Transverse piezoelectric coefficient

The coefficient is called the transverse piezoelectric coefficient. The converse piezoelectric effect, relating strain, e to the applied electric field E is similarly simplified to... 

The charge Q generated on the PVDF film is proportional to the bending displacement Z of the beam, Q = GZ, where G is a constant dependent on the transverse piezoelectric coefficient dsi, and the dimensions and Young s moduli of individual layers of the composite beam [Shen et al. (2004)]. The transfer function from Z s) to the measured voltage V/(s) can then be written as... 

The dynamic press allows measurements of the longitudinal, transverse and shear piezoelectric coefficients in the frequency range from 0.01 Hz to about 100 Hz. The lower limit is determined by the insulation resistance of the sample and cables, and charge drifts associated... 

Of central importance for understanding the fundamental properties of ferroelec-trics is dynamics of the crystal lattice, which is closely related to the phenomenon of ferroelectricity [1]. The soft-mode theory of displacive ferroelectrics [65] has established the relationship between the polar optical vibrational modes and the spontaneous polarization. The lowest-frequency transverse optical phonon, called the soft mode, involves the same atomic displacements as those responsible for the appearance of spontaneous polarization, and the soft mode instability at Curie temperature causes the ferroelectric phase transition. The soft-mode behavior is also related to such properties of ferroelectric materials as high dielectric constant, large piezoelectric coefficients, and dielectric nonlinearity, which are extremely important for technological applications. The Lyddane-Sachs-Teller (LST) relation connects the macroscopic dielectric constants of a material with its microscopic properties - optical phonon frequencies ... 

Davis et al. [42] have recently introduced the terms rotator and extender for a variety of ferroelectrics based on oxygen octahedra, in order to classify them with respect to whether the shear or the collinear effect dominates in the piezoelectric response. In extenders, the dominant polarization extension is directly related to the collinear piezoelectric effect, whereas in rotators the dominant contribution to the piezoelectric effect is the polarization rotation, that is directly related to the shear piezoelectric effect. Thus, extenders are ferroelectrics with a large longitudinal piezoelectric coefficient 33 that is related to a large relative dielectric susceptibihty %33, while rotators are ferroelectrics with large shear coefficients dis and 24. which are related to transverse susceptibilities and %2z. correspondingly. Electrostrictive... 

Coefficients d, d2i and d-ij, describe the longitudinal piezoelectric effect (see symbol L in Table 5.1). The normal mechanical stress component causes piezoelectric polarization parallel to it in such case. Second possibihty is the piezoelectric polarization perpendicular to the applied normal mechanical stress. Such piezoelectric effect is so called transversal effect (see symbol T in Table 5.1) and it is characterized by one of the coefficients di2, d -i, J21, dj2, dn or J32. Application of shear mechanical stress might result in the piezoelectric polarization perpendicular to the plane of applied shear. Such shear piezoelectric effect is called longitudinal shear (see symbol 5l in Table 5.1) and it is characterized by one of the piezoelectric coefficients du, d25 or d e- Second possibility of shear piezoelectric effect is the piezoelectric polarization parallel to the plane of the applied shear stress. Such effect is called transversal shear (see symbol in Table 5.1 and in Fig. 5.2). This effect is related to one of the piezoelectric coefficients J15, di, d24, d26, d- orc 35. 

The condition for the maximum twinniug suppression is fulfilled for example for the quartz bar of the orientation (XYa) 150° for the transversal piezoelectric effect. The mechanical load is applied in the direction of rotated length axis at this time. Electrodes cover the surfaces perpendicular to the xi -axis. Condition Eq. (7.8) cannot be fiilfilled for the quartz elements for the longitudinal piezoelectric effect at all. The longitudinal piezoelectric coefficient is equal to zero for such orientations. Practical apphcation must be designed in order to get the twiiming suppression as high as possible simultaneously with sufficient piezoelectric coefficient. 

Temperature dependence of the piezoelectric du and du coefficients is displayed in Fig. 7.4. The piezoelectric coefficient of X-cut and XY-cut (it is d 2 = —du for quartz) for transversal effect is changing significantly (decreasing) with increasing temperature. Second independent piezoelectric coefficient du contributes in an opposite sense (see Fig. 7.4). It makes possible to find special quartz cut orientation with compensated temperature dependence in transversal mode. Piezoelectric coefficient is independent on the temperature for such cut practically in certain limited temperature range. 

Sensors for the transversal or shear mode applications could be basically made from /3-quartz. The maximum piezoelectric coefficient reaches its value = -0.93 X 10 CN for the (XYa) 45 cut orientatioa Sensor with such element orientation does not loose its piezoelectric properties also near the a-p quartz phase transition. 

Composites with 1-3 connectivity pattern could be also transversely poled (TP). PZT tubes with the electrodes on the inner and outer radius surfaces are dispersed in the polymer matrix (Zhang et al. (1993 Wang et al. 1995). Volume in the tube is either filled by the polymer or left empty and end-capped by the additional polymer cover plate. Under the assumption of the isotropic PZT ceramics the effective piezoelectric coefficients could be calculated for single tube... 

When piezoelectrics are used in hydrostatic pressure conditions, such as hydrophone applications, the hydrostatic piezoelectric coefficient determines performance. The hydrostatic coefficients take into account the transverse piezoelectric effect from directions orthogonal to the poling axis. They are the hydrostatic strain coefficient... 

Analogously to the piezoelectric coefficients, is the coupling factor related to the transverse vibration, perpendicular to the polarized direction, while k s is related to the vibration of thick specimens parallel to the direction of polarization. Thus... 

Of greater interest in recent years have been the peculiar piezolectric properties"" of polyfvinylidene fluoride). In 1969 it was observed" that stretched film of the polymer heated to 90°C and subsequently cooled to room temperature in a direct current electric field was 3-5 times more piezoelectric than crystalline quartz. It was observed that the piezolectric strain coefficients were higher in the drawn film and in the normal directions than in the direction transverse to the film drawing. 

The above experimental methods were devoted to the study of the piezoeleetric coefficient as this one is flie relevant parameter of ferroelectrets. Ferroelectric polymers Uke PVDF and its copolymers show transversal and longitudinal piezoelectric activity depending on the degree and type of stretching (uniaxial vs. biaxial) causing molecular orientation. 

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