Piezoelectric relaxation

The piezoelectric constant of polymer films is usually a function of the frequency of the applied strain, and the constant is expressed by a complex quantity. In other words, the open-circuit voltage across the film surfaces is not in phase with the applied strain and the short-circuit current is not in phase with the strain rate. This effect, first pointed out by Fukada, Date and Emura (1968) and designated piezoelectric relaxation or dispersion, will be discussed in this review in terms of irreversible thermodynamics and composite-system theory. 

When the induced voltage Fopen is not completely in phase with the applied strain, or the induced current is not completely in phase with the applied strain rate (piezoelectric relaxation), the e-constant becomes a complex quantity as follows ... 

In Case (A), as will be discussed in 4.3, the piezoelectric relaxation is described as a coupling of dielectric relaxation and mechanical relaxation. In Case (B), on the other hand, the mechanical relaxation in the amorphous phase plays an important role in the piezoelectric relaxation ( 4.4). 

A Model Theory of Piezoelectric Relaxation for a Two-Phase System... 

In Table 1 the characteristic values of piezoelectric relaxation are listed. Values of Ad are estimated from the difference between the high-... 

The piezoelectric effect has been shown to exhibit a relaxational nature and the complex piezoeletric constant is a function of frequency and temperature. In Group (A), the relaxation is ascribed to either the nature of the crystallite itself or the viscoelasticity of the amorphous phase in which the crystallites are embedded. In the former case, the piezoelectric relaxation is a cross-coupling phenomenon of dielectric relaxation and mechanical relaxation of the crystallite. In the latter, on the other hand, the relaxation is governed by the mechanical relaxation of the amorphous phase. 

Piezoelectric Relaxation and Nonlinearity investigated by Optical Interferometry and Dynamic Press Technique... 

Investigation of the piezoelectric relaxation in ferroelectric ceramics using dynamic press 257... 

Maxwell-Wagner piezoelectric relaxation and clockwise hysteresis... 

Piezoelectric relaxation and Kramers-Kronig relations in a modified lead titanate composition... 

We show in Figure 13.8 that in the case of a well-behaved piezoelectric relaxation (counterclockwise hysteresis) presented in Figure 13.7, the Kramers-Kronig relations are indeed fulfilled. Closer inspection of the data show that the relaxation curves can be best described by a distribution of relaxation times and empirical Havriliak-Negami equations [19]. It is worth mentioning that over a wide range of driving field amplitudes the piezoelectric properties of modified lead titanate are linear. Details of this study will be presented elsewhere. 

Figure 13.8 Ilustration of the validity of the Kramers-Kronig relations for the piezoelectric relaxation in Sm-modified lead titanate ceramics. The imaginary component is calculated from the real using numerical method and Kramers-Kronig relations and compared with experimentally determined data.

Frequency dependence of the piezoelectric response in soft pzt is very different from the piezoelectric relaxation described in the previous section, Figure 13.9. The data presented in Figure 13.9 suggest logarithmic frequency dependence [20] of the piezoelectric coefficient. However, analysis of its imaginary component reveals possibility that we are in this case in a... 

Y Suzuki, N Hirai, M. Ikeda. Piezoelectric relaxation of wood I. Effects of wood species and fine structure on piezoelectric relaxation. Mokuzai Gakkaishi 38 20-28, 1992. 

For a system with s single relaxation time, the elastic, dielectric, and piezoelectric relaxations are represented by the following equations ... 

To understand the piezoelectric relaxations, one must consider the composite structure of polymers consisting of piezoelectric crystalline regions and nonpiezoelecttk non-crystalline regioitt. The simplest model for siidi compoailc structures is a spherical dis-penion system as shown in Figure 3. 

We may assume that the crystalline propertieB c, and c, remain constant with increasing temperature. At the glass transition temperature, the amorphous properties c, and c, change with inaeasing temperature. The increase of c, results in the increase of both e and d. but the increase of c, results in the increase of r and the deaease of d. Wrious examples of piezoelectric relaxation will be described later. 

Elastic and dielcclric relaxatioas are oommonly observed for most polymers. The onset of thermal molecular motions infiueoces the elastic and dielectric properties. Pi-ezoelectridty is a cross effect of the elastic and dielectric effects. Since the plezoclec-tridty expresses the internal strain of the polymer, the piezoelectric relaxation reflects the change of the internal strain. This is the most interesting characteristic ai the piezoelectric relaxation. 

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