History and recent progress in piezoelectric polymers

Electrets of carnauba wax and resin have exhibited good stability of trapped charges for nearly 50 years. Dipolar orientation and trapped charge are two mechanisms contributing to the pyro-, piezo-, and ferroelectricity of polymers. Since the 1950s, shear piezoelectricity was investigated in polymers of biological origin (such as cellulose and collagen) as well as synthetic optically active polymers (such as polyamides and polylactic acids). Since the discovery of piezoelectricity in poled polyvinylidene fluoride (PVDF) in 1969, the pyro-, piezo-, and ferroelectricity were widely investigated in a number of polar polymers, such as copolymers of vinylidene fluoride and trifluoroethylene, copolymers of vinylcyanide and vinylacetate, and nylons. Recent studies involve submicron films of aromatic and aliphatic polyureas prepared by vapor deposition polymerization in vacuum and the piezoelectricity of polyurethane produced by the coupling of electrostriction and bias electric fields. Gramophone pickups using a piece of bone or tendon were demonstrated in 1959. Microphones using a stretched film of polymethyl glutamate were reported in 1968. Ultrasonic transducers using elongated and poled films of PVDF were demonstrated in 1972. Headphones and tweeters using PVDF were marketed in 1975. Hydrophones and various electromechanical devices utilizing PVDP and its copolymers have been developed during the past 30 years. This paper briefly reviews the history and recent progress in piezoelectric polymers.     

Effects of remanent field on an elliptical flaw and a crack in a poled piezoelectric ceramic

Commonly used piezoelectric ceramics such as PZT and PLZT are polarized ferroelectric polycrystals. After poling, remanent strains and a remanent polarization exist in a ceramic material. Remanent field can affect the electroelastic field and consequently plays a critical role in fracture of poled ceramics. Based on a linear constitutive law, the electroelastic field and the energy release rate of an elliptical cavity (or a crack) in a poled piezoelectric are re-examined in this study by including the effects of remanent field. It is noted that the remanent field generally has a minor effect on the stress field and a pronounced effect on the electric field at the apex of the major axis of an elliptical flaw. When the permittivity of the cavity is small, the effect of remanent polarization is similar to that of a very strong electric field applied along the poling direction. However, for the case of a conducting flaw, the remanent field does not influence the electroelastic field and energy release rate. Energy release rate of a flaw in a poled ferroelectric ceramic with and without the remanent polarization is generally different.     

Electromechanical properties of lead zirconate titanate piezoceramics under the influence of mechanical stresses

In lead zirconate titanate piezoceramics, external stresses can cause substantial changes in the piezoelectric coefficients, dielectric constant, and elastic compliance due to nonlinear effects and stress depoling effects. In both soft and hard PZT piezoceramics, the aging can produce a memory effect that will facilitate the recovery of the poled state in the ceramics from momentary electric or stress depoling. In hard PZT ceramics, the local defect fields built up during the aging process can stabilize the ceramic against external stress depoling that results in a marked increase in the piezoelectric coefficient and electromechanical coupling factor in the ceramic under the stress. Although soft PZT ceramics can be easily stress depoled (losing piezoelectricity), a DC bias electric field, parallel to the original poling direction, can be employed to maintain the ceramic poling state so that the ceramic can be used at high stresses without depoling.     

Effects of magneto-electric loadings and piezomagnetic/piezoelectric stiffening on multiferroic interface fracture

Interface fracture of a multiferroic composite is studied by the methods of integral transform and singular integral equation. Parametric studies on the stress intensity factor yield three conclusions. (a) The multiferroic composite is more likely to fracture in electric field than in magnetic field. (b) Under magnetostriction, piezomagnetic stiffening does not affect the interface crack, but the influence of piezoelectric stiffening is notable. Under electrostriction, inverse results are obtained. (c) In magnetic loading cases, the piezomagnetic layer should be softer and the piezoelectric strip stiffer; however, if electric loading is applied instead, opposite conclusion should be expected.     

