Piezoelectricity and Pyroelectricity

For quartz aystals cut in the most common direction (the so-caUed AT cut) and processed in the most advantageous oscillation direction, the Sauerbrey Eq. (2.9) is valid. It describes the relationship between the firequency/ and the mass m of a thin film at the crystal surface  

Equation (2.6) demonstrates that a relatively low mass change Am can bring about very high values of mass change A/. For Af given in Hz,/o in MHz, Am in grams, and A in cm, the Sauerbrey equation acquires the following form  

A mass change of lOng/cm would bring about a frequency change of 2.3Hz with a crystal oscillating at the base frequency/o = 10 MHz. Such frequency deviations can be measured precisely without too much effort. 

The pyroelectric effect is similar to the piezoelectric effect. Mechanical deformations generate electric voltages. Such deformations are caused by temperature changes with pyroelectric materials. 

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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). 

Dielectric, piezoelectric and pyroelectric properties of LiTa03 derived ceramics containing additives of LiF and MgF2 were investigated and reported on in [407]. The materials were prepared at 900°C by means of two methods Reaction sintering, yielding powdered polycrystalline material ... 

These materials are piezoelectric and pyroelectric ferroelectricity has not been clearly proven [443]. 

The compounds K5Nb3OFi8 and Rb5Nb3OFi8 display promising properties for their application in electronics and optics. The compounds can be used as piezoelectric and pyroelectric elements due to sufficient piezo- and pyroelectric coefficients coupled with very low dielectric permittivity. In addition, the materials can successfully be applied in optic and optoelectronic systems due to their wide transparency range. High transparency in the ultraviolet region enables use of the materials as multipliers of laser radiation frequencies up to the second, and even fourth optical harmonic generation. 

Ferroelectric materials are capable of being polarized in the presence of an electric field. They may exhibit considerable anomalies in one or more of their physical properties, including piezoelectric and pyroelectric coefficients, dielectric constant, and optoelectronic constant. In the latter case, the transmission of light through the material is affected by the electric field, which produces changes in refractive index and optical absorption coefficient. Varying the applied field changes the phase modulation. 

PVDF is mainly obtained by radical polymerisation of 1,1-difluoroethylene head to tail is the preferred mode of linking between the monomer units, but according to the polymerisation conditions, head to head or tail to tail links may appear. The inversion percentage, which depends upon the polymerisation temperature (3.5% at 20°C, around 6% at 140°C), can be quantified by F or C NMR spectroscopy [30] or FTIR spectroscopy [31], and affects the crystallinity of the polymer and its physical properties. The latter have been extensively summarised by Lovinger [30]. Upon recrystallisation from the melted state, PVDF features a spherulitic structure with a crystalline phase representing 50% of the whole material [32]. Four different crystalline phases (a, jS, y, S) may be identified, but the a phase is the most common as it is the most stable from a thermodynamic point of view. Its helical structure is composed of two antiparallel chains. The other phases may be obtained, as shown by the conversion diagram (Fig. 7), by applying a mechanical or thermal stress or an electrical polarisation. The / phase owns ferroelectric, piezoelectric and pyroelectric properties. 

Various crystalline materials with desired properties have been synthesized, and this has driven the utilization of single crystals in the production of semiconductor, opto-electronic, piezoelectric, and pyroelectric materials. 

A wide array of ferroelectric, piezoelectric and pyroelectric materials have titanium, zirconium and zinc metal cations as part of their elemental composition Many electrical materials based on titanium oxide (titanates) and zirconium oxide (zirconates) are known to have structures based on perovskite-type oxide lattices Barium titanate, BaTiOs and a diverse compositional range of PZT materials (lead zirconate titanates, Pb Zr Tij-yOs) and PLZT materials (lead lanthanum zirconate titanates, PbxLai-xZryTii-yOs) are among these perovskite-type electrical materials. 

The unique piezoelectric and pyroelectric properties of semicrystalline films of PVDF arise from changes in the polarization imparted to the overall film by the crystalline P-phase. The polar nature of the P-phase is, in turn, a direct result of the parallel alignment of the dipole moment of the repeat units in the unit cell (Figure 11.1). The crystal polarization is defined as the dipole moment density of the crystal ... 

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. 

