Direct piezoelectricity

Piezoelectric Transducers Certain ciystals produce a potential difference between their surfaces when stressed in appropriate directions. Piezoelectric pressure transducers generate a potential difference proportional to a pressure-generated stress. Because of the extremely high electrical impedance of piezoelectric crystals at low frequency, these transducers are usually not suitable for measurement of static process pressures. 

J. Horacek and P. Skladal, Improved direct piezoelectric biosensors operating in liquid solution for the competitive label-free immunoassay of 2,4-dichlorophenoxyacetic acid. Anal. Chim. Acta 347, 43-50 (1997). 

C. Steegborn and P. Skladal, Construction and characterization of the direct piezoelectric immunosensor for atrazine operating in solution. Biosens. Bioelectron. 12,19-27 (1997). 

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),... 

The total pyroelectric response at constant stress, p , is the sum of the primary pyroelectic response, given by p, and the secondary pyroelectric response, which is the product of the direct piezoelectric stress coefficient gs, and the thermal expansion coefficients ... 

Cohen, J., Edelman.S. Direct piezoelectric effect in polyvinyl chloride films. J. Appl. Phys. 42, 893 (1971). 

PIEZOELECTRIC EFFECT. The interaction of mechanical and electrical stress-strain variables in a medium. Thus, compression of a crystal of quartz or Rochelle salt generates an electrostatic voltage across it, and conversely, application of an electric field may cause the ciystal to expand or contract in certain directions, Piezoelectricity is only possible in crystal classes which do not possess a center of symmetry. Unlike clcctrostricdon, the effect is lineal in the field strength. 

Piezoelectric materials are materials that exhibit a linear relationship between electric and mechanical variables. The direct piezoelectric effect can be described as the ability of materials to convert mechanical stress into an electric field and the reverse, to convert an electric field into a mechanical stress. The use of the piezoelectric effect in sensors is based upon the latter property. 

Piezoelectric materials are materials that exhibit a linear relationship between electric and mechanical variables. Electric polarization is proportional to mechanical stress. The direct piezoelectric effect can be described as the ability of materials to convert mechanical stress into an electric field, and the reverse, to convert an electric field into a mechanical stress. The use of the piezoelectric effect in sensors is based on the latter property. For materials to exhibit the piezoelectric effect, the materials must be anisotropic and electrically poled ie, there must be a spontaneous electric field maintained in a particular direction throughout the material. A key feature of a piezoelectric material involves this spontaneous electric field and its disappearance above the Curie point. Only solids without a center of symmetry show this piezoelectric effect, a third-rank tensor property (14,15). 

The term piezoelectric nonlinearity is used here to describe relationship between mechanical and electrical fields (charge density D vs. stress a, strain x vs. electric field E) in which the proportionality constant d, is dependent on the driving field, Figure 13.1. Thus, for the direct piezoelectric effect one may write D = d(a)a and for the converse effect x = d(E)E. Similar relationships may be defined for other piezoelectric coefficients (g, h, and e) and combination of electro-mechanical variables. The piezoelectric nonlinearity is usually accompanied by the electro-mechanical (D vs. a or x vs. E) hysteresis, as shown in Figure 13.2. By hysteresis we shall simply mean, in the first approximation, that there is a phase lag between the driving field and the response. This phase lag may be accompanied by complex nonlinear processes leading to a more general definition of the hysteresis [2],... 

Figure 13.3 Dynamic press for measurements of the direct piezoelectric effect.

All materials undergo a small change in dimensions when subjected to an electric field. If the resultant strain is proportional to the square of the field it is known as the electrostrictive effect. Some materials show the reverse effect - the development of electric polarization when they are strained through an applied stress. These are said to be piezoelectric (pronounced pie-ease-oh ). To a first approximation the polarization is proportional to the stress and the effect is said to be direct . Piezoelectric materials also show a converse effect, i.e. the development of a strain x directly proportional to an applied field. 

If a piezoelectric plate (Fig. 6.1), polarized in the direction indicated by P, carries electrodes over its two flat faces, then a compressive stress causes a transient current to flow in the external circuit a tensile stress produces current in the opposite sense (Fig. 6.1(a)). Conversely, the application of an electric field produces strain in the crystal, say a negative strain reversal of the field causes a positive strain (Fig. 6.1(b)). The changes in polarization which accompany the direct piezoelectric effect manifest themselves in the appearance of charges on the crystal surface (see Eq. (2.71)) and, in the case of a closed circuit, in a current. 

S]). The direct piezoelectric effect is the production of electric displacement by the application of a mechanical stress the converse piezoelectric effect results in the production of a strain when an electric field is applied to a piezoelectric crystal. The relation between stress and strain, expressed by Equation 2.7, is indicated by the term Elasticity. Numbers in square brackets show the ranks of the crystal property tensors the piezoelectric coefficients are 3rd-rank tensors, and the elastic stiffnesses are 4th-rank tensors. Numbers in parentheses identify Ist-rank tensors (vectors, such as electric field and electric displacement), and 2nd-rai tensors (stress and strain). Note that one could expand this representation to include thermal variables (see [5]) and magnetic variables. 

The sensor is illustrated schematically in Fig. 1. The piezoelectric-excited millimeter-sized cantilever (PEMC) sensor is a macro-cantilever that comprises piezoelectric layer (lead zirconate titanate PZT) layer bonded to a nonpiezoelectric layer of a few millimeters in length and 1 mm in width (9,21). We use the direct piezoelectric effect to excite the cantilever, and the same PZT film senses the resulting response. PZT film is bonded to a base glass... 

Figure 15.19 a) The direct piezoelectric effect is that polarization charges are created by stress, ih) The inverse effect is that a strain is produced as a result of the applied voltage. 

White R. M. and Volltmer F. W., Direct piezoelectric coupling to surface elastic waves, Appl. Phys. Lett., 7, 314,1965. 

In a normal dielectric, the observed polarisation of the material is zero in the absence of an electric field, and this does not change if the material is heated or subjected to mechanical deformation. In a piezoelectric solid a surface electric charge develops when the solid is subjected to a mechanical stress such as pressure, even in the absence of an external electric field. This is called the direct piezoelectric effect. The effect is reversible and the inverse (or converse) piezoelectric effect, in which a voltage applied to a crystal causes a change in shape, also occurs in piezoelectric crystals. The piezoelectric effect generally varies from one direction to another in a crystal, and in some directions a crystal may show no piezoelectric effect at aU whereas in other directions it is pronounced. 

Show that the units for the direct piezoelectric coefficient, d, of CN- and mV- are equivalent. [Note answer is not shown at the end of this book.]... 

R. M. White and F. W. Voltmen (1965) Direct piezoelectric coupling to surface electric waves , Applied Physics Letters, 7,314-16. 

Polymer electrets can be operated as sensors or actuators. Their operation is very similar to that of a piezoelectric material and their direct piezoelectric transducer coefficient (d33) is higher than that of solid PVDF ferroelectric polymers [97]. If a compressive force is apphed to the film, the pores will deform preferentially with respect to the polymer material. Unlike charges within the polymer will be pushed closer together and the potential measured at the contacts will change accordingly. Similarly, the application of a voltage across the electrodes will yield a change in thickness in the material. 

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). 

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