Giant magneto-electric effect in laminate composites

It has been discovered that laminate composites of longitudinally magnetized magnetostrictive and transversely poled piezoelectric layers (a L-T laminate composite) have a giant magneto-electric (ME) effect under a low magnetic bias. The ME voltage coefficient is over 110 mV/Oe at a magnetic bias H=500 Oe. This value is 5-10 times higher than that previously reported for transverse magnetized/transverse polarized (T-T) laminates of the same layer compositions at the same bias. In this paper, we also report the magneto-elasto-electric bieffect equivalent circuit of the L-T laminate composite and the corresponding theoretical formula of the magneto-electric voltage coefficient.     

Love waves propagation in a piezoelectric layered structure with initial stresses

Summary. The propagation behavior of Love waves in a piezoelectric layered structure with inhomogeneous initial stress is studied. Solutions of the mechanical displacement and electrical potential function are obtained for the isotropic elastic layer and transversely isotropic piezoelectric substrate, respectively, by solving the coupled electromechanical field equations. Firstly, effects of the inhomogeneous initial stress on the dispersion relations and phase velocity of Love wave propagation are discussed. Then the influence of the initial stress gradient coefficient on the stress, mechanical displacement and electrical potential distribution in the layer and the substrate is investigated in detail. The results reported in this paper are not only meaningful for the design of surface acoustic wave (SAW) devices with high performance, but also effective for evaluating the residual stress distribution in the layered structures.     

Anisotropic microhardness in single-crystal and polycrystalline BaTiO3

The room-temperature hardness of single-crystal and dense polycrystalline BaTiO₃ was investigated by microindentation. The longer diagonal of the Knoop indenter was oriented either parallel or perpendicular to the poled axis of the material. The hardness of the unpoled sample was isotropic. However, hardnesses in the poled samples were anisotropic, with the highest hardnesses resulting when the longer diagonal was parallel to the poled axis. The hardness anisotropy may be due primarily to residual stresses caused by the piezoelectric coupling effect.     

Comparison between piezoelectric method and ultrasonic signal analysis for crack detection in type II multilayer ceramic capacitors

In this paper we present a comparison between two non-destructive techniques for crack detection in MLCCs. First, if a type II MLCC is biased with a DC field, the capacitor becomes temporarily ‘poled’ and can act as a transducer. This is induced by a residual piezoelectric effect used in the impedance spectroscopy method. Second, we used a scanning ultrasonic system working in the 10–100 MHz frequency bandwidth. To understand the ultrasonic signature, we used time-of-flight (TOF) detection with short-time Fourier transform (STFT) analysis to determine the depth and nature of defects with high accuracy. An application of digital signal processing to the characterization of defects is presented for a lot of MLCCs with cracks defects. For comparison, the same lot was tested with the piezoelectric method. The two techniques are closely correlated. © 1998 John Wiley & Sons, Ltd.     

On the effect of remanent polarization on electro-mechanical fields near an elliptic cavity in poled or depolarized piezoelectric ceramics

In this paper the effect of remanent polarization on electric-mechanical fields near an elliptic cavity in piezoelectric ceramics is studied. The analysis is based on the application of exact electric boundary conditions at the rim of the elliptic cavity, thus avoiding the common assumption of electric impermeability. Expressions for electromechanical fields near the elliptic cavity are derived in a closed form in terms of complex potentials. The result shows that the problem of remanent polarization is similar to the problem of general strain mismatch and the effect of remanent polarization on fracture in poled or depolarized piezoelectric ceramics can not be omitted. When the permitivity of the medium in a cavity is small, the effect of remanent polarization is identical to the effect of a considerable strong positive electric field and the tangent stress at the major axial apex of the elliptical cavity is tensile. Such behavior explains why the positive electric field promotes the crack growth while the negative electric field retards the crack growth and accounts for the anisotropy of fracture toughness under mechanical loads. The results show that the effect of remanent polarization on electromechanical fields near an elliptic cavity depends not only on the geometry of the elliptic cavity, i.e. the ratio of the minor semi-axis to major semi-axis, but also on the ratio of permitivity of the medium in the cavity to permitivity of the piezoelectric ceramic.     

Effect of water content on the piezoelectric properties of nylon 11 and nylon 7

A study of the effect of absorbed water on the piezoelectric properties of Nylon 11 and Nylon 7 films has been carried out. Films were prepared by slow cooling from the melt or by quenching rapidly into ice water. Poled films were soaked in distilledde-ionized water and the piezoelectric strain coefficientd ₃₁, piezoelectric stress coefficiente ₃₁, dielectric constant, and elastic modulusc measured continuously as the films dried out in a stream of dry nitrogen gas. The results obtained show that the piezoelectric response of poled Nylon 11 and Nylon 7 films is sensitive to adsorbed water, the sensitivity being greater for Nylon 7 than for Nylon 11. These observations are discussed in terms of the effect of water on molecular relaxation of these polymers.     

