectricity in the material. Due to the presence of domain wall structure, the remanent polarization Pr is always smaller than the spontaneous polarization Ps. 

Y. Muraia. K Tlunasliima, and N. Koizumi, Dielectric hysteresis loop in alicyclic and aromatic pcdyamidcs, Jpn. J. AppL Pkys J1 L354 (1994). 

Fig. 1. Hysteresis loop of dielectric displacement, DI, versus appHed electric field where F is coercive field and PI j, PI, and P/ are the saturated,...

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],... 

Lithium ferrite itself (x = 0.5) has a high Curie temperature and can be fabricated so as to give a square hysteresis loop satisfactory for digital-computer memory cores. In this application, the dielectric losses connected with the presence of mobile charge carriers can cause a dramatic loss in core quality. The mobile carriers may be introduced by... 

Alternating fields cause domain walls to oscillate. At low fields the excursions of 90°, 71° or 109° walls result in stress-strain cycles that lead to the conversion of some electrical energy into heat and therefore contribute to the dielectric loss. When peak fields are sufficient to reverse the spontaneous polarization the loss becomes very high, as shown by a marked expansion of the hysteresis loop (Fig. 6.9). 

Fig. 4 (a) Temperature variation of magnetization of InMnOj at 100 Oe. Inset shows the magnetic hysteresis loops at 10 and 300 K, (b) Temperature variation of the dielectric constant for different frequencies (from ref, 24),... 

As mentioned above, domain switching in ferroelectrics is accompanied by domain nucleation, moving domain walls and restructuring of dipoles and charges. A characteristic feature of this irreversible process is the appearance of a hysteresis loop in the dependence of dielectric displacement... 

Phase transitions may be detected by the corresponding anomaly in the temperature dependence of the quadrupole coupling constant. For example, in monomethylamine a phase transition occurs at 80 °K and a hysteresis loop has been observed in the frequency vs. temperature curve with a broadening of the lines just before the transitions 24> This transition has been confirmed by the N.M.R. study of the proton line width and by the dielectric behavior, but no precise explanation has been given. 

Ferroeleciric substances exhibit a hysteresis loop on the curves of the dependence of polarization on electric field intensity (Fig. 193). In the case of non-ferroelectric substances, this dependence is linear and its slope is related to the permittivity value. Figure 193 indicates that with ferroelectrics, the permittivity depends on the field intensity as well as on the direction of changes in the field intensity. When the electric field is cut oft, the dielectric shows remanent polarization (electrical analogy with ferromagnetic substances). 

It was recently reported by Gu et al. [207] that magnetoresistive PANI/ FCjO nanocomposites (Figure 2.19) with negative dielectric permittivity, synthesized using a facile surface-initiated polymerization method, do not show hysteresis loop with zero coercMty thus indicating the superpara-magnetic behavior at room temperature. 

The hysteresis loops studies appear to be very informative for nanograin ceramics also. In particular, above we have discussed above the relaxor state induced by the grain sizes. The studies of the relaxor state have been made on the basis of dielectric response analysis. In Ref. [27], the additional firm evidence of relaxor state has been obtained with the help of hysteresis loops measurements. In Fig. 2.16 we report the shape of hysteresis loops in ferroelectric relaxors at different temperatures. It is seen, that at r > (Tm = 363 K is the temperature of dielectric permittivity maximum for PbSci/2Nbi/202 (PSN)) there is no residual polarization, while it is nonzero at T< r. Similar behavior has been observed for 730 nm thick Pbo.76Cao.24Ti03 (PCT) film with average grain sizes 86 nm and Tm = 553 K. 

The piezoelectric hysteresis loops have been studied additionally to above dielectric hysteresis. This kind of loop is shown on Fig. 2.17. It has been recorded on PZT nanotube with outer diameter 700 and 90 nm wall thickness with the help of piezoatomic force microscopy (see Refs. [42, 43]). The obtained loop is the direct evidence of ferroelectric properties of the nanotube. Square form of the loop speaks about sharp polarization switching at coercive voltage 2 V. The residual (at zero voltage) piezoelectric coefficient d ff is of the same order as for the thin PZT film. 

The first area of ferroelectric ceramic application was that of capacitor engineering, where the dielectric effect is exploited. Most ceramic capacitors are, in reality, high-dielectric-constant ferroelectric compositions in which the ferroelectric properties (hysteresis loop) are suppressed with suitable chemical dopants while retaining a high dielectric constant over a broad temperature range. Historically, the first composition used for such capacitors was BaTi03 and its modifications, but today lead-containing relaxors and other compositions are also included. 

---