Piezoelectric effects

The full tensor form of the piezoelectric constitutive equations can be written by adding the linear elastic (Hook s law) and dielectric responses to Equation (16.1) [1]  

Actually, D and x can also be used as independent variables. By choosing one of the electric variables (E and D) and one of the elastic variables (X and x) as the two independent variables, different piezoelectric constitutive equations can be written to describe the piezoelectric response under different conditions. In addition to Equation (16.2), there are three more sets of piezoelectric constitutive equations. 

Based on the symmetry of a material and Neumann s principle, the number of independent elements for each material property can be reduced [2], For instance, for an unstretched polymer, like poly(vinylidene fluoride) (PVDF) poled along its 3-direction, its structure belongs to the point group oom and its properties are  

It should be noted that the dielectric and elastic properties of a piezoelectric material are strongly dependent on its mechanical and electrical condition. For example  

A few months later, Lippman (1881) predicted the existence of the inverse piezoelectric effect By applying a voltage on the quartz plate, a deformation should be observed. This effect was soon confirmed by the Curie brothers (Curie and Curie, 1882), who designed a clever experiment to measure the tiny displacement, as shown in Fig. 9.2. Here, a light-weight lever with an arm of about 1 100 amplifies the displacement by two orders of magnitude. An optical microscope further amplifies it by two orders of magnitude. The displacement is then measured by an eyepiece with a scale. 

The definitions of the parameters for describing piezoelectric effect are shown in Fig. 9.3. A voltage V is applied on a rectangular piece of piezoelectric material. Inside it, the electrical field intensity is 

The piezoelectric coejficients are defined as the ratios of the strain components over a component of the applied electrical field intensity, for example, 

Because strain is a dimensionless quantity, the piezoelectric coefficients have dimensions of meters/volt in SI units. Their values are extremely small. In the literature, the unit 10 mA is commonly used. For applications in STM, a natural unit is A/V, or 10 m/V. Using primitive means as shown in Fig. 9.2, the Curie brothers (Curie and Curie, 1882) obtained a value of 0.021 

A/V for the parallel piezoelectric coefficient for quartz, which matches accurately the results of modern measurements (Cady 1946). 

The application of an AC voltage to electrodes attached to a piezoelectric material causes it to oscillate. In a QCM, the piezoelectric effect is used to determine small changes in mass as a result of a change in oscillation frequency of the crystal. 

The reason for the prevalence of AT-cut crystals is simply frequency stability around room temperature. Much like a swinging pendulum stores, releases, and even loses energy during a cycle, a quartz crystal stores and loses energy as it oscillates. There is a particular frequency on the spectrum where each crystal will store a maximum amount of energy while losing a minimal amount of energy. This is called the resonant frequency and is determined by 

As can be seen from the equation, a thicker crystal results in a lower resonant frequency. Likewise, when a rigid material is added to the surface of the crystal, effectively increasing its thickness, the frequency will decrease according to the Sauerbrey equation  

The implicit assumption in the Sauerbrey equation is that you have a thin, rigid, uniform film. Since the crystal s intrinsic properties are known, a calibration factor, Cp can be calculated for any crystal frequency and the aforementioned equation can be reduced to 

This equation shows that there is a direct, inverse correlation between a change in frequency and mass. 

As pointed out in the introductory chapter, there are many multifunctional materials that can be applied to realize adaptive structural systems. They are distinguished by means of excitation mechanism, application range, and maturity of development. While research in material science will widen the choice in the future, currently only piezoelectric materials are suitable for the intended purpose. Therefore, the piezoelectric effect and its constitutive description is examined in detail in this chapter. 

Piezoelectricity represents the interdependence between mechanical and electrostatic fields, which is approximately proportional for the majority of applications. The direct piezoelectric effect describes the electrostatic reaction to a mechanical load, while the converse piezoelectric effect describes the mechanical reaction to an electrostatic load. Thorough portrayals of the physical background are given by Cady [41], Ikeda [103], Tichy and Gautschi [174] as well as application oriented presentations by Chopra [53], Janocha [106], Elspass and Flemming [72]. 

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The measurement of mass using a quartz crystal microbalance is based on the piezoelectric effect.When a piezoelectric material, such as a quartz crystal, experiences a mechanical stress, it generates an electrical potential whose magnitude is proportional to the applied stress. Gonversely, when an alternating electrical field is... 

Polymer Ferroelectrics. In 1969, it was found that strong piezoelectric effects could be induced in the polymer poly(vinyhdene fluoride) (known as PVD2 or PVDF) by apphcation of an electric field (103). Pyroelectricity, with pyroelectric figures of merit comparable to crystalline pyroelectric detectors (104,105) of PVF2 films polarized this way, was discovered two year later (106.)... 

