Piezoelectric mechanisms

A piezoelectric crystal develops surface charges as a result of bulk polarisation due to the formation of internal dipoles or to the rearrangement of existing dipoles. To give an idea of how polarisation can be produced on the application of pressure, two examples are described below. 

When this idea is applied to a crystal, the results for all the tetrahedra need to be added together. If 

The piezoelectric effect can also be generated in a crystal already containing dipoles. In some materi- 

In the case of crystals showing spontaneous polarisation, the elementary dipoles are already 

The requirement that the piezoelectric effect is restricted to noncentrosymmetric crystals implies that piezoelectricity should not be observed in a polycrystalline solid. This is because the individual grains will polarise in random directions that will cancel overall. It is possible to get around this problem in some piezoelectric materials, as described in Section 11.3.8. 

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Kar, S., McWhorter, S., Ford, S.M., Soper, S.A., Piezoelectric mechanical pump with nanoliter per minute pulse-free flow delivery for pressure pumping in microchannels. Analyst 1998, 123, 1435-1441. 

Structural Requirements for Piezoelectric Polymers. The piezoelectric mechanisms for semicrystalline and amorphous polymers differ. Although the differences are distinct, particularly with respect to polarization stability, in the simplest terms, four critical elements exist for all piezoelectric polymers, regardless of morphology. These essential elements are (.1) the presence of permanent molecular dipoles, (2) the ability to orient or align the molecular dipoles, (5) the ability to sustain this dipole alignment once it is achieved, and (4) the ability of the material to undergo large strains when mechanically stressed (3). 

Araki, N., (2004). "Crystallographic Study for the piezoelectric mechanism of langasite under high pressure, electric field high low temperature." Master-Diesis of Nagoya Institute ofTechnoIogy. 

Ink-jet has shown a great potential in the last years as one of the most versatile and attractive deposition techniques for patterning polymers and inorganic particles. It has become the most used technique for many industrial and scientific applications, like chemical and gas sensors among others (Chang et al. 2004, 2005 de Cans et al. 2004 Pierik et al. 2008 Barry et al. 2009 Chang et al. 2010 Fujie et al. 2012). The method is the same as ink-jet-type printers on paper, as it delivers the exact amount of the materials on demand in a form of droplets of fiuids on the desired surfaces. Nowadays ink-jet-type polymer printers can deliver between 2,000 up to 13,000 in. droplets in a second. They use capillary nozzles, which can be controlled by piezoelectric mechanisms. 

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 ... 

Fokker Bond Tester. An ultrasonic inspection technique commonly used for aircraft structures is based on ultrasonic spectroscopy [2]. Commercially available instruments (bond testers) used for this test operate on the principle of mechanical resonance in a multi-layer structure. A piezoelectric probe shown in Figure 3b, excited by a variable frequency sine signal is placed on the surface of the inspected structure. A frequency spectrum in the range of some tens of kHz to several MHz is acquired by the instrument, see Figure 3a. 

A standard probe (type MWB or SWB) is fixed to the probe holder and is mechanically connected to a further piezoelectric receiver. A noise generator, which is coupled to any point of the test object, provides a low frequency noise signal which is picked up by the piezoelectric receiver. The intensity of the signal allows the evaluation of the coupling quality. 

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... 

Fig. 3. An overview of atomistic mechanisms involved in electroceramic components and the corresponding uses (a) ferroelectric domains capacitors and piezoelectrics, PTC thermistors (b) electronic conduction NTC thermistor (c) insulators and substrates (d) surface conduction humidity sensors (e) ferrimagnetic domains ferrite hard and soft magnets, magnetic tape (f) metal—semiconductor transition critical temperature NTC thermistor (g) ionic conduction gas sensors and batteries and (h) grain boundary phenomena varistors, boundary layer capacitors, PTC thermistors.

Ferroelectric Ceramic—Polymer Composites. The motivation for the development of composite ferroelectric materials arose from the need for a combination of desirable properties that often caimot be obtained in single-phase materials. For example, in an electromechanical transducer, the piezoelectric sensitivity might be maximized and the density minimized to obtain a good acoustic matching with water, and the transducer made mechanically flexible to conform to a curved surface (see COMPOSITE MATERIALS, CERAMiC-MATRix). 

