Resonance methods were used to determine the variation of several piezoelectric, elastic and dielectric constants, as well as the corresponding electromechanical coupling factors of soft and hard doped Pb(ZrxTi1-x)O3 (PZT) ceramics, with compositions near the morphotropic phase boundary (MPB), as a function of temperature ranging from −165 °C to 195 °C. The material constants were obtained by analyzing the fundamental resonance of the impedance or admittance spectra as a function of frequency for several sample resonance geometries. The piezoelectric constants d33 and −d31, as well as the dielectric constants εT33, generally increased with temperature for both soft and hard PZT samples. However, the elastic constants sE11 and -sE12 exhibited abnormal variations seen as broad peaks over parts of the tested temperature range. Furthermore, thermal hystereses were observed in all the studied material constants during the heating and cooling cycles. Finally, it was noted that, overall, the material constants of soft PZT varied significantly more than those of hard PZT under changing temperature conditions.
Electric-field-induced phase transitions and piezoelectric properties of <001>-oriented Pb(Mg1/3Nb2/3)O3-32%PbTiO3 (PMN-PT) single crystals have been investigated as a function of temperature. It was found that the phase transitions and piezoelectric properties for PMN-PT crystals are strongly dependent on temperature. The measurements of polarization and longitudinal strain as a function of a unipolar electric field show that the field for the induced monoclinic-tetragonal phase transition decreases linearly with temperature in the range between 23 °C and 75 °C. Raising the temperature can stabilize the tetragonal phase in <001>-oriented PMN-PT crystals. The effective longitudinal piezoelectric constant, d33, in the monoclinic phase increases with temperature. Meanwhile in the field-induced tetragonal phase, d33 is much smaller and has little change with temperature. The electric-field-induced phase transition from a cubic phase to a tetragonal phase was observed at 125 °C.
Dielectric elastomers are known to produce large transverse strains in response to electrically induced Maxwell stresses and thus provide a useful form of electromechanical actuation. The transverse strain response of silicone (Dow Corning HS III RTV) based Maxwell stress actuators have been measured earlier as a function of driving electric field, frequency and pre-load. Experimental results show that a pre-load initially causes an increase in the strain. However, this increase appears to be a function of the relative geometries of the electroded area and of the specimen itself. The transverse strains in these materials decrease when larger values of pre-load are applied. Models of hyperelasticity that are capable of describing the large deformation of polymer materials have been used to interpret our results. Numerical finite element simulations of the material’s behavior using a hyperelastic model provides good agreement with most of our observations on the electric field and pre-strain dependencies of the transverse strain.
Some electroactive polymers produce large electric-field-induced strains that can be used for electromechanical actuation. The measurement of the strain response, especially the dynamic response under high driving fields, is difficult. We have developed a transverse strain measurement system based on the Zygo laser Doppler interferometer. The system can measure transverse strain responses of polymer samples of different sizes over a wide displacement range and a frequency range from DC up to 100 Hz. We have used this interferometric system to investigate the strain response of Maxwell stress actuators fabricated from silicone (Dow Corning HS III RTV) and thermoplastic polyurethane (Dow Pellethane 2103) films. The static and dynamic strain responses of the materials to a variety of driving electric fields such as step fields, AC fields and DC bias fields have been measured as functions of amplitude and frequency. The strain response has a quadratic relationship with the driving field and shows a strong dependence on the frequency of the applied field. Of the two kinds of polymers investigated, HS III silicone polymer shows higher strain and breakdown fields. High transverse strains of 3.25 % (static) and 2.08 % (dynamic at 1 Hz) for HS III silicone polymers have been obtained. In addition, the effect of mechanical tensile load on the transverse strain has also been studied. The experimental data are interpreted in terms of measured material properties and small strain models for dielectric film actuators.
Single crystals of the relaxor ferroelectric solid solution family Pb(Zn1/3Nb2/3)O3-PbTiO3 (PZN-PT) have been shown to produce very high levels of electric field induced strains with large electromechanical coupling coefficients when poled aong the <001> direction. These materials also exhibit a high dielectric permittivity and they are therefore very promising materials for transducer and actuator applications. We have carried out a systematic investigation of the dielectric and piezoelectric properties of different compositions, using specimens manufactured by TRS Ceramics Inc. Both the dielectric and piezoelectric strain responses of these crystals have been studied as a function of temperature and applied electric field. The applied field and temperature dependences of the rhombohedral to tetragonal and the tetragonal to cubic phase transitions have been determined. Our results suggest that a DC bias field can be used to stabilize the tetragonal phase. The strain measurements have been used to determine the d33 values in both phases as a function of temperature. The PZN-PT crystals have their polar direction along the <111> axis but not much has been reported on the piezoelectric properties of crystals poled in this direction. We have used laser Doppler interferometry to measure the piezoelectric strains as a function of DC bias field applied in the <111> direction in PZN-PT crystals and we have determined values of the piezoelectric coefficients as a function of the DC bias field. High d15 values over 3000 pC/N have been observed along <111> direction.
