Piezoelectricity electrostriction constant

As will be shown in the theory, the electrostriction effect plays an important role in the piezoelectric effect of polymer films. Moreover, a knowledge of the complex electrostriction constant as a function of frequency reveals a new aspect of the relaxational behavior of polymers. In this review a new method for measuring complex electrostriction constant with varying frequency will be presented with some results for poly(vinylidene fluoride). 

In the usual experiment where E0 = 0, the term kSE in Eq. (9) does not make any contribution as far as the electrical response with the same frequency as the mechanical excitation is concerned. However, as will be described in 2.2 and 2.4, the piezoelectric constant of a polymer film is sometimes a function of the electrostriction constant which plays an important role in the anisotropy and relaxational behavior of the piezoelectric effect. 

It must be noted that the above consideration for Case (A) assumes that the material is elastically heterogeneous but homogeneous in its dielectric property. If we assume heterogeneity in the electrostriction constant, CJC changes with strain, keeping //(//2 — ) constant, and hence another possibility of piezoelectricity may be introduced however, we will not take this complication into account in the following. 

III. Methods for Measuring the Piezoelectricity and Electrostriction Constant of Polymer Films 3.1. Measurement of the Piezoelectric Constant... 

A) When an alternating voltage (frequency = to) is applied to the film, the film is strained with frequencies to and 2 to. The former is the inverse piezoelectric effect and the latter the electrostriction effect. By measuring the strain amplitude of the 2to component, we can obtain the electrostriction constant (Oshiki and Fukada, 1971). 

Fig. 28. Piezoelectric stress constant obtained from inverse piezoelectric effect and electrostriction constant of drawn and polarized poly(vinylidene fluoride) film plotted against temperature. Draw ratio = 7. Polarized at 90° C under the field of 400 kV/ctn for 3 hours. Frequency of applied voltage = 37.5 Hz. (Oshiki and Fukada, 1971) Broken line represents dielectric constant at 21.5 Hz for roll-drawn poly (vinylidene fluoride) film (Peterlin and Eiweil, 1969)...

The electrostriction effect, beside its effect on the piezoelectricity, gives a new insight onto relaxations in polymers when the electrostriction constant is obtained over a wide frequency range. It provides us with a knowledge of the strain dependence of relaxation time. 

In Sect. 7.3, Eqs. (18) and (19) describe the Maxwell stress forces acting on a conductive tip when a combined d.c./a.c. voltage is applied. For the PFM set-up we have to complete the total interaction force by the additional effects of piezoelectricity, electrostriction and the spontaneous polarisation. Both electromechanical effects cause an electric field-induced thickness variation and modulate the tip position. The spontaneous polarisation causes surface charges and changes the Maxwell stress force. If the voltage U(t)=U[)c+UAc sin((Ot) is applied, the resulting total force Ftotai(z) consists of three components (see also Eq. 19) Fstatic, F(0 and F2m. Fstatic is the static cantilever deflection which is kept constant by the feedback loop. F2a contains additional information on electrostriction and Maxwell stress and will not be considered in detail here (for details see, e.g. [476]). The relevant component for PFM is F(0 [476, 477] ... 

From tensor algebra, the tensor property relating two associated tensor quantities, of rank / and rank g, is of rank (/-b g). Hence, the physical property connecting /, and aj is the third-rank tensor known as the piezoelectric effect, and it contains 3 = 27 piezoelectric strain coefficients, dyk. The piezoelectric coefficients are products of electrostriction constants, the electric polarization, and components of the dielectric tensor. 

EFFECTS OF POISSON S RATIO AND ELECTROSTRICTION CONSTANT ON PIEZOELECTRICITY IN POLY(VINYLIDENE FLUORIDE)... 

In this paper, we report experimental results of the Poisson s ratio and electrostriction constant of PVDF and discuss the role of their constants to the piezoelectric effect by using the theory developed by Wada and Hayakawa. 

The dielectric constant e and piezoelectric constant eai were measured by using the apparatus developed by Furukawa et al The electrostriction constant K3i=Oe3/8S) was calculated by measuring an apparent piezoelectric constant under low frequency A.C bias (0.004 Hz). 

W. R. Cook Jr. Piezoelectric, Electrostrictive, Dielectric Constants, Electromechanical Coupling Fac- 4.31 tors, Landolt-Bbrnstein, New Series 111/29, ed. by... 

The most direct experimental access to this effect is the direct measurement of deformation (changes of specimen thickness, e.g.) under the action of an electric field. In piezoelectric ciystals, however, this effect is masked to a large extent by the superimposed converse piezoelectric effect, hnear in the electric field. Nevertheless, Uchino etal (1982) andLnymes (1983) have constmcted measuring apparatus based on an interferometric techniqne. By compensating the linear piezoelectric response Luymes (1983) measured an electrostriction constant of a-quartz. 

In Eq. (20) the three terms are related to the Maxwell stress (first), piezoelectric effect (second) and electrostriction (third). In order to obtain information about ferroelectricity via piezoresponse measurements, we need a link between the spontaneous polarisation and the piezoelectric constant. According to Furukawa and Damjanovic, piezoelectricity in ferroelectrics can be explained as electrostriction biased by the spontaneous polarisation if their paraelectric phase is nonpolar and centrosymmetric [461, 495, 496]. Therefore the d33 constant depends on the spontaneous polarisation P5 ... 

Based on Equations (16.9) and (16.15), the Maxwell effect and electrostrictive effect result in the same relationship between the strain and electric field and they therefore share some common features. For instance, an apparent piezoelectric effect can be observed when a DC bias is applied the strain response can be enhanced by the nonuniformity of the electric field, which can be created either by employing nonuniform materials or by the presence of the space (trapping) charge. Due to the electrostrictive effect and the appearance of the space charge, an insulation material can exhibit piezoelectricity and is known as an electret [9, 10]. The piezoelectric constant of an electret depends on the space charge and its distribution as well as the nonuniformity in the elastic properties and electrostrictive coefficient of the materials. 

For an E-M device, there are various considerations regarding the material properties. Besides their piezoelectric constants and electrostrictive coefficients, many other properties are also critical to the E-M performance. 

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