Converse piezoelectricity

Equations (6) and (7) express these relationships. are the elastic compliance constants OC are the linear thermal expansion coefficients 4 and d jj,are the direct and converse piezoelectric strain coefficients, respectively Pk are the pyroelectric coefficients and X are the dielectric susceptibility constants. The superscript a on Pk, Pk, and %ki indicates that these quantities are defined under the conditions of constant stress. If is taken to be the independent variable, then O and are the dependent quantities ... 

Converse piezoelectricity is a specific kind of a more general phenomenon known as electrostriction. Electrostriction is the deformation of a material exposed to an electrical field. Nearly all dielectrics... 

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 ... 

Width of the dead zone of the interface height step Converse piezoelectric constant Dielectric displacement... 

The piezoelectric crystals are patterned with two excitation electrodes (electronic surface films) on their opposite sides. Due to the converse piezoelectricity phenomenon, when -> alternating voltage is applied to the attached electrodes mechanical oscillations occur within the crystal lattice. These oscillations are stable only at the natural resonant frequency of the crystal. 

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. 

These features of the Raman bands of the ZnO nanostructures can be extremely powerful for the in situ identification of orientation of ZnO nanostructures employed in a converse piezoelectric actuator directly in an assembled state [45]. While their study focused on ZnO nanostructures, the authors noted that the general features (Raman bands and the waveguiding effect) described are equally applicable to other wurtzite type nanostructures and the approach suggested might serve as a universal tool for the versatile characterization of GaN, ZnS, and CdSe from the wurtzite family, which are utilized for optoelectronics, lasing, and piezoelectricity. 

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... 

H.10.2.1 Piezoelectricity, Converse Piezoelectricity, Piezoelectric Materials, and Oscillators... 

Khan A, Hussain M, Nur O, Willander M, Broitman E. Analysis of direct and converse piezoelectric responses from zinc oxide nanowires grown on a conductive fabric. Phys Status SolidiA 2015 212(3) 579-84. 

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