Piezoelectric hysteresis loops

Figure 19.10 (a) Piezoelectric hysteresis loops of 256 points (each approx. 30x30nm) obtained by combining phase and amplitude of the induced piezoelectric vibration, (b) Average of the 256 loops [17]. 

By combining the amplitude with the phase information, the piezoelectric hysteresis loops of each point can be calculated and is depicted in 3-dim in Figure 19.10 (a). Figure 19.10 (b) shows the averaged piezoelectric loop of the 256 points. Since the piezoelectric response (amplitude) is in first approximation proportional to the effective dss this averaged loop can be compared with that obtained with a double beam interferometer and therefore used to... 

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. 

Fig. 2.17 Piezoelectric hysteresis loop for PZT nanotube, measured by means of atomic force microscopy [42]...

Desfeux, R., Detalle, M., Wang, G.S., and R miens, D. (2008) Local piezoelectric hysteresis loops for the study of electrical properties of 0.7Pb(Mgi/3Nb2/3)O3-0.3PbTiO3 thin films bottom electrode dependence and film thickness effect. Ferroelectrics, 362 (1), 21-29. 

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],... 

Figure 13.6 Piezoelectric coefficient d and tan<5p of a single phase Bi4Ti30i2 ferroelectric ceramic with highly anisotropic grains, at room temperature. On the right are shown charge-pressure hysteresis loops at selected frequencies, with a clockwise hysteresis at 0.07 Hz and counter-clockwise hysteresis at 70 Hz. See [17] for details.

Barium titanate is ferroelectric and, by implication, also pyroelectric and piezoelectric. The characteristic of a ferroelectric is that it is polarized in the absence of an applied electric field and the direction of polarization can be reversed. Figure 31.10 shows a rectangular hysteresis loop for a singledomain single crystal of BaTiOs. This loop was obtained at room temperature using a 50 Hz supply. 

The buffer-fly curve of FMR fi-equencies vs. applied electric field was observed and shown in Fig. 2 (b), which resembled the widely observed piezoelectric strain vs. electric field butterfly curves for piezoelectric materials and matched the ferroelectric P-E hysteresis loop of PMN-PT single crystal as well. This once again confirmed that the change of FMR fi equency of the FeGaB film results from the ME coupling induced strain in the FeGaB film. 

The peak field-induced response, particularly the mechanical strain Sp, was used to quantify the response of each tested PZT stack. Meanwhile, the piezoelectric hysteresis related to a S-E loop was characterized as... 

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... 

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