Electrostrictive Ceramics Research Articles

Mechanics of electroelastic bodies under biasing fields

This is a review article on the mechanics of small-amplitude motions superposed on finite biasing or initial fields in an electroelastic body. It begins with a summary of the nonlinear theory of electroelasticity, which is the theoretical foundation for the theory of small fields superposed on a bias. This theory, obtained by different approaches, and the development of structural theories for electroelastic beams, plates, and shells under biasing fields are discussed. Applications of these theories for small fields superposed on biasing fields in the buckling of thin electroelastic structures, frequency stability of piezoelectric resonators for time-keeping and telecommunication, acoustic wave sensors based on frequency shifts due to biasing fields, characterization of nonlinear electroelastic materials by propagation of small-amplitude waves in electroelastic bodies under biasing fields, and electrostrictive ceramics which operate under a biasing electric field are reviewed. A summary of some current and possible future research topics in this field is given. The article contains 166 references.

Effect of uniaxial stress on the large-signal electromechanical properties of electrostrictive and piezoelectric lead magnesium niobate lead titanate ceramics

The electromechanical performance characteristics of electrostrictive 0.9 Pb(Mg1/3Nb2/3)O3–0.1 PbTiO3 and piezoelectric 0.7 Pb(Mg1/3Nb2/3)O3–0.3 PbTiO3 ceramics have been investigated under uniaxial stress (σ). The results demonstrate that the large-signal electromechanical properties of electrostrictive ceramics are decreased with increasing σ, whereas those of the piezoelectric are increased but accompanied by significantly increased hysteretic losses.

Comparison of the Nonlinear Coefficient of a Second-Higher Term between PZT ferroelectric and PMN electrostrictive ceramics

Comparison of the Nonlinear Coefficient of a Second-Higher Term between PZT ferroelectric and PMN electrostrictive ceramics

Comparison of Nonlinearity between Lead Magnesium Niobate Electrostrictive and Lead Zirconate Titanate Piezoelectric Ceramics

Nonlinear phenomena, such as generation of higher harmonic voltages, change in resonance frequency and current-jumping, were compared between lead zirconate titanate (PZT) piezoelectric and lead magnesium niobate (PMN) electrostrictive ceramics. This comparison was carried out in order to discuss the effect of domain wall motion on the nonlinear behavior that appears during high-power driving at around resonance frequency. A dc bias of 700 V was applied to PMN to produce piezoelectric resonance. Sufficient piezoelectric resonance was consequently obtained for the discussion of the nonlinear behavior. In contrast to PZT with a marked nonlinear behavior, any nonlinear phenomenon did not appear in PMN without any domain walls.

Nonlinear strain and DC bias induced piezoelectric behaviour of electrostrictive lead magnesium niobate-lead titanate ceramics under high electric fields

Laser Doppler interferometry has been used to determine the strain and piezoelectric response of Pb(Mg1/3Nb2/3)O3-PbTiO3 (PMN-PT) electrostrictive ceramics as a function of electric fields up to 4 MV m-1, frequencies between 0.1 Hz and 2.5 kHz and DC bias fields up to 3 MV m-1. The strain and polarization of PMN-15 with a composition of 0.9PMN-0.1PT and PMN-38 with a composition of 0.85PMN-0.15PT both produced by TRS ceramics, have been measured at room temperature. The strain and polarization responses of PMN-15 ceramics under an electric field up to 4 MV m-1 have been fitted to a polynomial model. The results suggest that a quadratic dependence of strain on polarization is not valid for large electric fields and that higher-order terms must be included. Our measurements showed that the effective piezoelectric coefficient, d33, of PMN-15 ceramics had a maximum value of 800 pm V-1 at a bias field of 0.67 MV m-1 and had little frequency dependence in the frequency range from 1 Hz up to 2.5 kHz. PMN-38 ceramic showed a maximum d33 of 1200 pm V-1 at a bias field of 0.43 MV m-1 and the d33 of this material showed a clear frequency dependence from 1 Hz up to 2.5 kHz.