Potassium Phosphates. The K2O—P20 —H2O system parallels the sodium system in many respects. In addition to the three simple phosphate salts obtained by successive replacement of the protons of phosphoric acid by potassium ions, the system contains a number of crystalline hydrates and double salts (Table 7). Monopotassium phosphate (MKP), known only as the anhydrous salt, is the least soluble of the potassium orthophosphates. Monopotassium phosphate has been studied extensively owing to its piezoelectric and ferroelectric properties (see Ferroelectrics). At ordinary temperatures, KH2PO4 is so far above its Curie point as to give piezoelectric effects in which the emf is proportional to the distorting force. There is virtually no hysteresis. 

Pyroelectrics. Pyroelectric ceramics are materials that possess a uoique polar axis and are spontaneously polarized ia the abseace of an electric field. Pyroelectrics are also a subset of piezoelectric materials. Ten of the 20 crystal classes of materials that display the piezoelectric effect also possess a unique polar axis, and thus exhibit pyroelectricity. In addition to the iaduced charge resultiag from the direct pyroelectric effect, a change ia temperature also iaduces a surface charge (polarizatioa) from the piezoelectric aature of the material, and the strain resultiag from thermal expansioa. 

The measured relationships between piezoelectric polarization and strain for x-cut quartz and z-cut lithium niobate are found to be well fit by a quadratic relation as shown in Fig. 4.4. In both materials a significant nonlinear piezoelectric effect is indicated. The effect in lithium niobate is particularly notable because the measurements are limited to much smaller strains than those to which quartz can be subjected. The quadratic polynomial fits are used to determine the second- and third-order piezoelectric constants and are summarized in Table 4.1. Elastic constants determined in these investigations were shown in Chap. 2. 

The compressibility of polymers is strongly nonlinear at pressures of a few GPa. In order to consider the nonlinearity of the piezoelectric effect at shock pressure, it is of interest to consider the piezoelectric polarization in terms of the volume compression as shown in Fig. 5.9. The pressure-versus-volume relation for PVDF is not accurately known, but the available data certainly provide a relative measure of changes in compressibility. When considered versus volume, the piezoelectric polarization is found to to be remarkably linear. Thus, large volume compression does not appear to introduce large nonlinearities. Such a behavior will need to be considered when the theory of piezoelectricity for the heterogeneous piezoelectric polymer is developed. 

Piezoelectric energy is a form of electric energy produced by certain solid materials when they are deformed. (The word piezo has its roots in the Greek word piezein meaning to press. ) Discovery of the piezoelectric effect is credited to Pierre and Jacques Curie who observed in 1880 that certain quartz crystals produced electricity when put under pressure. 

Another important hut little-known piezoelectric effect is found in some electronic systems. Speaking produces pressure variations that propagate through the air. Forces are produced on anything in contact with this vibrating air so that when contact is with a piezoelectric crystal, tiny voltage variations are produced. A ci ystal microphone is designed to make use of this piezoelectric effect. 

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. 

Crystals with one of the ten polar point-group symmetries (Ci, C2, Cs, C2V, C4, C4V, C3, C3v, C(, Cgv) are called polar crystals. They display spontaneous polarization and form a family of ferroelectric materials. The main properties of ferroelectric materials include relatively high dielectric permittivity, ferroelectric-paraelectric phase transition that occurs at a certain temperature called the Curie temperature, piezoelectric effect, pyroelectric effect, nonlinear optic property - the ability to multiply frequencies, ferroelectric hysteresis loop, and electrostrictive, electro-optic and other properties [16, 388],... 

In general terms, the pyroelectric coefficient of a free sample consists of three components. The first, called the real coefficient, depends on the derivative of spontaneous polarization with respect to the temperature. The second is derived from the temperature dilatation and can be calculated based on mechanical parameters. The third coefficient is related to the piezoelectric effect and results from the temperature gradient that exists along the polar axis of the ciystal. 

The most characteristic feature of any crystal is its symmetry. It not only serves to describe important aspects of a structure, but is also related to essential properties of a solid. For example, quartz crystals could not exhibit the piezoelectric effect if quartz did not have the appropriate symmetry this effect is the basis for the application of quartz in watches and electronic devices. Knowledge of the crystal symmetry is also of fundamental importance in crystal stmcture analysis. 

Explanation of the piezoelectric effect external pressure causes the deformation of a coordination tetrahedron, resulting in a shift of the centers of gravity of the electric charges... 

These two anciently served as a means of ignition. They still can. Although the sparking of flint and steel is strictly a mechanical phenomenon, any subsequent fires will not be. Other forms of silica still serve as igniters to this day, via the piezoelectric effect. 

The utilization of the piezoelectric effect has been discussed both for photosynthesis11) and phototaxis8). This involves an organelle with quasi-cristalline properties as a transducer similar to the paraflagellar rod described for some euglenoid flagellates115). 

In contrast to high density arrays low density arrays are made by deposition of pre-synthesized oligonucleotides or proteins on activated surfaces. There are several printing techniques for fabricating microarrays Non-contact biochip arrayers, commonly based on the piezoelectric effect, can apply controlled sub-nanoliter probe volumes to pre-specified locations on the chip surface. Due to the fact that the dispenser does not touch the surface, a non-contact arrayer provides low risk of contamination and is most suitable for printing on soft materials such as hydrogels. 

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