Inverse piezoelectric effects

Fig. 9.2. The inverse piezoelectric effect. A thin and long quartz plate, QQ, is sandwiched between two tin foils. By applying a voltage to the tin foils, the quartz plate elongates or contracts according to the polarity of the applied voltage. To measure the very small displacement. Curie (1889a) used a lever ABD with a small piece of glass V attached at its end, the displacement of which is then measured with an optical microscope. (After Curie, 1889a.)...

A few months later, Lippman (1881) predicted the existence of the inverse piezoelectric effect By applying a voltage on the quartz plate, a deformation should be observed. This effect was soon confirmed by the Curie brothers (Curie and Curie, 1882), who designed a clever experiment to measure the tiny displacement, as shown in Fig. 9.2. Here, a light-weight lever with an arm of about 1 100 amplifies the displacement by two orders of magnitude. An optical microscope further amplifies it by two orders of magnitude. The displacement is then measured by an eyepiece with a scale. 

The reasoning of Lippman (1881) for the inverse piezoelectric effect is based on thermodynamics. Consider the experiment shown in Fig. 9.1. The increment of the total energy due to an applied voltage V is... 

The ac current is generated by a combination of piezoelectric effect and inverse piezoelectric effect. In other words, it is a double piezoelectric response. 

Independent-orbital approximation 159 Inertial steppers 275 Invariant functions 361 Inverse piezoelectric effect 214 Iridium 115... 

Ferroelectrics. Among the 32 crystal classes, 11 possess a centre of symmetry and are centrosymmetric and therefore do not possess polar properties. Of the 21 noncentrosymmetric classes, 20 of them exhibit electric polarity when subjected to a stress and are called piezoelectric one of the noncentrosymmetric classes (cubic 432) has other symmetry elements which combine to exclude piezoelectric character. Piezoelectric crystals obey a linear relationship P,- = gijFj between polarization P and force F, where is the piezoelectric coefficient. An inverse piezoelectric effect leads to mechanical deformation or strain under the influence of an electric field. Ten of the 20 piezoelectric classes possess a unique polar axis. In nonconducting crystals, a change in polarization can be observed by a change in temperature, and they are referred to as pyroelectric crystals. If the polarity of a pyroelectric crystal can be reversed by the application on an electric field, we call such a crystal a ferroelectric. A knowledge of the crystal class is therefore sufficient to establish the piezoelectric or the pyroelectric nature of a solid, but reversible polarization is a necessary condition for ferroelectricity. While all ferroelectric materials are also piezoelectric, the converse is not true for example, quartz is piezoelectric, but not ferroelectric. 

Electrostriction. As distinct from inverse piezoelectric effect, electrostriction is a phenomenon in which the strain and the electrical field inducing the strain are related by Sy = where My are electrostriction coefficients. Several relaxor... 

Fig. 7. Sketch of the apparatus for measuring inverse piezoelectric effect in polymer films. B vibrating cantilever beam, E electromagnetic exciter, P electromagnetic pick-up, S specimen film, M weight, C oscillator, Vt, V2 and V3 voltmeters, Sw switch, V d.c. bias source for measuring electrostriction effect. Drawn after Kawai (1) (1969) by permission of the Japan Society of Applied Physics...

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)...

As previously shown [26,27] 7 covers the regime between 0 < 7 < 1. Thus the inverse piezoelectric effect always dominates the overall interaction in pfm. Therefore, pfm effectively reveals the local polarization distribution close to the sample surface [11,21,22,28,29],... 

The inverse piezoelectric effect is the strain e of a crystal due to the application of... 

The anisotropic properties described in Sections 4.4,1 to 4,4,5 are not all independent. The strain e is not only a function of the mechanical stresses a to which the crystal is submitted, it is equally a function of the electric field E (inverse piezoelectric effect) and of the temperature AT (thermal expansion) ... 

The piezoelectric effect (Fig. 4) was discovered by Pierre and Jacques Curie in 1880. The direct piezoelectric effect consists of the ability of crystalline materials (ceramics) to generate an electrical charge in proportion to an externally applied force. The direct effect is used in force transducers. According to the inverse piezoelectric effect, an electric field parallel to the direction of polarizatitMi induces an expansion of the ceramic (Preumont 1997). 

Certain crystals, such as quartz, feature a physical relationship between mechanical force and electric charge. When the crystal lattice ions are elastically shifted relative to one another due to an external force, an electric polarization can be detected by means of metallic electrodes on the surface. This so-called piezoelectric effect was first scientifically explained by the brothers Jacques and Pierre Curie in 1880 and forms the basis for piezo sensors (see Sect. 7.3). The effect is reversible and is then called reciprocal or inverse piezoelectric effect. If, for instance, an electric voltage is applied to a disc shaped piezo crystal, the thickness of the crystal changes due to the reciprocal piezoelectric effect. It is this property that is made use of in actuators. 

As shown in Table 8.1, the piezoelectric effect causes the creation of charges in a dielectric and ferroic materiaL respectively, in response to an applied stress field. The opposite effect-that is, the induction of strain (deformation) by applying an outside electric field-is called the inverse piezoelectric effect. Piezoelectricity requires that no symmetry center exists in the crystal structure. The piezoelectric properties of ceramic materials are described by four parameters (i) the dielectric displacement D (ii) the electric field strength E (iii) the applied stress X and (iv) the strain (deformation) x. These are related by two equations that apply to the (direct) piezoelectric effect D = e x and E = h x, and two equations that apply to the inverse piezoelectric effect x = g D and x = d E. The four coefficients e, h, g, and d are termed the piezoelectric coefficients. 

Since the electro-optic tensor has the same symmetry as the tensor of the inverse piezoelectric effect, the linear electro-optic (Pockels) effect is confined to the symmetry groups in which piezoelectricity occurs (see Table 8.3). The electro-optic coefficients of most dielectric materials are small (of the order of 10 m V ), with the notable exception of ferroelectrics such as potassium dihydrogen phosphate (KDP KH2PO4), lithium niobate (liNbOs), lithium tantalate (LiTaOs), barium sodium niobate (Ba2NaNb50i5), or strontium barium niobate (Sro.75Bao.25Nb206) (Zheludev, 1990). For example, the tensorial matrix of KDP with symmetry group 42m has the form... 

Flgure 10.1 Schematic diagrams detailing (a) the direct piezoelectric effect for compression and tensile stress and (b) the inverse piezoelectric effect with either tension or compression suffered by the material on subjecting to an external electric field. 

Electrostriction A behaviour related to the inverse piezoelectric effect is electrostriction, i.e. changes in volume and shape of the materials due to application of a near EM field. In contrast to piezoelectricity, electrostriction is a nonlinear effect which occurs with all dielectric but it is pronounced only in a group of dielectrics, called relaxers. 

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