Piezoelectric voltage constant

There are five important figures of merit in piezoelectrics the piezoelectric strain constant d, the piezoelectric voltage constant g, the electromechanical coupling factor k, the mechanical quality factor Qm, and the acoustic impedance Z. These figures of merit are considered in this section. 

The induced electric field E is related to an external stress X through the piezoelectric voltage constant g (an important figure of merit for sensor applications) ... 

The direct effect coefficients are defined by the derivatives (5D/SX) = d (piezoelectric strain coefficient), (5D/5x) = e, -(5E/5X) = g (piezoelectric voltage constant) and -(5E/5x) = h. The converse-effect coefficients are defined by the derivatives (8x/5E) = d, (5x/5D) = g, -(5X/5E) = e, and -(5X/5D) = h. As the piezoelectric coefficients are higher-rank tensors, their mathematical treatment is rather tedious. Fortunately, in higher symmetric crystals the number of tensorial components will be drastically reduced due to symmetry constraints. An example is shown below. 

The piezoelectric voltage constant, also known as the g factor, denotes the electric field generated by materials per unit of mechanical stress applied. Like the piezoelectric charge constant, these values can also be classed in terms of directions (i.e. g y)-... 

Fig. 28. Piezoelectric stress constant obtained from inverse piezoelectric effect and electrostriction constant of drawn and polarized poly(vinylidene fluoride) film plotted against temperature. Draw ratio = 7. Polarized at 90° C under the field of 400 kV/ctn for 3 hours. Frequency of applied voltage = 37.5 Hz. (Oshiki and Fukada, 1971) Broken line represents dielectric constant at 21.5 Hz for roll-drawn poly (vinylidene fluoride) film (Peterlin and Eiweil, 1969)...

Material Piezoelectric constant, d (pC/N) Piezoelectric voltage coefficient, (V m/N)... 

The piezoelectric voltage coefficient gh is given by gh = djso and the large dielectric constant of the material (1800) produces a very low... 

Figure Bl.19.39. Schematic of the themiocoiiple probe in a scaiming themial profiler. The probe is supported on a piezoelectric element for modulation of tip-sample distance at frequency oi and to provide positioning. The AC thennal signal at oi is detected, rectified, and sent to the feedback loop, which supplies a voltage to the piezostack to maintain the average tip-sample spacing constant. (Taken from [209], figure 1.)...

The experimental set-up usually utilizes a piezoelectric tripod as a support of the tip (Fig. 5.36). This is movable vertically and laterally over the examined surface the vertical distance is fixed by a feedback loop to a constant tunnelling current at each point of the scan. The contours of the surface are thus visualized by voltage changes needed to move the piezoelectric tripod to a desired position. 

The piezoelectric stepper, nicknamed the louse, was the first successful stepper used in UHV STM (Binnig and Rohrer, 1982). A schematic of the louse is shown in Fig. 12.1. As shown, the actuating element of the louse is a piezoelectric plate (PP), which can be expanded or contracted by applying a voltage (100 to 1000 V). It is resting on three metal feet (MF), separated by high-dielectric-constant insulators (I) from the metal ground plate (GP). 

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 ... 

A) When an alternating voltage (frequency = to) is applied to the film, the film is strained with frequencies to and 2 to. The former is the inverse piezoelectric effect and the latter the electrostriction effect. By measuring the strain amplitude of the 2to component, we can obtain the electrostriction constant (Oshiki and Fukada, 1971). 

---