Hydrostatic coefficient, piezoelectric

Singular polar direction (i.e. in pyroelectric materials) in the crystal is accompanied by the existence of special kind of piezoelectric effects. Such crystals could be piezoelectrically polarized by the application of hydrostatic pressure. Hydrostatic 

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The development of active ceramic-polymer composites was undertaken for underwater hydrophones having hydrostatic piezoelectric coefficients larger than those of the commonly used lead zirconate titanate (PZT) ceramics (60—70). It has been demonstrated that certain composite hydrophone materials are two to three orders of magnitude more sensitive than PZT ceramics while satisfying such other requirements as pressure dependency of sensitivity. The idea of composite ferroelectrics has been extended to other appHcations such as ultrasonic transducers for acoustic imaging, thermistors having both negative and positive temperature coefficients of resistance, and active sound absorbers. 

Generally, there are three different hydrostatic piezoelectric coefficients dh (equal to the sum in brackets in Eq. (5.25)). Hydrostatic coefficients could be easily calculated from the matrix of piezoelectric coefficients. In Tourmaline (symmetry class 3m) only one hydrostatic piezoelectric coefficient exhibit non-zero value... 

Lead titanate exhibits only one stmctural phase transition from paraelectric cubic mhm to ferroelectric tetragonal 4mm phase. Curie temperature is relatively high 490° C. Lead titanate has the biggest anisotropy in the tetragonal lattice parameter ratio c/a = 1.06 among all perovskite crystals. Due to the anisotropy it exhibits relatively high hydrostatic piezoelectric coefficient dh (higher than PZT ceramics). 

Another possibly applicable crystal is Lithium sulfate (Li2S04.H20). It could be used below 90° C for its relatively high piezoelectric coefficients (especially for hydrostatic coefficient dh = 16.4 x 10 CN ) as a hydrostatic pressure sensor. Especially high hydrostatic piezoelectric coefficient (1000-2000 x 10 CN ) exhibits also the semiconductive ferroelectric crystal SbSI (see Fig. 7.18). Its hydrostatic piezoelectric coefficient is extremely high, but strongly temperature dependent especially at room temperature 22° C. 

Fig. 7.27 ElFeetive hydrostatic piezoelectric coefficients for 1-3 composite. Piezoelectric phase is PZT5 [Table I. in Smith (1993)] with...

The best today s composite structure with 2-2-0 (air cavity) connectivity - Moonie - uses flextensional principle (Dogan et al. 1997 Fernandez et al. 1998 Xu et al. 1991 Zhang et al. 1999). Composite is made from the ceramic disc (PZT ceramics) and from two metallic plates (e.g. brass) with small air cavities (Fig. 7.29) glued together. By means of the metallic caps the hydrostatic pressure on major transducer surface is transferred to the longitudinal tension of the ceramic disc. This stress transfer will improve significantly the effective hydrostatic piezoelectric coefficient of the structure due to the different signs of ( 33 and d-n coefficients in PZT ceramics. The effective hydrostatic coefficient d could be further tuned in the value by the... 

Another example of the piezoelectric composite stmctures either with 3-0 or 3-1 connectivity is the miniature piezoelectric hollow sphere transducer (Alkoy et al. 1997 Fernandez et al. 1996 Meyer et al. 1994). Technique allowing for the manufacturing of the extremely small thin-walled bubbles (1-6 mm in diameter and 80 xm wall thickness) from PZT slurry has been developed. Such bubbles could be electroded and poled either radially (3-0 coimectivity) or cylindrically (3-1 connectivity) if the hole is drilled through the bubble (Fig. 7.30). Composite stracture vibrates in radial (breathing) or in thickness mode. Effective hydrostatic piezoelectric coefficient as well as significantly enhanced with... 

The coupling between mechanical and dielectric properties is also evident in the hydrostatic piezoelectric coefficient, dh which is given by (55) ... 

When piezoelectrics are used in hydrostatic pressure conditions, such as hydrophone applications, the hydrostatic piezoelectric coefficient determines performance. The hydrostatic coefficients take into account the transverse piezoelectric effect from directions orthogonal to the poling axis. They are the hydrostatic strain coefficient... 

It b very difficult to measure the direct piezoelectric coefficient d without constraining the sample dimensions, thus introducing errors. A commonly used technique to determine d b first to measure the hydrostatic piezoelectric coefficient, d. as well as d) and then to calculate dn using the relation... 

In this chapter, composite materials most frequently used in electromechanical uansducer and the ways of their production are presented. When choosing composite materials that will be optimal for some applications, so-called figures of merit ate taken into consideration, which consider the most sensitive parameters characterizing the use of properties and enable one in a simple way to choose the materials to be included in the composite. One useful figure of merit for the electromechanical transducer is the product of the hydrostatic piezoelectric coefficient and the voltage hydrostatic piezoelectric coefficient gi where c is the electric permittivity of... 

Perforated PZT-polymer composites have been fabricated [4] by drilling holes in sintered PZT blocks and filling with epoxy. In some cases the perforation was left empty but capped with alumina plates and the whole structure encapsulated in epoxy these are referred to as perforated 3-2-0 or 3-1-0 composites. The maximum hydrostatic piezoelectric coefficients attained for these composites are generally significantly greater than those associated with solid PZT, and values of have been reported that are greater than 200 times the figure of merit for solid PZT. 

