Piezoelectric effect converse

Electrostatic field components transverse to the direction of polarization induce shear mode actuation, see Eq. (4.20). The particular shear strains or 

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Figure 13.2 Piezoelectric hysteresis for converse piezoelectric effect in a rhombohedral PZT thin film [3].

In the converse piezoelectric effect one usually applies voltage V or electric field E on the sample and measures displacement AZ or strain A///. From relation Al = 0Z33 V for the longitudinal effect, we see that even for materials with exceptionally high piezoelectric coefficient (do3 = 2000pm/V in pzn-pt) the displacement Al is only around 2 nm if 1 V is applied on the sample. For the same voltage the displacement is reduced to 0.2 nm in a typical pzt composition and to only tn 2 pm in quartz. The displacement can be increased by application... 

The origin of the nonlinearity and hysteresis in the films is most likely due to displacement of domain walls [4], If domain walls move in a medium with a random distribution of pinning center, the response of the material can be described, in the first approximation by Rayleigh relations. We next demostrate how optical interferometry can be sued to verify whether this particular model applies to the investigated pzt thin film. In the case of the converse piezoelectric effect, when the driving field E is varied between — Eo and Eo, the piezoelectric strain x is hysteretic and can be expressed by the following Rayleigh relations ... 

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. 

Hu Y, Gao Y, Singamaneni S, Tsukruk VV, Wang ZL (2009) Converse piezoelectric effect induced transverse deflection of a free-standing ZnO microbelt. Nano Lett 9 2661-2665... 

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. 

In the converse piezoelectric effect, a voltage (or electric field, E, the stimulus) applied to a piezoelectric material will induce a change in shape (strain, e, the response), given by... 

The coefficient is called the transverse piezoelectric coefficient. The converse piezoelectric effect, relating strain, e to the applied electric field E is similarly simplified to... 

Electrostriction is related to the converse piezoelectric effect. At modest electric field strengths, the piezoelectric equations given previously are adequate and there is a linear relationship between strain and electric field. However, at higher electric field strengths, these equations need to be extended to include a further term quadratic with respect to the electric field. The strain is now given by... 

Displacement actuators (converse piezoelectric effect) This class contains various actuators - loudspeakers, camera shutters, buzzers, ink-jet printers, microrobots, relays, pumps, fuel injection systems, and others. 

Certain materials produce electric charges on their surfaces as a consequence of applying mechanical stress. The induced charges are proportional to the mechanical stress. This is called the direct piezoelectric effect and was discovered in quartz by Piere and Jacques Curie in 1880. Materials showing this phenomenon also conversely have a geometric strain proportional to an applied electric field. This is the converse piezoelectric effect. The root of the word piezo means pressure hence the original meaning of the word piezoelectricity implied pressure electricity . 

In the converse piezoelectric effect, the stress or strain forces are generated by the electric field applied to the crystal. Thus, we have... 

The superscripts d) and (c) refer to the direct and converse piezoelectric effect, respectively. Given this equality of and dj the superscripts are redundant and are, therefore, omitted. 

Let us now look at the interrelations holding between the material coefficients listed in Table 4.2. In the context of coupling effects it has already been shown that the direct and the converse piezoelectric effects are described by identical material coefficients. This follows immediately from their definition as second derivatives of the associated thermodynamic potential, recognizing the fact that the order of differentiations may be reversed. Direct and converse effects are described by relations between different pairs of variables. The equality of the coefficients governing the direct and the converse effects reduces the number of independent material coefficients for each selection of the triple of independent variables. It does not, however, represent a relation between material coefficients derived from different thermodynamic potentials. 

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