Piezoelectric parameters

All acoustic, electric, and piezoelectric parameters can be displayed in a single graph, which is not just a cartoon. The graph, in conjunction with the Kirchhoff laws, predicts the behavior of the resonator. Anyone who can... 

Figure 4.24. The change in the dipole moments and the physical properties of BaTi03 at different temperatures. At the phase transitions between rhombic (Rh), orthorhombic (Or), tetragonal (T), and cubic (C), the dielectric constants (e), the cell constants (c), the heat capacity Cp, and the piezoelectric parameter d change discontinuously.

Table 4.6. Characteristic Piezoelectric Parameters of Some Single Crystals...

Figure 8. Plots of eai/Ps vs, piezoelectric parameter for drawn and annealed films.

In a transducer for use in a hearing aid, a PZT film of thickness h = 5 fim is deposited on a polysilicon substrate of thickness hg = 150 fim. The tetragonal film is prepared with its c—axis coincident with the 2 3—axis of the system coordinate frame, which is perpendicular to the film-substrate interface. The array of piezoelectric parameters for the PZT film material is... 

To summarize the ferroelectric and piezoelectric properties of the discussed polymers, some important ferroelectric and piezoelectric parameters are tabulated in Table 4. As discussed in the previous sections, the ferroelectric and piezoelectric properties of polymeric and polymeric composite systems depend on various factors, such as crystallinity, pohng conditions, glass transition temperature, and before and after electrical poling treatments (electrical, mechanical, and thermal treatments). In addition to the factors mentioned above, for composite systems, laminates or blends, fraction of constituents, and interfacial polarization are also important. Therefore, the... 

Rezvani and Linvill [106] have developed an all-electrical technique for the measurement of piezoelectric parameters of PVDF. A thin polymer film with thin evaporated-metal electnides on each side is held under a slight tension between two rigid supports. The metal electrode on one side is etched away in the middle to form two separate electrodes, one on each end. A voltage applied between one of the electrodes a the electrode on the opposite side develops a stress in the film, which in turn changes Ibe voltage between the second elecliode and the electrode on the oppoaile side. The pie-... 

Today, the term electret is associated first of ail with a thin polyethylene (PE) or polytetrafluoroethylene (FTFE) (119], containing an implanted and highly persistent space charge. Sudb electrets have wide and diversified applications (118,119] however, tteir piezoelectric parameters are low. With regard to piezoelectric properties of electrets, different polymer-ferroelectric ceramic materiab have been made (4,12,16]. 

This chapter discusses materials known as electroactive composites. These are mixtures of an electroactive (or in the present context, ferroelectric) ceramic phase and a polymer phase. Early sections will look at the individual phases, making use of piezoelectric parameters defined in Chapter 5. A summary of theoretical models will then be given, before preparation and characterization are discussed. Finally, the problems associated with producing an active device and examples of working systems will be considered. 

Some electrical properties are shown in Table 3. Values of other parameters have been pubflshed (146). Polymorphism of the PVDF chains and the orientation of the two distinct dipole groups, —CF2— and —CH2—, rather than trapped space charges (147) contribute to the exceptional dielectric properties and the extraordinarily large piezoelectric and pyroelectric activity of the polymer (146,148,149). 

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 principle of operation of a quartz balance can be easily described if an AC potential is placed across a quartz piezoelectric crystal, the crystal will oscillate spatially and the amplitude of this oscillation is greatest at the resonance frequency of the crystal. This resonance frequency, /0, is a function of several parameters, including the mass of the crystal, and the mass of foreign material placed on the crystal. In fact, the change in the resonance frequency, A/0, on placing some foreign material on it is given approximately... 

The nonlinear optical and dielectric properties of polymers find increasing use in devices, such as cladding and coatings for optical fibres, piezoelectric and optical fibre sensors, frequency doublers, and thin films for integrated optics applications. It is therefore important to understand the dielectric, optical and mechanical response of polymeric materials to optimize their usage. The parameters that are important to evaluate these properties of polymers are their dipole moment polarizability a, hyperpolarizabilities 0... 

Sonication using ultrasonic cleaner baths remains a popular extraction approach particularly for controlled-release products. In sonication, an ultrasonic wave of 20-40 kHz generated by a piezoelectric transducer is used to produce the formation and collapse of thousands of microscopic bubbles (cavitations) in the water bath to facilitate the break up of the solid particles and the subsequent dissolution of the API. Note that parameters such as the wattage power of the sonicator, presence of the perforated tray, depth of the water level, bath temperature and the number of sample flasks sonicated might all affect the extraction rate. For... 

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... 

In addition to the parameters discussed in the previous section, that is, the piezoelectric coefficients dsi, d3i, and the velocity of sound, c, there are several other parameters that are important for applications in STM. 