Processing, Characterization, and Dielectric Studies on K(Ta1−xNbx)O3 for Use at Cryogenic Temperatures

Development of the next generation space telescope, to supplement the Hubble Space Telescope, has heightened the need for cryogenic actuators. High performance electromechanical materials are needed for use from 10 to 77 K. The use of piezoelectric materials to satisfy this need involves major property trade‐offs; consequently, alternative materials are of interest—the electrostrictive ceramics. The electrostrictors operate above their “Curie” (transition) temperature, and have electromechanical properties that can be superior to conventional piezoelectric materials. Because work on the electrostrictive materials is limited, the K(Ta,Nb)O3 solid solution system has been chosen as a viable material for use at cryogenic temperatures. These solid solutions have predicted transition temperatures in the range of 4 to 150 K. Two separate KTaO3 powders were synthesized with 10 and 17.5 mol% Nb2O5 doping levels. The powders were synthesized via a conventional mixed oxide route and materials were fabricated using a tape cast and laminating technique. Powders and samples were characterized using laser scattering, scanning electron microscopy, and surface area analysis to determine particle size distribution and morphology, powder X‐ray diffractometry for phase composition, and dielectric response as a function of frequency and temperature. Tape casting and lamination produced final samples that were fabricated to ∼88% of theoretical density. Dielectric measurements resulted in Curie temperatures of 248 and 123 K, and weak‐field permittivity values of ∼2700 and 4000 for 17.5 and 10 mol% additions of Nb2O5 to KTaO3.

Quasistatic coupling coefficients for electrostrictive ceramics

A generalized definition of the coupling coefficient, useful for the evaluation of transducers that incorporate an electrostrictive active element, is introduced. The definition is expressed under quasistatic conditions and becomes zero when no bias is applied (assuming that the effects of remanence are negligible), and remains zero under zero bias even when a significant prestress is present. This reflects a property of the piezoelectric coupling coefficient, which vanishes when the ceramic becomes depoled. The behavior of this definition thus differs from that of another definition, introduced elsewhere, which produces a significant nonzero result at zero bias. [See C. Hom et al., “Calculation of quasi-static electromechanical coupling coefficients for electrostrictive ceramic materials,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 41, 542–551 (1994).] The present definition also leads in a natural way to a coupling coefficient for biased piezoelectric ceramics, and an equation is given for that case. Moreover, in the case of a biased electrostrictive ceramic it is found that a coupling coefficient derived from an equivalent circuit [J. C. Piquette and S. E. Forsythe, “Generalized material model for lead magnesium niobate (PMN) and an associated electromechanical equivalent circuit,” J. Acoust. Soc. Am. 104, 2763–2772 (1998)] gives an excellent approximation to the exact value, and is found to be accurate to within a few percent for drive amplitudes as high as 75% of the bias. It is shown that maximizing the coupling coefficient automatically discriminates against transducer designs (and operating conditions) that would produce significant harmonic distortion.

Apparent Young's modulus in PMN-PT electrostrictive ceramics

Some electrostrictive ceramics like 0.9 PMN-0.1 PT show large reduction of the apparent Young's modulus (more than 50%) as a function of the electric field. In the literature, this result is always obtained in the direction of the applied electric field. We performed some measurements of the elastic modulus in the direction perpendicular to the electric field and we found an unexpected small variation (less than 6%). This result shows that the apparent mechanical properties are much more dependent of the direction of the electrical field than known previously.