The nonlinear behavior of the dielectric and piezoelectric resopnse of <001> oriented Pb(Zn1/3Nb2/3)O3-xPbTiO3 (PZN-PT) single crystals for x=4.5% and x=8% have been investigated as a function of AC electric fields and DC bias field. At relatively low applied fields, the polarization and strain of PZN-PT single crystals poled along the <001> direction show little hysteresis and have a linear dependence on the applied field, which is a consequence of engineered domain stability. Hence, the dielectric and piezoelectric coefficients of the material do not exhibit any field dependence. However, when the applied electric field exceeds a threshold value, the strain and dielectric responses become nonlinear. The dielectric and piezoelectric constants are a function of the applied field, and hysteresis loops are observed. The results suggest that the observed nonlinear behavior in the PZN-PT single crystals is caused by domain motion/switching in response to the large AC fields. Applying a positive DC bias can effectively stabilize the domain configuration in the crystals and enhance linear responses. The threshold field, at the onset of nonlinearity, is found to have a linear relation with DC bias field in the field range investigated.
Sensors and actuators based on piezoelectric ceramics are finding an increasingly large variety of applications under a very wide range of environmental conditions and applied signals. Some actuator applications require the piezoelectric materials to support large mechanical loads and produce high strain output. In order to accomplish this requirement of higher strains, large electric fields must be applied. This results in a significant non-linear behavior and hence affects the performance of the material. It is therefore important to understand the behavior and properties of these materials over a large range of temperature, frequency and applied electric fields and mechanical stresses. We have measured some of the dielectric, elastic and piezoelectric constants of soft (EC-65, EC-76) and hard (EC-64, EC-69) lead zirconate titanate (PZT) piezoelectric ceramics, manufactured by EDO Ceramics, as a function of temperature, frequency, applied field and applied stress. We have also determined the dependence of the piezoelectric constants on an applied DC bias voltage or stress. The time dependence of the piezoelectric response in the piezoelectric ceramics has also been studied. A summary of the results will be presented. Most of these results can be understood on the basis of the extrinsic contributions to the piezoelectric response that arises from the existence of domains in the material.
Piezoelectric transducers are often used under compressive stress in smart structure and other applications and it is therefore important to know properties of these materials as a function of applied stress. We have developed an experiment that allows us to find the piezoelectric charge coefficient as a function of uniaxial stress in the poled direction . Both dynamic and static measurements were carried out and the corresponding values of the charge coefficient d33 were obtained as a function of applied stress. These coefficients differ from each other because of the different proportions of reversible and irreversible domain changes that contribute to them and each coefficient can be important in specific applications. Results on a range of PZT ceramics manufactured by EDO Corporation are presented; in general, they show a non- linear behavior with an initial increase in d33 as the stress increases followed by a significant decrease. The time dependence of the measurement has also been investigated.
We present a non-linear theory for electromechanical materials based on a Taylor's series expansion of the thermodynamic potentials to 3rd and higher order terms in field and stress, and we show that this general theory is applicable to both piezoelectric and ideal electrostrictive materials depending with an appropriate choice of material coefficients. The model allows for the non-zero piezoelectric behavior found in some nominally electrostrictive materials. The quasistatic non-linear equations used to describe low frequency electromechanical devices are shown to account for saturation in both strain and polarization as well as the stress dependence. The `reversible' electrostrictive ceramic PMN/PT/La (0.9/0.1/1%) operating above Tmax is used to illustrate the suitability of the model. Under a DC bias field, these materials behave as a piezoelectric ceramic material with C∞) symmetry. The effective piezoelectric is found to be linear as a function of the DC bias field up to about 0.5MV/m. Above 0.5 MV/m, the piezoelectric and the electromechanical coupling constants begin to saturate due to higher 4th order electrostriction (S ∝ kE4 with k negative), which is shown to be the result of the saturation in the dielectric response. A switchable, low field, linear component of the piezoelectric voltage coefficient, g, is found in the S vs D response. The g coefficient is found to change sign depending on the sign of the measurement field. These materials behave as a tunable piezoelectric with the piezoelectric coefficient being directly proportional to the electrostrictive coefficient and the DC bias field, up to saturation.
Electrostrictive materials, such as the ceramic PMN/PT/La, operating above Tmax with a DC bias field behave as a piezoelectric ceramic materials with CINF symmetry. The effective piezoelectric and electromechanical coupling coefficients are found to be linear as a function of the DC bias field up to about 0.5MV/m, while the elastic constant and the dielectric constant are found to have a quadratic dependence on the DC bias field. Above 0.5 MV/m the piezoelectric and the electromechanical coupling constants begin to saturate due to higher 4th order electrostriction. In essence these materials behave as tunable piezoelectric materials with the piezoelectric coefficient being directly proportional to the electrostrictive coefficient and the DC bias field up to saturation>. The properties of DC biased resonators of this material are derived from a non-linear theory based on the Taylor's series expansion of the thermodynamic potentials to 3rd and higher order terms in field and stress. The resonance equations for the DC biased length extensional resonator are presented and it is shown that DC biased resonance techniques can be used to measure the electrostrictive and other higher order coefficients at frequencies of interest to the ultrasonics community. The experimental apparatus used to measure these properties will be described and the limitations with regards to isolation of the measurement signal and the DC bias signal will be discussed. We will show that these materials, in conjunction with standard piezoelectric ceramics, offer the transducer design engineer an extra degree of freedom and the feasibility of unique transducer designs that will allow, for example, multiple beam patterns from the same circular/linear array using an adjustable DC bias profile on the array or the possible use of the field dependence of the compliance to fabricate electrically active backing materials. In conclusion we discuss how a better understanding of the macroscopic theory of piezoelectric and electrostrictive materials can benefit the transducer designer.
