Piezoelectricity intrinsic

The above conclusions introduce intrinsic limitations to the use of the ID conjugated systems in nonlinear optical devices. Although these may benefit (38) from the high nonlinearities,their response speed will be limited by the motion of such defects. These may also be formed by other means than light and this will clearly have implications on photoelastic, pyroelectric and piezoelectric effects as well. We point out that materials like polydiacetylenes may show appreciable quadrupolar pyroelectric effect (39). 

Non-labelled immunosensors rely on various principles (Fig. 3.27.A). Either the antibody or the antigen is immobilized on the solid matrix to form a sensing device. The solid matrix should be sensitive enough at the surface to detect immunocomplex formation. Electrode, membrane, piezoelectric and optically active surfaces may in principle be used to construct non-labelled immunosensors. The antigen or antibody to be determined is dissolved in a solution and reacted with the complementary matrix-bound antibody or antigen to form an immunocomplex that alters the physical e.g. the electrode potential or intrinsic piezofrequency) or optical properties of the... 

From Eq, (1) it is clear that a model of crystal polarization that is adequate for the description of the piezoelectric and pyroelectric properties of the P-phase of PVDF must include an accurate description of both the dipole moment of the repeat unit and the unit cell volume as functions of temperature and applied mechanical stress or strain. The dipole moment of the repeat unit includes contributions from the intrinsic polarity of chemical bonds (primarily carbon-fluorine) owing to differences in electron affinity, induced dipole moments owing to atomic and electronic polarizability, and attenuation owing to the thermal oscillations of the dipole. Previous modeling efforts have emphasized the importance of one more of these effects electronic polarizability based on continuum dielectric theory" or Lorentz field sums of dipole lattices" static, atomic level modeling of the intrinsic bond polarity" atomic level modeling of bond polarity and electronic and atomic polarizability in the absence of thermal motion. " The unit cell volume is responsive to the effects of temperature and stress and therefore requires a model based on an expression of the free energy of the crystal. 

When an electric field E is applied, Eq changes by an amount proportional to E, as usually expressed by (a — 1) E/4n, where e is the dielectric constant. When a strain is applied to the film, changes in and hence changes in polarization are divided into two components 1. displacement equal to the macroscopic displacement and 2. residual displacement. The latter is the internal strain and causes the intrinsic piezoelectricity. The effect of internal strain on P is expressed by eu, where e is the intrinsic piezoelectric constant and u is the elongational strain along the x-axis. The electric displacement D can therefore be written... 

The above theory reveals that the piezoelectricity of polymer film can be classified into four cases at its origin (A) The intrinsic piezoelectricity due to internal strain in the crystal, (B) the intrinsic piezoelectricity due to strain-dependence of spontaneous polarization, (Q the piezoelectricity originated from the polarization charge qp arising from strain-independent persistent polarization P0, and (D) the piezoelectricity from the true charge gt embedded in the film. It must be emphasized that in cases (Q and (D) heterogeneous strain Au = (u — Sl/T) must exist in the film. 

Intrinsic Piezoelectricity Due to Strain Dependence of Spontaneous Polarization... 

As has been described in 2.3, a polar crystal exhibiting spontaneous polarization Ps shows the intrinsic piezoelectricity due to strain-dependence of Ps (Sawada, 1961). The phenomenological theory of this effect will be described in the following. 

Some polymer crystals have no symmetry center and hence exhibit intrinsic piezoelectricity (Rez, 1962). However, since the polymer film is in general composed of numerous crystallites, the piezoelectricity... 

Polymers which have been found to exhibit intrinsic piezoelectricity for a uniaxially drawn film are, beside polypeptides, polypropylene oxide) (PPO) (Furukawa and Fukada, 1969), cellulose (wood) and its derivatives (Fukada, 1970), board paper and polyethylene terephthalate) (PET) (Wada and others, 1966). These films have an anisotropic piezoelectricity as defined by Eq. (61). 

The relaxational behavior of the intrinsic piezoelectricity of a polymer film arises from two origins. 