Complete set of material properties of [011](c) poled 0.24Pb(In(1/2)Nb(1/2))O(3)-0.46Pb(Mg(1/3)Nb(2/3))O(3)-0.30PbTiO(3) single crystal

A complete set of elastic, piezoelectric, and dielectric constants of [011](c) poled multidomain 0.24Pb(In(1/2)Nb(1/2))O(3)-0.46Pb(Mg(1/3)Nb(2/3))O(3)-0.30PbTiO(3) ternary single crystal has been determined using resonance and ultrasonic methods and the temperature dependence of the dielectric permittivity has been measured at 3 different frequencies. The experimental results revealed that this [011](c) poled ternary single crystal has very large transverse piezoelectric coefficient d(32) = -1693 pC/N, transverse dielectric constant ε(11)/ε(0) ~ 7400 and a high electromechanical coupling factor k(32) ~ 90%. In addition, its coercive field is 2 times of that of the corresponding binary 0.7Pb(Mg(1/3)Nb(2/3))O(3)-0.30PbTiO(3) single system with much better temperature stability. Therefore, the crystal is an excellent candidate for transverse mode electromechanical devices.     

多相周期压电纤维复合材料反平面变形问题的解析解

研究了具有周期微结构的多相压电纤维复合材料在反平面变形下的电弹性场。通过在各非均匀相内引入非均匀的广义本征应变,将原问题等价为带有周期广义本征应变的均匀介质问题,建立了两者间的等价条件。利用等价问题各区域交界处的广义应力连续条件和广义位移协调条件,并结合双准周期Riemann边值问题理论和等价条件,获得了各相材料电弹性场的解析解,进而由平均场理论预测了材料的有效压电系数。比较了相同压电材料体积分数下中空压电纤维、碳芯压电结构纤维和实心压电纤维复合材料有效压电系数的差异,讨论了压电结构纤维中非压电芯刚度及压电结构纤维与基体间涂层的刚度对有效压电系数的影响。研究结果可为高灵敏度压电复合材料的设计提供有价值的参考。     

Analysis of vibration waveforms of electromechanical response to determine piezoelectric and electrostrictive coefficients

We developed a possible method to determine both coefficients of piezoelectricity (d) and electrostriction (M) at the same time by a waveform analysis of current and vibration velocity in the resonance state. The waveforms of the current and vibration velocity were theoretically described using the equations of motion and piezoelectric constitutive equations, considering the dissipation effect. The dissipation factor of the d coefficient and M coefficient is dielectric loss tangent tan δ. The waveforms measured in all of the ceramics, such as Pb(Zr,Ti)O(3) (PZT), Pb(Mg,Nb)O(3) (PMN), and 0.8Pb(Mg(1/3)Nb2/3)O(3)-0.2PbTiO(3) (PMN-PT), were well fitted with the calculated waveform. This fitting produced both the d and M coefficients, which agreed with those determined via the conventional methods. Moreover, the respective contributions of both piezoelectricity and electrostriction to the d value determined in the resonance-antiresonance method were clarified.     

Technique for nonuniform poling of piezoelectric element and fabrication of Gaussian transducers

A new technique has been developed to polarize piezoelectric ceramic elements with a nonuniform electric field. Used as an ultrasonic transducer, the piezoelectric element will produce a corresponding nonuniform sound field. Ultrasonic transducers for generating specific field profiles can therefore be made by having a predetermined spatial pattern of polarization strength poled into the piezoelectric element. One of the desirable beam profiles is a Gaussian; it has the advantages of being free from near-field fluctuations and far-field sidelobes, and it is much easier to model than the usual piston transducers. This method was used to fabricate Gaussian beam transducers, and their measured field profiles compared well with the Gaussian beam model. Such transducers containing the built-in Gaussian amplitude profile can be electroded and mounted in the same manner as conventional piston transducers.     