The electrical response of a piezoelectric material is a function of the electrode configuration relative to the direction of the applied mechanical stress. For a coefficient dy, the first subscript is the direction of the electric field or charge displacement, and the second subscript gives the direction of the mechanical deformation or stress. The C2v crystallographic symmetry typical of S5mthetic oriented, poled polymer film leads to cancellation of all but five of the dtj components W31, ds2, ds3, di5, and 24)- If the film is poled and biaxially oriented or unoriented, dsi = ds2 and di5 = 24. Most natural biopolymers possess Pco symmetry which yields a matrix that possesses only the shear piezoelectricity components dis and 25. Because the dss constant is difficult to measure without constraining the lateral dimension of the sample, it is typically determined from equation 7 which relates the constants to the hydrostatic piezoelectric constant, dsh. 

Bur et aL [17] observed similar behaviors in the pyroelectric and hydrostatic piezoelectric coeffidents in measurements made on the same material undergoing the same beat treatments. The decreases in the remanent polarization and in the pyroelectric and piezoelectric coefficients were attributed to a bro range of Curie temperatures resulting from a broad range of crystallite size. It was shown that the crystallinity at room tem-... 

Such polymers as PVDF, in particular, have wide applications [3] sometimes its properties are advantageous for some reasons, e.g., low electric permittivity and small thickness, but limit ite application in other devices. When, for example, hydrophones, which are electroacoustic transducers used in a water environment, b use of the low transducer capacity made of PVDF, amplifiers should be placed very near. Moreover, vduge sensitivity in the open system given in dB in the relation 1/piPa determined by a product giz, (where g indicates hydrostatic piezoelectric voltage coefficient and Xj is transducer thickness), is low for transducers m of PVDF films. 

Composites which will be applied in hydrophones should possess, besides low acoustic impedance, high hydrostatic values of piezoelectric coefficients dt and since the figure of merit is a product. 

The coefficients di and 24 associated with shear deformation are seldom used as there are a lack of practical applications using the shear mode. The most important piezoelectric coefficients for determining a material s suitability for a particular device are the d j and g j components and the hydrostatic coefficients dh and The coefficient is a measure of the charge generated owing to the application of a hydrostatic pressure. As the stresses are uniform in all three directions, d is simply... 

The application of PVDF as a transducer material is also subject to certain limitations, however. The low value of 33 (20pCN ) inhibits its use as an active device. Its large negative value of 31 (—4.5 pC N ) lowers the hydrostatic strain coefficient, d, and, finally, the material s low Curie temperature makes for a strong temperature dependence of the piezoelectric coefficients and problems with depoling at higher temperatures. 

In bulk material, the resistivity is independent of crystal orientation because silicon is cubic. However, if the carriers are constrained to travel in a very thin sheet, eg, in an inversion layer, the mobility, and thus the resistivity, become anisotropic (18). Mobility is also sensitive to both hydrostatic pressure and uniaxial tension and compression, which gives rise to a substantial piezoresistive effect. Because of crystal symmetry, however, there is no piezoelectric effect. The resistivity gradually decreases as hydrostatic pressure is increased, and then abrupdy drops several orders of magnitude at ca 11 GPa (160,000 psi), where a phase transformation occurs and silicon becomes a metal (35). The longitudinal piezoresistive coefficient varies with the direction of stress, the impurity concentration, and the temperature. At about 25°C, given stress in a (100) direction and resistivities of a few hundredths of an O-cm, the coefficient values are 500—600 m2/N (50—60 cm2/dyn). 

Because of the very large differences in mechanical compliance between the two phases, the hydrostatic pressures experienced by the polymer phase transfer forces to the rods magnifying the stress in them in the poled direction. This magnified stress increases the charge induced on to the electrode tending to compensate for the inactive polymer. As a result, in typical practical cases, the piezoelectric charge coefficient fi/13) is not very sensitive to volume fraction of PZT . 

A molecular theory of the direct piezoelectric effect in poled amorphous piezoelectric polymers has been developed. An expression for the hydrostatic coefficient appears in the original paper (41). Later, this theory was extended, and an equation for dsi was obtained (44,45). By differentiating equation 14 and modifying it to account for dimensional effects such as stretching (44,46),... 

Because both coefficients J33 and J31 for PZT ceramics exhibit different signs, the uniaxially reinforced and TP 2-2 composites could reach the highest effective hydrostatic coefficient values. It is interesting, that the effective FOM in Eq. (7.37) does not depend on the aspect ratio (i.e. on the ratio of the composite s thickness T vs. the piezoelectric plate thickness t) but the value of (Eq. (7.38)) does (Fig. 7.28). 

In general, there are two characteristics to be considered when conducting an initial assessment of a material s suitability for a device first the appropriate piezoelectric or pyroelectric coefficients to determine the degree of sensitivity and optimum mode of operation (e.g. thickness or hydrostatic) and secondly, the effect of temperature on these properties, thus defining the maximum and minimum operating temperatures at which the material can be used efficiently. 

In hydrostatic mode the piezoelectric strain coefficient is deter-... 

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