Biased resonance measurements as predictors of large-signal performance of PMN-PT

The large-signal performance of electrostrictive materials, such as lead magnesium niobate-lead titanate, is of critical importance to sonar and actuator designers. However, obtaining these large signal parameters properly, particularly under compressive prestress, is expensive and time consuming. The complexity of these measurements precludes them as a method for quickly and easily screening materials. Traditionally, resonance measurements, which otherwise are relatively simple to perform, have been used, but they suffer from the drawback that the material parameters obtained are at the incorrect frequency and under no prestress. Furthermore, the significance of the results of resonance measurements for nonlinear materials is unclear. It has recently been suggested [Hom and Shankar, IEEE Trans. Ultrason. Ferroelectr. Freq. Control UFFC-46, p. 1422, 1999] that dc biased resonance measurements on electrostrictive ceramics would be an accurate predictor of the coupling factor and optimum bias point. Here, dc biased resonance measurements on several formulations, with varying dielectric maximum temperatures, are analyzed to determine which composition has the highest predicted coupling factor. This prediction is compared with large signal quasistatic measurements conducted on NAVSEAs SDECS (stress-dependent electromechanical characterization system). The predictive ability of the resonance measurements is analyzed as a function of temperature. [Work supported by ONR.]

Investigations of electrostrictive Pb(Mg1/3Nb2/3)O3–PbTiO3 ceramics under high-power drive conditions: Importance of compositional fluctuations on residual hysteresis

The high-field polarization behavior of electrostrictive Pb(Mg1/3Nb2/3)O3–PbTiO3 ceramics has been investigated as a function of measurement frequency, drive field, and temperature. It was observed that hysteretic losses increase with increasing frequency. Significant variations in loss were found between specimens of similar composition obtained from different sources, which became more pronounced with increasing temperature. The results indicate that careful synthesis and processing are crucial to the thermal stability of electrostrictive ceramics in high-power source applications. Further investigations revealed the potential use of accelerated aging by substituent introduction for mitigation of thermal stability concerns.

The field and frequency dependence of the strain and polarisation in piezoelectric and electrostrictive ceramics

A laser Doppler interferometer system has been used to measure the strains of ferroelectric ceramics. The strains and polarisation of piezoelectric and electrostrictive ceramics have been investigated as a function of electric fields up to 4 MV/m in the frequency range from 0.01 Hz up to 1 kHz. The field and frequency dependence of the appropriate material constants have been calculated. Results on a range of piezoelectric PZT and electrostrictive PMN-PT ceramic materials are presented.

Temperature dependence of electrostrictive properties of PMN-PT-LA ceramics

The temperature dependence of the material properties of PMN-PT-La (0.85/0.15/1%) electrostrictive ceramics manufactured by TRS Ceramics Inc. have been investigated. The measurements reported here include: the temperature and frequency dependence of dielectric permittivity and dissipation, the quasi-static strain as a function of applied electric field, and the DC biased resonance characterisation of the dielectric, elastic and electromechanical coefficients at temperatures below, near, and above Tmax.

Characterization of 0.9PMN-0.1PT Patches for Active Vibration Control of Plate Host Structures

Current applications in active vibration control mainly use piezoceramic actuators (PZT). With the aim of improving vibration absorption, electrostrictive actuators have been elaborated. These electrostrictive ceramics show very attractive properties for active vibration control applications. Yet, their non-linear electromechanical behavior tempers these numerous advantages and considerably complicates their use. In usual active vibration control applications, dynamic electric fields with varying magnitudes and frequencies are applied to the ceramic. Earlier measurements, performed at ONERA, showed that the ceramic behavior is strongly sensitive to operating parameters (electric field magnitude, excitation frequency, and surrounding temperature). It is demontrated in this paper that this sensitivity can be reduced to a sensitivity of the material to its own temperature. Indeed, a significant heating of electrostrictive ceramics occurs when they are subjected to a variable electric field. This heating turns out to be, itself, dependent on operating parameters. An experimental electric model of stress-free electrostrictive patches is here presented, taking into account this thermal phenomena. This model is then used to develop constitutive relations for these materials with the view of using them as actuators in active vibration control of thin plate structures.

