Piezoelectric, defined material

A chemical microsensor can be defined as an extremely small device that detects components in gases or Hquids (52—55). Ideally, such a sensor generates a response which either varies with the nature or concentration of the material or is reversible for repeated cycles of exposure. Of the many types of microsensors that have been described (56), three are the most prominent the chemiresistor, the bulk-wave piezoelectric quartz crystal sensor, and the surface acoustic wave (saw) device (57). 

For many problems it is convenient to separate the piezoelectric (i.e., strain induced) polarization P from electric-field-induced polarizations by defining D = P + fi , where s is the permittivity tensor. For uniaxial strain and electric field along the 1 axis, when the material is described by Eq. (4.1) with the E term omitted. 

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.

Probably the best measure of the effectiveness of a piezoelectric material is its electromechanical coupling constant, k, defined as... 

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... 

The material properties appearing in Eqs. (6)-(9) are defined by the partial derivatives of the dependent variables (P, c, e) with respect to the independent variables. At this point, to maintain consistency with the literature on the P-phase of PVDF, we label c as the 1 axis, a as the 2 axis, and, b as the 3 axis. In evaluating the piezoelectric and pyroelectric responses we consider changes in polarization along the 3 axis only polarization along the 1 and 2 axes remains zero, by symmetry, for all the cases considered here. The direct piezoelectric strain 03 , pC/N) and stress (gaj, C/iiE) coefficients are defined in Eqs. (10) and (11),... 

In such measurements, it is very important to specify the excitation level and the frequency at which the measurement was made. As can be seen in Figure 2.2, even when the sample hysteresis is low, the piezoelectric coefficients of materials are field-dependent quantities. Thus, there is some curvature of the strain-field response. Typically the low-field response is defined as the piezoelectric coefficient measured near the origin (often at field levels < 1 / 10th... 

The electromechanical coupling coefficient (k) is a measure of the ability of a piezoelectric material to transform mechanical energy into electrical energy, and vice versa. It is defined [5] by... 

Measurements of the surface tension and surface stress of solids are not easy. Some attempts have been made to measure the surface energy, or at least to determine the PZC, of solid electrodes attached to piezoelectric materials (36, 37). More often there is a reliance on studies of differential capacitance (Section 13.4.3) (35, 38). In principle, these measurements could provide all of the information needed to describe the surface charges and relative excesses however, one must first know the PZC. Evaluating it for a solid electrode/electrolyte system is not straightforward, and indeed, as discussed below, the PZC is not uniquely defined for a polycrystalline electrode. The most widely used approach is to evaluate the potential of minimum differential capacitance in a system involving dilute electrolyte. The identification of this potential as the PZC rests on the Gouy-Chapman-Stem theory discussed in Section 13.3,... 

Piezoelectricity is defined as an electric polarization that occurs in certain crystalline materials at mechanical deformation [69]. The polarization is proportionate to the deformation and the polarity changes with change in deformation. In reverse, electric polarization produces mechanical deformation in piezoelectric crystals. The piezoelectric materials also possess pyroelectric properties, i.e., electric polarization is generated at temperature change. 

It is clear that a sharp Curie tenperature cannot be defined for relaxor materials in the same way as for simple materials such as BaTiOj. To take account of this, a depolarisation temperature, is taken as the temperature at which a partial or complete loss of polarisation, and a consequent degradation in piezoelectric performance, occurs. In materials with relative permittivity behaviour similar to that in Figure 6.18b,... 

The piezoelectric effect, discovered in 1880 by French physicists Jacques and Pierre Curie, is defined as the linear electromechanical interaction between the mechanical and electrical state (in a crystalline material with no inversion symmetry), such that... 

Finally, it is worth mentioning that a phenomenon analogous to the difference between the normal and giant flexoelectricity of calamitic and bent-core nematics, respectively, exists in crystals, ceramics and polymers too. The flexoelectric response (defined in Eq. (3.1)) of perovskite-type ferroelectrics, " of relaxor ferroelectric ceramics and polyvinylidene fluoride (PVDF) films are four orders of magnitude larger than the flexoelectricity of dielectric crystals. In those sohd ferroelectric materials the polarization induced by flexing is evidently of piezoelectric origin. 

At times, particularly with amorphous materials, the term electret is used instead of piezoelectric to describe a material the term was introduced as an electric counterpart to the magnet, defined as all materials that are able to retain at least a quasi-permanent electric polarization within and perhaps trap charge on the surface (or within in a porous material). Polytetrafluor-ethylene (PTFE) is a powerful electret material. The critical difference among the terms is that electrets retain polarization in thermod3mamic wowequilibrium, pyroelectric materials retain polarization in equilibrium, ferroelectrics permit... 

In attempting to use these equations to solve problems, a complete and consistent set of electromechanical boundary conditions are needed. Tiersten [5] provides such a derivation, though solution of anything beyond simple problems requires computation. Fortunately, the mechanical and electrical boundary crmditions are usually separable , = u or M,Ty = niTij and n,D, = iiiD or p = p. The starred terms represent constants, time-varying values, or values defined within another media adjacent to the piezoelectric material. The outward vector normal to the boundary surface is given by... 

Typically, a piezoelectric material s properties are measured through a series of experiments on a set of samples, and these measurements give results easily substituted into the matrix representations of the material. Unfortunately, very few of the components within each of the matrices are defined with the measured data, but the remaining data may be calculated using relations between... 

Choosing a thickness-polarized, thickness-vibrating piezoelectric element as an example, we can define the applied voltage V current i dimensions b, h, and / and the output force and velocity F and u the cross-sectional area bounded by b and I can be defined by A here it is assumed this area is electroded on the top and bottom faces of the element and that b and / are much greater than h. Treating it as a collection of discrete circuit elements as shown in Fig. lb, the Van Dyke circuit allows the analysis of one resonance within the isolated element. Most piezoelectric materials are capacitive insulators, and the shunt capacitance Cs = is the constant capac-... 

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