It must in any case be noted that the piezoelectricity of polymer films due to charges is not an intrinsic property of polymers it varies from sample to sample and can be remarkably enhanced by drawing and/or poling, as will be described in following sections. 

Group (A) includes materials with intrinsic piezoelectricity and dtA is twice the d-eonstant for elongation along the direction at 45° to the draw-axis. The value depends on the degree of orientation and degree of crystallinity. 

Figure 2.1 Schematic illustrations of intrinsic and extrinsic contributions to the piezoelectric constant of perovskite ferroelectrics. (a) and (b) correspond to the intrinsic unit cell shape (a) without and (b) with applied electric field, (c) and (d) correspond to the extrinsic response associated with the change in position of a non-180° domain wall (shown as a black line) (c) before and (d) after an electric field is applied. Note that both intrinsic and extrinsic responses lead to a change in shape of the material due to application of an electric field (and hence to a piezoelectric response). In both cases, the actual distortions are significantly exaggerated to make visualization easier.

In many ferroelectric materials, the net piezoelectric effect is a result of both intrinsic and extrinsic responses. Here, intrinsic refers to the response that would result from an appropriately oriented single crystal (or ensemble thereof, in a polycrystalline sample). The extrinsic response is typically the result of motion of non-180° domain walls. The principle of these... 

Piezoelectric coefficients are also temperature dependent quantities. This is true for both the intrinsic and the extrinsic contributions. Typically, the piezoelectric response of a ferroelectric material increases as the transition temperature is approached from below (See Figure 2.3) [3], Where appropriate thermodynamic data are available, the increase in intrinsic dijk coefficients can be calculated on the basis of phenomenology, and reflects the higher polarizability of the lattice near the transition temperature. The extrinsic contributions are also temperature dependent because domain wall motion is a thermally activated process. Thus, extrinsic contributions are lost as the temperature approaches OK [4], As a note, while the temperature dependence of the intrinsic piezoelectric response can be calculated on the basis of phenomenology, there is currently no complete model describing the temperature dependence of the extrinsic contribution to the piezoelectric coefficients. 

Two types of contributions to dielectric and piezoelectric properties of ferroelectric ceramics are usually distinguished [6], [9-12], One type is called an intrinsic contribution, and it is due to the distortion of the crystal lattice under an applied electric field or a mechanical stress. The second type is called an extrinsic contribution, and it results from the motion of domain walls or domain switching [8], To provide an understanding of material properties of pzt, several methods to separate the intrinsic and extrinsic contributions were proposed. These methods are indirect, and are based on measurements of the dielectric and piezoelectric properties of ferroelectric ceramics [8], [10-12], In the experiments reported in this paper a different approach is adopted, which is based on measurements of high-resolution synchrotron X-ray powder diffraction. The shift in the positions of the diffraction peaks under applied electric field gives the intrinsic lattice deformation, whereas the domain switching can be calculated from the change in peak intensities [13,14],... 

The scanner controlling the tip position and tip scanning is made from piezoelectric materials. The intrinsic physical and mechanical properties of piezoelectric materials, such as nonlinear piezoelectricity, hysteretic piezoelectricity and creep deformation affect the performance of the scanner. Such properties can generate distortion of SPM imaging during scanning. 

There are mainly two kinds of piezoelectric polymer materials as mentioned before. First, the polymer materials intrinsically have the piezoelectric effect. This kind of polymer materials mainly are PVDF and its copolymer of trifluoroethylene (PVDF-TrFE) (Furukawa, 1989), nylon-11 (Newman et al., 1980), and polyuria (Hattori et al., 1996). However, most polymer-based piezoelectric generators are fabricated from PVDF and its copolymers. The other polymer materials might endow the generator with thermo-resisting properties, while it has not been verified yet. 

Bellaiche L, Vanderbilt D (1999) Intrinsic piezoelectric response in perovskite alloys PMN-PT versus PZT. Phys Rev Lett 83(7) 1347-1350... 

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