Nano piezoelectric/piezomagnetic energy harvester with surface effect based on thickness shear mode

BackgroundEnergy harvesters with piezoelectric materials are widely discussed for the new kinds of smart structures. However, reports on the energy harvesters at the nano scale which have large potential applications in the future are rather limited.MethodsIt’s well known that the surface or interface stress can affect the mechanical properties of nanostructures. This work proposes the nano energy harvester with piezoelectric/piezomagnetic structure, in which the thickness-shear mode is considered by the surface stress model.ResultsThe vibration motion and output power density are derived and calculated. The peak value of the power density can be enlarged by increasing the residual surface stress and the surface effect on the nano-plate energy harvester can be influenced by both the surface piezoelectric and piezomagnetic elastic constants. Moreover, the harvesting ability can be improved by increasing the thickness of the piezoelectric layer.ConclusionThe capability of the energy harvester depends on the residual surface stress and the surface material constants. The proposed model provides the possibility of applying nano composite structures to the energy harvester.     

Enhanced magnetoelectric effect in multiferroic composite beams due to flexoelectricity and transverse deformations

This paper is concerned with the exploration of the role of transverse normal and shear deformations on enhancing the magnetoelectric (ME) coefficient of multiferroic bilayer composite beams composed of a piezoelectric layer and a piezomagnetic layer. Analytical models have been derived based on the displacement field which accounts for both the transverse normal and shear deformations, Timoshenko beam theory and Euler Bernoulli beam theory. The induced flexoelectricity in the piezoelectric layer due to axial strain gradient and transverse shear strain gradient has also been taken into consideration for estimating the ME coefficient. It has been found that the contribution of transverse normal strain in the piezoelectric layer for enhancing the ME coefficient is significantly larger than that due to axial strain, transverse shear strain and flexoelectricity. For the particular values of the thicknesses of the piezoelectric layer and the piezomagnetic layer, the ME coefficient remains invariant for both thick and thin multiferroic composite beams.     

Application of the concepts of fracture mechanics to the failure of conductive cracks in piezoelectric ceramics

In the present paper, we report the success of applying the concepts of fracture mechanics to the failure of electrically conductive cracks in piezoelectric ceramics. We reexamine the charge-free zone model and the experimental results on poled lead zirconate titanate ceramics. We use the secant piezoelectric constant to describe the piezoelectric behavior at high electric field near a conductive crack tip. With this modification, the charge-free zone model provides more physical insight into the failure behavior of electrically conductive cracks in piezoelectric ceramics.     

Poled Composites with Nd-Mn-Doped PZT Fibers Under Bipolar Electrical Load

Using the sol-gel process, Nd-Mn-doped PZT fibers were produced. The PZT was doped with 2 mol% neodymium and 1.1 mol% manganese. For characterization, the fibers were embedded in a polymer. The resulting 1-3 composites were poled with constant electric field. Strain and polarization were measured by applying a bipolar sinusoidal voltage of high amplitude. Instead of the expected shifted butterfly-shaped strain hysteresis, an asymmetric strain-field relation was observed. It is characterized by a rather linear region in direction of the poling field and an inflated region without strain switching for reversed polarity. Within the temperature range from room temperature to 80degC, the strain switching seems to be suppressed. Measurements of the piezoelectric coefficient at superimposed electric field prove the blocking of strain switching. Cyclation experiments with sesquipolar load show a pronounced linearity of the strain loops that declines after more than 2 times 10⁴ cycles.     

Full tensorial elastic, piezoelectric, and dielectric properties characterization of [011]-poled PZN-9%PT single crystal

Transverse piezoelectric property of 0.91Pb(Zn(1/3)Nb(2/3))O(3)-0.09PbTiO(3) (PZN-9%PT) single crystal poled along [011] direction under different fields have been investigated, the poling field giving the best property was between 350 and 650 V/mm at room temperature. Full tensorial elastic, dielectric, and piezoelectric properties of PZN-9%PT single crystal poled along the [011] direction under 500 V/mm have been determined by resonance and ultrasonic methods. It was found that the electromechanical coupling coefficients k(32) and k(33) can reach 0.90 and 0.89 and the piezoelectric coefficients d(32) and d(15) are -1705 and 2012 pC/N, respectively. This complete set of physical properties can provide convenience for piezoelectric device fabrication and domain engineering studies.