Piezoelectric voltage coefficient

Composite ferroics. Ingenious experiments have been performed with composites made from a ferroic and another material (Newnham Cross, 1981 Lynn et al, 1981 Rittenmeyer et al, 1982 Safari et al, 1982). For example, in a piezoelectric like PZT, the piezoelectric voltage coefficient g can be defined for a given direction (say Z = 33) thus, 33 = where d and k stand for piezoelectric coefficient... 

For low frequency electromechanical applications in which the acoustic wavelength is much larger than the scale of component phases, some of the ceramic-polymer composites have piezoelectric voltage coefficients orders of magnitude larger than solid PZT. Such materials have obvious applications in hydrophones and other listening devices. 

The coupling factor between electrodynamics and translational mechanics is not classically used as such but as a piezoelectric voltage coefficient g (in m C ) divided by a characteristic length. In an anisotropic three-dimensional material, this coefficient is a tensor that links the stress F a to the electric field E and is equivalent to the multiplication of the coupling factor with the spatial integration of the stress (i.e., the lineic density of the force) ... 

Sensitivity. The sensitivity of a piezoelectric material is taken to be equal to the generated open-circuit voltage that drop>s across to the contact with the distance t (= thickness) divided by the applied stress or the product g t, where g is the relevant piezoelectric voltage coefficient. The voltage coefficient g is connected with the charge coefficient d via the dielectric permittivity = CrCo according to... 

Currently, quartz is often utilized in accelerometers. Due to their high piezoelectric voltage coefficient lithium sulfate and tourmaline are often applied in commercial hydrophones especially to measure shock and pressure waves. Rochelle salt can be found in acoustic pickups and special devices to measure acoustic pressure. Due to their long-term stable piezoelectric properties natural crystals are in particular perfect for sensor applications where the monitoring of a quantity has to be made over long periods [85]. 

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

Piezoelectric voltage coefficient (gffi The tensor that defines the generation of strain on application of electric field is known as the piezoelectric voltage coefficient. 

Such polymers as PVDF, in particular, have wide applications [3] sometimes its properties are advantageous for some reasons, e.g., low electric permittivity and small thickness, but limit ite application in other devices. When, for example, hydrophones, which are electroacoustic transducers used in a water environment, b use of the low transducer capacity made of PVDF, amplifiers should be placed very near. Moreover, vduge sensitivity in the open system given in dB in the relation 1/piPa determined by a product giz, (where g indicates hydrostatic piezoelectric voltage coefficient and Xj is transducer thickness), is low for transducers m of PVDF films. 

Polymer composites based on PMN—PZT/PDMS have piezoelectric voltage coefficients and mechanical quality factors that decrease with increasing the filler ratio of PMN—PZT and yielded 82 pW of power from a piezoelectric energy harvester with dimensions of 200 mm by 3 mm (Lee et al., 2013). 

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

Composite piezoelectric materials may be represented by the so-called simple series, simple parallel and the modified cubes diphasic models (Fig. 6.4). The modified cubes model was developed as a generalization of the series, parallel and cubes models. It is adapted for the representation of 0-3 composite sheet materials. Estimated values of the average longitudinal piezoelectric strain coefficient 33 and the average piezoelectric voltage coefficient 33 for the composite may be evaluated in terms of these models. References to the piezoelectric ceramic and the polymer phase will be indicated by superscripts 1 and 2 respectively. 

Polymer electrets can be operated as sensors or actuators. Their operation is very similar to that of a piezoelectric material and their direct piezoelectric transducer coefficient (d33) is higher than that of solid PVDF ferroelectric polymers [97]. If a compressive force is apphed to the film, the pores will deform preferentially with respect to the polymer material. Unlike charges within the polymer will be pushed closer together and the potential measured at the contacts will change accordingly. Similarly, the application of a voltage across the electrodes will yield a change in thickness in the material. 

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 change in velocity across the element v — is linearly proportional to the input voltage V and permittivity e, and inversely proportional to the circular frequency ca and piezoelectric stress coefficient e. 

The thermodynamical derivation of piezoelectricity includes two steps (1) The relevant mechanical or electrical quantities are calculated as partial derivatives of the Gibbs free energy with respect either to one of the two mechanical or to one of the two electrical observables, respectively. (2) The second partial derivative of the Gibbs free energy with respect to the other domain (electrical or mechanical, respectively) yields one of the piezoelectric coefficients. Because there is one intensive (force-like or voltage-like) observable, namely, mechanical stress and electrical field, and one extensive (displacement-like) observable, namely, mechanical strain and electrical displacement, in each of the two domains, we have four possible combinations of one mechanical and one electrical observable in total. Thus, we obtain four different piezoelectric coefficients that are usually abbreviated as d, e, g, and h. As the sequence of the two partial derivations can be reversed, we arrive at two different expressions for each coefficient one for direct piezoelectricity (mechanical stimulus leads to an electrical response) and one for inverse or converse piezoelectricity (electrical stimulus leads to a mechanical response). For example, the piezoelectric d coefficient is given by the two alternative terms ... 

Z-voltages of the piezoelectric tube and obtained the slopes of the lines, which are attributed to the friction coefficients of the sample surfaces. 

Fig. 9.3. Definition of piezoelectric coefficients. A rectangular piece of piezoelectric material, with a voltage V applied across its thickness, causes a strain in the x as well as the z directions. A piezoelectric coefficient is defined as the ratio of a component of the strain with respect to a component of the electrical field intensity.

A typical measuring circuit is shown in Fig. 9.15. A signal generator supplies a sinusoidal signal with 600 fl output impedance. The current is amplified at sensitivity of 10 AfV. The ac voltages are measured by ac digital voltmeters. The experiment is performed with a PZT-4 tube, provided by EBL, Inc., with L = 25.4 mm, D = 12.7 mm, h = 0.50 mm, and Y= 7.5 X 10 N/m. The lowest resonance frequency is 5 kHz. The results of measurements are shown in Fig. 9.16. The current, about 1 xA, can easily be measured with 1% accuracy. The current from the two x quadrants agrees well with that from the two y quadrants. In terms of the units mentioned, the piezoelectric coefficient dn can be obtained from directly measurable quantities as ... 

In many microelectromechanical systems (mems) based on piezoelectric thin films, flexure is deliberately used to amplify the available displacements (or alternatively to increase the sensitivity of a sensor). For simplicity (and to keep poling and actuation voltages low), films are often poled and driven by electrodes at the top and bottom surfaces. As a result, the critical piezoelectric coefficient is often e31 j, rather than d33j [24], For the direct effect, the effective film coefficient, e3ij can be defined by... 

In the converse piezoelectric effect one usually applies voltage V or electric field E on the sample and measures displacement AZ or strain A///. From relation Al = 0Z33 V for the longitudinal effect, we see that even for materials with exceptionally high piezoelectric coefficient (do3 = 2000pm/V in pzn-pt) the displacement Al is only around 2 nm if 1 V is applied on the sample. For the same voltage the displacement is reduced to 0.2 nm in a typical pzt composition and to only tn 2 pm in quartz. The displacement can be increased by application... 

The maximum scan size that can be achieved with a particular piezoelectric scanner depends upon the length of the scanner tube, the diameter of the tube, its wall thickness, the strain coefficients of the piezoelectric ceramic and the applied voltage. The sensitivity of the piezo depends on temperature its maximum scan range is approximately reduced by a factor 5-6 by cooling the piezo material from room temperature to liquid helium temperature (4.2 K). The process of calibration is described in Tutorial 3. 

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