For small and slow signals, in STM, the piezoelectric coefficients are the only relevant parameters. At relatively high frequencies, the dynamic response of the piezoelectric materials becomes important. The lowest resonance frequencies of the piezodrive are the limiting factor for the scanning speed. 

The total mass of particles per unit volume of air is one of the major parameters used to characterize particles in air and, along with size, is the basis of air quality standards for particulate matter (see Chapter 2). Methods of mass measurement include gravimetric methods, /3-ray attenuation, piezoelectric devices, and the oscillating microbalance. 

Piezoelectric microbalance The piezoelectric microbalance is a resonant frequency device. The piezoelectric effect is the development of a charge on some crystals such as quartz when a stress is applied the stress may be mechanical (e.g., added weight) or electrical. Such crystals may be used as part of a resonance circuit to provide very stable, narrow-band frequencies the quartz crystal is plated on two sides with a thin conducting layer and leads are connected to the resonance circuit so the crystal replaces an LC network. The obtained frequency of vibration (pu) depends on a number of parameters of the crystal but is usually 5-10 MHz. However, if a mass (Am) becomes attached to one side of the crystal, it changes the resonant frequency by an amount At , such that... 

Order parameters may also refer to underlying atomic structure or symmetry. For example, a piezoelectric material cannot have a symmetry that includes an inversion center. To model piezoelectric phase transitions, an order parameter, r], could be associated with the displacement of an atom in a fixed direction away from a crystalline inversion center. Below the transition temperature Tc, the molar Gibbs free energy of a crystal can be modeled as a Landau expansion in even powers of r (because negative and positive displacements, 77, must have the same contribution to molar energy) with coefficients that are functions of fixed temperature and pressure,... 

Naturally, the fixed composition phase transformations treated in this section can be accompanied by local fluctuations in the composition field. Because of the similarity of Fig. 17.3 to a binary eutectic phase diagram, it is apparent that composition plays a similar role to other order parameters, such as molar volume. Before treating the composition order parameter explicitly for a binary alloy, a preliminary distinction between types of order parameters can be obtained. Order parameters such as composition and molar volume are derived from extensive variables any kinetic equations that apply for them must account for any conservation principles that apply to the extensive variable. Order parameters such as the atomic displacement 77 in a piezoelectric transition, or spin in a magnetic transition, are not subject to any conservation principles. Fundamental differences between conserved and nonconserved order parameters are treated in Sections 17.2 and 18.3. 

The present chapter critically encompasses developments and achievements reached in MIP-based selective sensing combined with optical, piezoelectric (PZ) and electrochemical signal transduction. General procedures of MIP preparation along with methods of MIP immobilization for chemosensor fabrication are presented. Protocols of analyte determination involving measurement complexities, like template presence or absence, have been addressed in detail. Moreover, analytical parameters, such as detectability, sensitivity, selectivity, linear dynamic... 

Functional fibres, filaments and yams are the basic building blocks of electrotextiles. The textile industry has demonstrated a remarkable capability to incorporate both natural and man-made filaments into yarns and fabrics to satisfy a wide range of physical parameters which survive the manufacturing process and are tailored to specific application environments. Electronic components can be fabricated within and/or on the surface of filaments and can subsequently be processed into functional yams and woven into fabrics. Passive components such as resistors, capacitors and inductors can be fabricated in several different manners. Diodes and transistors can be made on long, thin, flat strands of silicon or formed in a coaxial way. Progress has been made in the development of fibre batteries and fibre-based solar cells. In addition, a variety of actuated materials (piezoelectric, etc.) can be made into multiple long strands (filaments) and subsequently be woven into fabric. 

When the experimentalist set an ambitious objective to evaluate micromechanical properties quantitatively, he will predictably encounter a few fundamental problems. At first, the continuum description which is usually used in contact mechanics might be not applicable for contact areas as small as 1 -10 nm [116,117]. Secondly, since most of the polymers demonstrate a combination of elastic and viscous behaviour, an appropriate model is required to derive the contact area and the stress field upon indentation a viscoelastic and adhesive sample [116,120]. In this case, the duration of the contact and the scanning rate are not unimportant parameters. Moreover, bending of the cantilever results in a complicated motion of the tip including compression, shear and friction effects [131,132]. Third, plastic or inelastic deformation has to be taken into account in data interpretation. Concerning experimental conditions, the most important is to perform a set of calibrations procedures which includes the (x,y,z) calibration of the piezoelectric transducers, the determination of the spring constants of the cantilever, and the evaluation of the tip shape. The experimentalist has to eliminate surface contamination s and be certain about the chemical composition of the tip and the sample. 

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