We describe an experiment in which a ramped or step stress can be applied to a piezoelectric sample and the charge generated on the sample can be determined by measuring the short-circuit current with a very high impedance electrometer. The low frequency direct piezoelectric charge coefficient, d33, can then be determined and is found to be substantially non-linear in stress up to pressures of 60 MPa for all the types of Lead Zirconate Titanate (PZT) that we have studied. When a step stress is applied, the generated current shows a time dependence after the application of the stress and we believe that this is due to the relatively slow movement of 90 degree(s) domain walls in the ceramic. Our results can be understood on the basis of an activation energy model and average activation energies for the PZT types studied ranged from 0.2 to 0.7 eV. The charge coefficient is thus a function of the applied stress and of the temperature and frequency of measurement.
A set of thickness resonators of PVDF-TrFE copolymer have been characterized as a function of the frequency and DC bias. The first six resonance peaks in the impedance spectra were analyzed to determine the degree of frequency dispersion in the complex elastic, piezoelectric, and dielectric constants. Modeling the dispersion in the material constants as a polynomial in the frequency f produced an excellent fit to the data over the 1 - 30 MHz frequency range. The samples were then tested for non- linearity by analyzing the fundamental resonance as a function of a DC bias field. The field dependence of the PVDF-TrFE samples was much smaller than for comparable samples of a soft PZT.
The results of our analysis of a set of lead zirconate titanate (PZT-5H)/hard polyurethane 1 - 3 piezoelectric composites produced by injection molding are presented. Two groups of samples with 15 and 30 volume percent PZT were analyzed using impedance resonance techniques. Results from the thickness, radial, length thickness, thickness shear, and the length extensional modes allow the determination of the effective material constants. The complete effective (sE, d, (epsilon) T) matrix is presented for the two compositions. The limitations of using resonance techniques to determine composite material properties are discussed.
This paper reports on our determination of the small signal properties of Motorola 3203 HD, including the effects of losses and dispersion, and it shows the limitations imposed by assuming that the material is loss-less. A set of PZT 3203 HD unloaded resonators manufactured by Motorola was cut to specifications outlined in the IEEE Standard on Piezoelectricity Std 176-1987 to ensure the appropriate boundary conditions of each resonance mode. Impedance spectra of the thickness, thickness shear, length and length thickness extensional modes were analyzed at the fundamental and second resonances using Smits' method while the analysis of the radial mode resonators was accomplished using a method that we had developed earlier. Using the results from the above analysis we have determined the 10 independent complex constants (S11E, S12E, S13E, S33E, S55E, d13, d33, d15, (epsilon) 11T, and (epsilon) 33T) that define the reduced matrix for a C(infinity ) piezoelectric material at the fundamental resonance frequency of the resonator. The use of complex material constants to account for the loss of linear systems is discussed and the relationship between the mechanical Q, dielectric tan(delta) , piezoelectric loss and the complex material constants are presented. The dispersion in the martial constants, except for S12E and S13E, was studied by evaluating the constants at the second resonance. The source of the major components of the dispersion has been determined to be due to external effects such as mode coupling for high impedance resonators and electrode sheet resistance for low impedance resonators. The size of loss components and the dispersion are shown to be significant and it is suggested that ignoring these effects will reduce the accuracy and predictive capabilities of transducer models.
The design of ferroelectric/piezoelectric smart structures is limited by the accuracy to which the material properties of the sensor/actuator materials are determined. In particular, it is important to understand the effects of losses, dispersion, and the non-linearities that become significant when large fields are applied. This paper presents the small signal properties, including losses of Motorola PZT 3203 HD, a typical piezoelectric material, and it reports on the field dependence of the material constants for large electric fields. A set of PZT 3203 HD unloaded resonators manufactured by Motorola was cut to specifications outlined in the IEEE Standard on Piezoelectricity Std 176-1987, to ensure the appropriate boundary conditions of each resonance mode. Quasi-static measurements were performed on some of the samples at various field levels above and below the coercive field of the material. The impedance/admittance spectra of the resonators were measured for different values of the DC bias field. In both cases the average slope as a function of field, which is a measure of the piezoelectric or the dielectric constant, was found to increase linearly with the maximum field applied. The values of the material constants determined from the DC biased spectra were found to be smaller by a factor of 4 - 6. This is attributed to differences in the nature of the measurements. The quasistatic measurements are done at high field and low frequency and involve irreversible domain switching. The DC bias measurement is at high frequency and the AC measurement field is much smaller and the domain motion is reversible.
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