Polarization piezoelectric

Fig. 10.3. Piezoelectric ceramic with groups of oriented dipoles (a group is indicated with one arrow) (a) Prior to orientation in an electric field, the dipoles point in random directions (b) while a strong electric field is applied the dipoles align (c) a polarized piezoelectric ceramic ready to use.

Most piezoelectric materials tend to be quite capacitive. The pyroelectric nature of all polarized piezoelectric materials can cause the development of significant charging across the material due to thermal expansion coupled to the direct piezoelectric effect causing a charge displacement from the thermal strain voltages of 1 kV are not unheard of in PZT after a temperature change of 50 °C, and caution is warranted in any application. However, a piezoelectric material... 

Among different (like flexoelectric, flexomagnetic etc.) flexoeffects, the influence of flexoelectric effect on the nanosystem properties had been studied in most details. One can conclude that even rather moderate flexoelectric effect significantly renormalizes all the polar, piezoelectric and dielectric properties and the correlation radius in particular. The effect also suppresses the size-induced phase transition from ferroelectric to paraelectric phase and thus stabilizes the ordered phase in ferroic nanoparticles. 

Fig. 13.1 Examples of nrai-polar, piezoelectric and pyroelectric crystals calcite (a), ZnS (b) and tourmalme (c). An arrow shows the direction of the polar axis in tourmaline...

Fukada, E. (2006) Recent Developments of Polar Piezoelectric Polymers , IEEE Transactions on Dielectrics and Electrical Insulation, 13, 1110-9. 

Fukada E (2006) Reeent developments of polar piezoelectric polymers. IEEE Trans Dielectr Electr Insul 13 1110-1119... 

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.)... 

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. 

Ferroelectrics. Ferroelectrics, materials that display a spontaneous polarization ia the abseace of an appHed electric field, also display pyroelectric and piezoelectric behavior. The distinguishing characteristic of ferroelectrics, however, is that the spontaneous polarization must be re-orientable with the appHcation of an electric field of a magnitude lower than the dielectric breakdown strength of the material. 

In the broad range of ceramic materials that are used for electrical and electronic apphcations, each category of material exhibits unique property characteristics which directiy reflect composition, processing, and microstmcture. Detailed treatment is given primarily to those property characteristics relating to insulation behavior and electrical conduction processes. Further details concerning the more specialized electrical behavior in ceramic materials, eg, polarization, dielectric, ferroelectric, piezoelectric, electrooptic, and magnetic phenomena, are covered in References 1—9. 

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. 

Shock compression of piezoelectric solids, even under short-circuit conditions, causes large electric fields of varying amplitude and polarity within the material. In the uncoupled approximation to the solution of the short-circuit... 

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. 

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. 

Fig. 4.6. Piezoelectric pulse diagrams can be used to obtain explicit representations of the time dependent electric fields in piezoelectric substances. The magnitudes and orientations of these electric fields are critical to development of shock-induced conduction. As an example, the diagram on the left shows the polarization and displacement relations for a location at the input electrode. The same functions for a location within the crystal is shown on the right (after Davison and Graham [79D01]).

The effect of shock-induced conduction is less distinct in ferroelectrics than in piezoelectrics but is nevertheless apparent from a number of studies. (See Davison and Graham [79D01] and Novitskii [79N03].) Differences in conduction with sample polarity, such as those seen in quartz but of opposite sign, are observed in ferroelectrics. 

The piezoelectric constant studies are perhaps the most unique of the shock studies in the elastic range. The various investigations on quartz and lithium niobate represent perhaps the most detailed investigation ever conducted on shock-compressed matter. The direct measurement of the piezoelectric polarization at large strain has resulted in perhaps the most precise determinations of the linear constants for quartz and lithium niobate by any technique. The direct nature of the shock measurements is in sharp contrast to the ultrasonic studies in which the piezoelectric constants are determined indirectly as changes in wavespeed for various electrical boundary conditions. 

In this chapter piezoelectric crystals and polymers ferroelectric and ferromagnetic solids resistance of metals shock-induced electrical polarization electrochemistry elastic-plastic physical properties. 

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