Hysteresis curves, ferroelectrics

Hysteresis curve of a ferroelectric crystal, v = initial (virginal) curve, Pr = remanent polarization, Ps = spontaneous polarization, Ec = coercive field... 

Photochemical control of properties of SmC LC phase was achieved by doping azobenzene A-4 possessing a chiral carbon atom to a ferroelectric LC A-5 [61]. When the SmC LC is in the surface stabilized state, the bulk dipole moment can be flipped by an external electric field. As the hysteresis curve for the Z form is narrower than that of E form, irradiation of UV light to cause E-... 

Nonvolatile ferroelectric random access memory (FRAM) devices Dynamic random access memory (DRAM) and static random access memory (SRAM) devices based on semiconductor technology are volatile that is, they wiU lose stored information when the power fails. Nonvolatile devices such as CMOS (complementary metal oxide semiconductors) and EEPROMs (electrically erasable read-only memories) are forbiddingly expensive for mass-produced electronic devices. As described above (see Section 8.3), the magnitude and direction of polarization of a ferroelectric ceramics can be reversed by applying an external electric field, and this method is used by FRAMs to store (or erase) data. As the materials have a nonlinear hysteresis curve, the polarization remains in the same state when the voltage is switched off (i.e., the information originally stored is maintained). In addition, FRAMs may be radiation-hardened for use in harsh environments such as outer space (Scott and Paz de Araujo, 1989). 

Apart from nonlinearities in their D(E) characteristics, the dielectric displacement D of ferroelectric materials also depends on the electric field history, a phenomenon known as ferroelectric hysteresis. The common approach to measure D(E) or P(E) hysteresis curves utilizes the Sawyer-Tower circuit (Sawyer and Tower 1930) (cf Fig. 9a) that operates in the voltage-voltage mode. 

The ferroelectric effect was discovered in 1920 by Valasek, who obtained hysteresis curves for Rochelle salt analogous to the B-H curves of ferromagnetism [5.5], and studied the electric hysteresis and piezoelectric response of the crystal in some detail [5.6]. For about 15 years thereafter, ferroelectricity was considered as a very specific property of Rochelle salt, until Busch and Scherrer discovered ferroelectricity in KH2PO4 and its sister crystals in 1935. During World War II, the anomalous dielectric properties of BaTiOs were discovered in ceramic specimens independently by Wainer and Solomon in the USA in 1942, by Ogawa in Japan in 1944, and by Wul and Goldman in Russia in 1946. Since then, many ferroelectrics have been discovered and research activity has rapidly increased. In recent decades, active studies have been made on ferroelectric liquid crystals and high polymers, after ferroelectricity had been considered as a characteristic property of solids for more than 50 years. 

Next, the contrasting, very strongly nonlinear response of a ferroelectric is shown in Fig. 5. The two stable states (-hP, -P) at zero field are the most characteristic feature of this hysteresis curve, which also illustrates the threshold (coercive force) that the external field has to overcome in order to... 

Fig. 27 indicates the apparent piezoelectric constant e of roll-drawn PVDF as a function of static bias field E0 (Oshiki and Fukada, 1972). The value of e at E0=0 represents the true piezoelectric constant e. The curve exhibits a hysteresis and the polarity of e changes according to the poling history. If the piezoelectricity in /)-form PVDF originates from the polarization charge due to spontaneous polarization, inversion of polarity of e would mean the inversion of the polarization by the external field and hence /S-form PVDF may be a ferroelectric material, as was first suggested by Nakamura and Wada (1971). 

Based on these assumptions the measurement of the large signal ferroelectric hysteresis with additional measurements of the small signal capacitance at different bias voltages are interpreted in terms of reversible and irreversible parts of the polarization. As shown for ferroelectric thin films in Figure 1.24, the separation is done by substracting from the total polarization the reversible part, i. e. the integrated C(V)-curve [18]. 

Figure 2.4 Strain-field curves for < 001 > oriented 0.91PbZn1/3Nb2/303-0.09PbTi03 single crystals. The sample in (a) was poled at room temperature, where the resulting domain state is unstable (due to induction of tetragonal material associated with the curved morphotropic phase boundary), yielding substantial hysteresis. In (b) the crystal was poled at low temperatures to keep it in the rhombohedral phase. When measured at room temperature, the piezoelectric response is much more linear and non-hysteretic, due to the improved stability of the ferroelectric domain state. Data courtesy of S. E. Park.

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). 

All measurements were started in accumulation and finished there too, after driving the voltage in the investigated range to inversion and back (e.g. -10 V to 10 V and backwards to -10 V we call this a 10 V loop ). Due to the polarisation of the ferroelectric layer, the CV curves show a hysteresis loop [30, 31], which depends on the maximal applied voltage in the CV mode. 

In general a ferroelectric perovskite single crystal will be composed of a roughly equal number of domains oriented in all the equivalent directions allowed by the crystal symmetry. The overall polarisation of the crystal will be zero. The application of an electric field will cause a polarisation switch and lead to a classical hysteresis loop in which the important values are P, (the remanent or residual polarisation when the electric field is reduced to zero), and E, (the coercive field, which is the reverse field required to reduce the polarisation to zero). Extrapolation of the high-field portion of the curve to =0 gives the value of the spontaneous polarisation P (Figure 6.9a). 

Finally we can note that the ferroelectric state of relaxors is characterised by an extremely narrow hysteresis loop with a low value for the remanent polarisation (Figure 6.19a). This sort of hysteresis loop can be considered to fall into the continuum described previously (Figure 6.9) and suggests that the microsttucture of the phases is at an even more reduced scale than the fine-grained ceramic samples. Indeed, the behaviour when the materials are either cooled in or without an external electric field (FC or ZFC) is also taken as indicative of a complex microstructure. The strain versus applied electric field loop has a U shape, rather like the central portion of the strain curve for an antiferroelectric (Figure 6.19b). 

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