Strain electric field-induced

For many problems it is convenient to separate the piezoelectric (i.e., strain induced) polarization P from electric-field-induced polarizations by defining D = P + fi , where s is the permittivity tensor. For uniaxial strain and electric field along the 1 axis, when the material is described by Eq. (4.1) with the E term omitted. 

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... 

The present work summarizes opportunities of using high-resolution synchrotron and standard xrd techniques for structural characterization as well as for investigations of structure-property-relationships. xrd will be used to determine quantitatively the phase content of morphotropic pzt. Temperature dependent measurements provide information about the phase transformation of morphotropic donor doped pzt ceramics and high-resolution synchrotron X-ray diffraction gives information about the extrinsic and intrinsic contributions to the electric field induced strain, xrd results are finally compared with electrical measurements to analyze the interactions among microstructure, phase content and properties. 

The electric field induced intrinsic strain for different crystallographic directions could be calculated from the shift in peak positions (see Figure 7.9). Figure 7.11 shows the result of the measurements for a rhombohedral pzt in [111] and [100] direction. Only one half of each cycle is shown for the sake of a clarity of the plot. The curve for the [100] direction reveals the typical shape of a butterfly loop for the electric field induced strain in ferroelectrics. However in [111] direction, which is parallel to the spontaneous polarization, strain is significantly smaller. From both curves, the so-called unipolar strain can be evaluated as the strain induced at the maximum electric field Emax with a reference to the remanent state (E = 0). The calculation gives strain values in [111] direction of 0.02% and for the [100] direction 0.15%. The observations are in good agreement with theoretical calculations made by Du et al. [22],... 

Figure 7.13 Electric field induced macroscopic strain measurements of tetragonal and rhombohedral co-doped pzt using lvdt...

In the presence of an in-plane electric field, electron spin can precess in the absence of any magnetic field at high temperature. This is understood that the inplane electric field induces a center-of-mass shift of the momentum which gives rise to an effective magnetic field proportional to the electric field [18]. The effect of strain on the spin R/D is also discussed and it is shown that one can effectively manipulate the spin R/D time by strain [29]. Cheng and Wu further discussed the spin R/D under identical Dresselhaus and Rashba terms [25]. A finite spin R/D time is obtained due to the cubic term in Eq. (2). 

Guiffard B, Seveyrat L, Sebald G, Guyomar D (2006) Enhanced electric field-induced strain in non-percolative carbon nanopowder/polyurethane composites. J Phys D Appl Phys 39 3053... 

Ren, X. (2004) Large electric-field-induced strain in ferroelectric crystals by point-defect-mediated reversible domain switching. Nat. Mater., 3, 91—94. 

Actuators are among the latest applications for thin sheets of piezoelectric materials. Actuators are small displacement elements for the precision positioning of optical and other motors and machinery. All of these piezoelectric devices operate on the principle of electric field-induced strain. 

Figure 16.2 Illustration of the electric-field-induced strain in soft polymer due to the Maxwell...

Many electrostrictive polymers have been developed in the last decade [1] and these newly developed electrostrictive polymers exhibit a high electric-field-induced strain, as shown in Figiure 16.5a, where the maximum thickness strain response of the polymer at different fields is given. A typical relationship between the strain response and the electric field observed in these polymers is shown in Figure 16.5b. All these electrostrictive polymers are polar polymers that contain polar units in the polymer chain. The electrostrictive strain response reflects the change in these polar units due to an electric field. 

In the case of polymeric elastomers exhibiting a large electric field-induced strain, two intrinsic mechanisms are considered as primary contributors electrostriction and the Maxwell stress effect. The contributions from both mechanisms exhibit a quadratic dependence with an applied electric field. For the newly developed electrostrictive graft elastomers, more than 95 % of the electric field-induced strain response is contributed by the electrostriction mechanism, while the contribution from the Maxwell stress effect is less than 5 %. Due to the relatively high elastic modulus ( 0.55 GPa), the grafted elastomer also exhibits a high elastic energy density of 0.44 MJ/m. ... 

Su et al. reported, in 2003, that the electric field-induced strain of the elastomer can be controlled by thermal annealing treatment, which can increase the crystallinity of the grafted electric field-responsive domains. The higher crystallinity is achieved, the higher electric field-induced strain is obtained. Since the mechanism... 

To understand the mechanisms of the electrostriction in the G-elastomers, a model has been established (Wang et al. 2003). The model simulation indicated that the mechanisms of the electric field-induced strain in the electrostrictive G-elastomers are attributed to the rotation of the polar crystal domains that formed by grafted molecular chains and the reorientation of the flexible backbone chains when an electric field is applied. 

By increasing the ratio of VDF/TrFE in the terpolymer, the electric field-induced strain level ean be raised due to the faet that the lattice strain between the polar conformation and nonpolar conformations increases with the VDF/TrFE ratio. 

Hao, J.G., Shen, B., Zhai, J.W., Chen, H., 2014. Phase transitional behaviour and electric field-induced large strain in alkaU niobate-modified Bi-0.5(Na0.80K0.20)(0.5(Ti03) lead-free piezoceramics. Journal of AppUed Physics 115, 034101. 

Ullah, A., Ahn, C.W., Hussain, A., and Kim, I.W. (2010) The effects of sintering temperatures on dielectric, ferroelectric and electric field-induced strain of lead-free Bio,s(Nao,78Ko.22)o.sTi03 piezoelectric ceramics synthesized by the sol-gel technique. Curr. Appl Phys., 10 (6),... 

The strain j Hes along the axis of the electric field, E, or most often along the axis of the induced polari2ation, P. The electrostrictive coefficients for the electric field and polari2ation are M and respectively. Electrostriction is a small effect. In contrast to pie2oeIectric materials, electrostrictive materials... 

Due to their high piezoelectric response, electrostriction in ferroelectrics, induced by an applied electric field, can be used as strain-inducing components (just as ferromagnetic materials can be exploited for their magnetostriction). Thus barium... 

Nonlinear properties of normal dielectrics can be studied in the elastic regime by the method of shock compression in much the same way nonlinear piezoelectric properties have been studied. In the earlier analysis it was shown that the shape of the current pulse delivered to a short circuit by a shock-compressed piezoelectric disk was influenced by strain-induced changes in permittivity. When a normal dielectric disk is biased by an electric field and is subjected to shock compression, a current pulse is also delivered into an external circuit. In the short-circuit approximation, the amplitude of this current pulse provides a direct measure of the shock-induced change in permittivity of the dielectric. 

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