The high-frequency dielectric constant is determined by the effects of electronic polarization. An accurate estimate of this property lends confidence to the modeling of the electronic polarization contribution in the piezoelectric and pyroelectric responses. The constant strain dielectric constants (k, dimensionless) are computed from the normal modes of the crystal (see Table 11.1). Comparison of the zero- and high-frequency dielectric constants indicates that electronic polarization accounts for 94% of the total dielectric response. Our calculated value for k (experimental value of 1.85 estimated from the index of refraction of the P-phase of PVDF. ... 

The material properties appearing in Eqs. (6)-(9) are defined by the partial derivatives of the dependent variables (P, c, e) with respect to the independent variables. At this point, to maintain consistency with the literature on the P-phase of PVDF, we label c as the 1 axis, a as the 2 axis, and, b as the 3 axis. In evaluating the piezoelectric and pyroelectric responses we consider changes in polarization along the 3 axis only polarization along the 1 and 2 axes remains zero, by symmetry, for all the cases considered here. The direct piezoelectric strain 03 , pC/N) and stress (gaj, C/iiE) coefficients are defined in Eqs. (10) and (11),... 

When the film is short-circuited and heated to high temperatures at which the molecules attain a sufficiently high mobility, a current is observed in the external circuit. This phenomenon is called pyroelectric effect, thermally stimulated current, or, when the film has been polarized by a static field prior to measurement, depolarization current. The conventional definition of pyroelectricity is the temperature dependence of spontaneous polarization Ps, and the pyroelectric constant is defined as dPJdd (6 = temperature). In this review, however, the term will be used in a broader definition than usual. The pyroelectric current results from the motion of true charge and/or polarization charge in the film. Since the piezoelectricity of a polymer film is in some cases caused by these charges, the relation between piezoelectricity and pyroelectricity is an important clue to the origin of piezoelectricity. 

A close correlation between the polarities of piezoelectricity and pyroelectricity was found for PVC and poly (vinylidene fluoride) (PVDF) films (Nakamura and Wada, 1971). However, it must be emphasized that the polarity of piezoelectricity is determined not only by the polarity of the charge distribution but also by that of heterogeneous strain. The origin of heterogeneous strain in the elongation of film may derive from heterogeneity in the structure of the film. 

Murayama.N. Piezoelectric and pyroelectric effects of polymer electrets. Microsymposium on Electrical Properties of Polymers, Tokyo (Jan. 1972). 

Commercial products based on copolymers of ethylene and TEE are made by free radical-initiated addition copolymerization.69 Small amounts (1 to 10 mol%) of modifying comonomers are added to eliminate a rapid embrittlement of the product at exposure to elevated temperatures. Examples of the modifying comonomers are perfluorobutyl ethylene, hexafluoropropylene, perfluorovinyl ether, and hexafluoro-isobutylene.70 ETFE copolymers are basically alternating copolymers,70 and in the molecular formula, they are isomeric with polyvinylidene fluoride (PVDF) with a head-to-head, tail-to-tail structure. However, in many important physical properties, the modified ETFE copolymers are superior to PVDF with the exception of the latter s remarkable piezoelectric and pyroelectric characteristics. 

The unique dielectric properties and polymorphism of PVDF are the source of its high piezoelectric and pyroelectric activity.75 The relationship between ferroelectric behavior, which includes piezoelectric and pyroelectric phenomena and other electrical properties of the polymorphs of polyvinylidene fluoride, is discussed in Reference 76. 

When this polymer is processed in a particular way, it becomes piezoelectric and pyroelectric. A piezoelectric substance produces an electric current when it is physically deformed or alternatively undergoes a deformation caused by the application of a current. A pyroelectric material is one that develops an electrical potential in response to a change in its temperature. 

Making the PVDF polymer piezoelectric and pyroelectric requires some very special processing, which makes it costly ( 10 per square foot). This expense seems a small price to pay for its near-magical properties. ... 

PROP White, amorphous powder or white, hexagonal crystals piezoelectric and pyroelectric. Undergoes hexagonal to tetragonal transition at 21°. Mp 2507°, bp 3900° (approx), d 3.025. Dissolves in cone H2SO4 and in fused KOH. Sltly sol in H2O. SYNS BERYLLIA BERYLLIUM MONOXIDE THERMALOX... 

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