Piezoelectric voltage

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. 

Theoretical investigations by Brand [ 135] and Brand and Pleiner [136] predicted that a monodomain liquid-crystalline elastomer exhibiting a cholesteric or a chiral smectic C phase should display piezoelectric properties due to a modification of the pitch of the helix under strain. So, a piezoelectric voltage should be observed across the sample when a mechanical field is applied parallel to the helicoidal axis. In this description, the crosslinking density is supposed to be weak enough to allow the motion of the director, and deformations of the sample (compression, elongation, etc.) are assumed to be much smaller than those that should lead to a suppression of the helix. The possibility of a piezoelectric effect do not only concern cholesteric and chiral smectic C phases, but was also theoretically outlined for more exotic chiral layered systems such as chiral smectic A mesophases [137]. 

From these theoretical and experimental works, it emerges that both chiral smectic C and cholesteric elastomers are piezoelectric and can lead to a piezoelectric voltage comparable to that of classical piezoelectric crystals, such as quartz. Thus they can be used potentially as piezoelectric elements, which can be produced in any shape needed. 

The piezoelectric strain tensor d and the piezoelectric voltage tensor g are classically used for linking the mechanical variables to the electrical ones. The piezoelectric strain tensor links the electric field E to the strain and the piezoelectric voltage tensor links... 

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) ... 

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) ... 

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]. 

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. 

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. 

In 1997, Chang et al. provided theoretical and experimental evidence that only a shear field produces piezoelectricity in cholesteric elastomers [16]. Applying a dynamic shear force perpendicular to the helicoidal axis, a nearly linear response is foimd between the piezoelectric voltage and the shear amplitude, as shown in Figure 13.3 for two frequencies. Only at larger shear displacement, the induced voltage tends toward saturation. 

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)-... 

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. 

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