Relaxations of a-PVDF have been investigated by various methods including dielectric, dynamic mechanical, nmr, dilatometric, and piezoelectric and reviewed (3). Significant relaxation ranges are seen in the loss-modulus curve of the dynamic mechanical spectmm for a-PVDF at about 100°C (a ), 50°C (a ), —38° C (P), and —70° C (y). PVDF relaxation temperatures are rather complex because the behavior of PVDF varies with thermal or mechanical history and with the testing methodology (131). 

The piezoelectric phenomena have been used to generate ultrasonic waves up to microwave frequencies using thin polyfvinylidene fluoride) transducers. In the audio range a new type of loudspeaker has been introduced using the transverse piezolectric effect on a mechanically biased membrane. This development has been of considerable interest to telephone engineers and scientists. 

Depth-sensing nanoindentation is one of the primary tools for nanomechanical mechanical properties measurements. Major advantages to this technique over AFM include (1) simultaneous measurement of force and displacement (2) perpendicular tip-sample approach and (3) well-modeled mechanics for dynamic measurements. Also, the ability to quantitatively infer contact area during force-displacement measurements provides a very useful approach to explore adhesion mechanics and models. Disadvantages relative to AFM include lower force resolution, as well as far lower spatial resolution, both from the larger tip radii employed and a lack of sample positioning and imaging capabilities provided by piezoelectric scanners. 

Perhaps the most dramatic exception to the perfectly elastic, perfectly plastic materials response is encountered in several brittle, refractory materials that show behaviors indicative of an isotropic compression state above their Hugoniot elastic limits. Upon yielding, these materials exhibit a loss of shear strength. Such behavior was first observed from piezoelectric response measurements of quartz by Neilson and Benedick [62N01]. The electrical response observations were later confirmed in mechanical response measurements of Waekerle [62W01] and Fowles [61F01]. 

For mechanical wave measurements, notice should be taken of the advances in technology. It is particularly notable that the major advances in materials description have not resulted so much from improved resolution in measurement of displacement and/or time, but in direct measurements of the derivative functions of acceleration, stress rate, and density rate as called for in the theory of structured wave propagation. Future developments, such as can be anticipated with piezoelectric polymers, in which direct measurements are made of rate-of-change of stress or particle velocity should lead to the observation of recognized mechanical effects in more detail, and perhaps the identification of new mechanical phenomena. 

The uncoupled response of a piezoelectric sample to elastic shock compression is determined on the assumption that the mechanical response of the material is independent of any electric fields that may be present. In this approximation, a steady shock is introduced into material at rest while the... 

Uncoupled solutions for current and electric field give simple and explicit descriptions of the response of piezoelectric solids to shock compression, but the neglect of the influence of the electric field on mechanical behavior (i.e., the electromechanical coupling effects) is a troublesome inconsistency. A first step toward an improved solution is a weak-coupling approximation in which it is recognized that the effects of coupling may be relatively small in certain materials and it is assumed that electromechanical effects can be treated as a perturbation on the uncoupled solution. 

A unique electrical-to-mechanical coupling effect called piezoelectric rate coupling has been predicted to occur in the neighborhood of a shock in... 

Changes in polarization may be caused by either the input stress profile or a relaxation of stress in the piezoelectric material. The mechanical relaxation is obviously inelastic but the present model should serve as an approximation to the inelastic behavior. Internal conduction is not treated in the theory nevertheless, if electrical relaxations in current due to conduction are not large, an approximate solution is obtained. The analysis is particularly useful for determining the signs and magnitudes of the electric fields so that threshold conditions for conduction can be established. 

The piezoelectric response investigation also provides direct evidence that significant inelastic deformation and defect generation can occur well within the elastic range as determined by the Hugoniot elastic limit. In quartz, the Hugoniot elastic limit is 6 GPa, but there is clear evidence for strong nonideal mechanical and electrical effects between 2.5 and 6 GPa. The unusual dielectric breakdown phenomenon that occurs at 800 MPa under certain... 

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