Piezoelectric current

Fig. 4.3. Typical normalized piezoelectric current-versus-time responses are compared for x-cut quartz, z-cut lithium niobate, and y-cut lithium niobate. The y-cut response is distorted in time due to propagation of both longitudinal and shear components. In the other crystals, the increases of current in time can be described with finite strain, dielectric constant change, and electromechanical coupling as predicted by theory (after Davison and Graham [79D01]).

As shown in Chap. 4, the piezoelectric current is directly related to the... 

If the film cannot be freely deformed in its plane, the piezoelectric current is called t/33 or dj. If the variation in the electric field is measured per unit of stress, g coefficients are obtained that are connected by the correlation of g = d/e where e is the dielectric constant depending on the film thickness. Constants g and tf are most widely used in the design of electromechanical transducers. The yield from the conversion of mechanical energy into electrical energy is represented by the electromechanical coupling coefficient ATjby Eq. (3.3). 

The varying piezoelectric currents are stored in a computer and are used to generate a topographical map of the surface. Because the current is very sensitive to the separation between tip and surface, this technique gives a very accurate profile of the surface. Atomic resolution can be attained, as shown by the STM image of gallium arsenide seen in Figure 4.12. 

Tobacco, sun exposure, and age reduce the faeil-ity to produee elastin. Piezoelectric currents develop beeanse of ionie ehaiges after irritation or injury. Fibroblasts ahgn along the electrie fields and determine the direetion of repair and proliferation. Certain speeialized fasciae such as the thoracolumbar fascia, tentorium cerebri, and the falx cerebri show lines of force based on ehronic normal stresses. 

A major advance in force measurement was the development by Tabor, Win-terton and Israelachvili of a surface force apparatus (SFA) involving crossed cylinders coated with molecularly smooth cleaved mica sheets [11, 28]. A current version of an apparatus is shown in Fig. VI-4 from Ref. 29. The separation between surfaces is measured interferometrically to a precision of 0.1 nm the surfaces are driven together with piezoelectric transducers. The combination of a stiff double-cantilever spring with one of a number of measuring leaf springs provides force resolution down to 10 dyn (10 N). Since its development, several groups have used the SFA to measure the retarded and unretarded dispersion forces, electrostatic repulsions in a variety of electrolytes, structural and solvation forces (see below), and numerous studies of polymeric and biological systems. 

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. 

Uncoupled solutions for current and electric field give simple and explicit descriptions of the response of piezoelectric solids to shock compression, but the neglect of the influence of the electric field on mechanical behavior (i.e., the electromechanical coupling effects) is a troublesome inconsistency. A first step toward an improved solution is a weak-coupling approximation in which it is recognized that the effects of coupling may be relatively small in certain materials and it is assumed that electromechanical effects can be treated as a perturbation on the uncoupled solution. 

In the use of piezoelectric crystals for stress-pulse measurements, it is convenient to describe the current pulse in terms of the initial current jump i for step loading based on Eq. (4.7) analogous to The piezoelectric cur-... 

The determination of piezoelectric constants from current pulses is based on interpretation of wave shapes in the weak-coupling approximation. It is of interest to use the wave shapes to evaluate the degree of approximation involved in the various models of piezoelectric response. Such an evaluation is shown in Fig. 4.5, in which normalized current-time wave forms calculated from various models are shown for x-cut quartz and z-cut lithium niobate. In both cases the differences between the fully coupled and weakly coupled solutions are observed to be about 1%, which is within the accuracy limits of the calculations. Hence, for both quartz and lithium niobate, weakly coupled solutions appear adequate for interpretation of observed current-time waveforms. On the other hand, the adequacy of the uncoupled solution is significantly different for the two materials. For x-cut quartz the maximum error of about 1%-1.5% for the nonlinear-uncoupled solution is suitable for all but the most precise interpretation. For z-cut lithium niobate the maximum error of about 8% for the nonlinear-uncoupled solution is greater than that considered acceptable for most cases. The linear-uncoupled solution is seriously in error in each case as it neglects both strain and coupling. 

Changes in polarization may be caused by either the input stress profile or a relaxation of stress in the piezoelectric material. The mechanical relaxation is obviously inelastic but the present model should serve as an approximation to the inelastic behavior. Internal conduction is not treated in the theory nevertheless, if electrical relaxations in current due to conduction are not large, an approximate solution is obtained. The analysis is particularly useful for determining the signs and magnitudes of the electric fields so that threshold conditions for conduction can be established. 

It has previously been shown that, within the approximation above, an arbitrary stress profile applied to a piezoelectric disk produces a current... 

Nonlinear properties of normal dielectrics can be studied in the elastic regime by the method of shock compression in much the same way nonlinear piezoelectric properties have been studied. In the earlier analysis it was shown that the shape of the current pulse delivered to a short circuit by a shock-compressed piezoelectric disk was influenced by strain-induced changes in permittivity. When a normal dielectric disk is biased by an electric field and is subjected to shock compression, a current pulse is also delivered into an external circuit. In the short-circuit approximation, the amplitude of this current pulse provides a direct measure of the shock-induced change in permittivity of the dielectric. 

As with the piezoelectric case, material constants are most easily determined from the initial jump in current i(O-l-), which, from Eq. (4.16), is... 

Fig. 5.4. The electrical signals from shock-compressed piezoelectric solids depend explicitly on the electrical circuit and mechanical arrangement (the sample thicknesses). In the current mode (low electrical impedance), the current pulse either follows the loading as a close analog, or, in the thin mode of PVDF, follows the derivative of the stress pulse in time.

Fig. 5.5. The electrical response of piezoelectric polymers under shock loading is studied experimentally by placing the thin PVDF element on the impact surface of a standard target, either the polymer, Kel F, z-cut quartz, or z-cut sapphire. The im-pactor is typically of the same material. The current pulse is recorded on transient digitizers with frequency responses from 250 to 1000 MHz.

For those cases in which a peak current value is achieved prior to wave transit time in the samples, the current provides a direct measure of the piezoelectric polarization in a time of a few nanoseconds. The data from such experiments are shown in Fig. 5.8. A relation showing a remarkable linearity with shock pressure is shown. 

Characteristic responses are readily obtained at pressures higher than 10 GPa, but differences have been observed with different loading arrangements. Piezoelectric responses at higher pressures are currently under study [92B01]. Dielectric relaxation and shock-induced conductivity may be involved. 

Since discovering and making use of the piezoelectric effect in naturally occurring crystals such as quartz and Rochelle salts, scientists have produced a wide range of piezoelectric materials in the laboratoi y. An early example is barium titanate, used in an electrical component called a capacitor. Currently, most piezoelectric materials are oxide materials based on lead oxide, zirconate oxide, and titanium. These very hard piezoelectric materials are termed piezoceramics. 

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