Electrostrictive ceramics for low-frequency active transducers

Electrostrictive ceramics based on Pb(Mg(1/3)Nb(2/3 ))O(3) have demonstrated promise as low-frequency active materials. They broaden the range of design options by providing a mix of properties unavailable in traditional piezoceramics. Typical properties are: 1000 microstrain on the interval 0-1 MV/m with a k(33) of 0.5; high-field electrical impedance ~5 times that of traditional piezoelectrics; graceful, predictable, and repeatable property variation with temperature, frequency, and prestress; recoverable change of properties with temperature. Unipolar excitation at fields less than 1 MV/m is typical to provide direct frequency conversion and prevent corona discharge and reliability issues within transducers. Although electrostrictive ceramics are not direct replacements for traditional piezoceramics, they have many similarities in physical and chemical properties. The differences are most obvious in the electromechanical response behavior with changes in bias field, drive level, frequency, and prestress. In addition, the "rules-of-thumb" for traditional piezoceramics, both processing and use, do not wholly apply to electrostrictive ceramics. The development and present state of the art in electrostrictive ceramics for low-frequency uses are detailed.

Hot topics in engineering acoustics

Underwater acoustic transduction has been undergoing great changes in modern device designs. After several decades of advancements in acoustic sensing technologies, current interests have included novel and application-specific designs in underwater acoustic projection. These changes are an outgrowth of advances in materials processing and manufacturing. The incorporation of newer materials is resulting in devices that are specifically tailored for individual applications as opposed to general designs that in the past have been used to cover a variety of applications. This presentation will introduce the concepts of the new materials advances, including piezocomposites, piezopolymers, electrostrictive ceramics, single crystals, hybrid piezoelectric ceramic/magnetostriction devices, and microflextensional drivers called cymbals. The state of development of these technologies will be introduced as they are being incorporated into new devices. The talk will show prototype designs and discuss future directions. [The continuing support of ONR 321 is gratefully acknowledged.]

Modeling resonance tests for electrostrictive ceramics

The electromechanical coupling coefficient represents a useful figure-of-merit for comparing the quality of different electroactive materials. However, the coupling coefficient for an electrostrictive ceramic is not a unique material parameter, because it depends strongly on the applied DC bias field, AC field amplitude and frequency, and stress. These dependencies make direct comparison between electrostrictors and piezoelectrics somewhat ambiguous. In this paper, we developed a pair of coupling parameters for electrostrictors that were strictly material constants and completely characterized the material's electromechanical quality. We proposed relatively simple, inexpensive resonance testing to measure these new parameters from the electrical admittance of a vibrating electrostrictive rod. The electromechanical coupling coefficient for a specific loading condition is computed from these parameters, allowing direct comparison between electrostrictive and piezoelectric materials.

The stress dependence of the piezoelectric d coefficient of piezoelectric and electrostrictive ceramic materials

An experiment has been developed to measure the piezoelectric d coefficient as a function of uniaxial stress on a piezoelectric or electrostrictive ceramic material. Measurements on piezoelectric ceramic specimens show that there is a very significant enhancement in the value of the piezoelectric coefficient as a function of applied stress with the value of the coefficient going up by a factor of about 2.5 over a 100-MPa range of applied stress. The increase in the piezoelectric coefficient continues until the stress is large enough for the ceramic to start depoling. Electrostrictive ceramics also show a similar trend, although their lack of mechanical strength prevents measurements over a large range of stress. Our results suggest that the performance of transducers can be enhanced by ensuring that the active piezoelectric material is under stress. [Funding support from the U.S. Office of Naval Research is gratefully acknowledged.]

The characterisation and modelling of electrostrictive ceramics for transducers

We have measured the electromechanical properties of the “reversible” electrostrictive ceramic (TRS Ceramics Inc) PMN/PT/La (0.9/0.1/1%) at room temperature, which is slightly above Tmax, the temperature at which the real part of the material's low frequency permittivity has a maximum. Under DC bias fields up to about 0.5 MV/m, the material behaves as a piezoelectric ceramic material with C\\infty symmetry. The effective piezoelectric and electromechanical coupling coefficients having a linear dependence on the bias field while the dielectric constant (at constant stress) and elastic constant (at constant field) are found to have a quadratic dependence on the bias field. Under higher bias fields, the piezoelectric and electromechanical coupling coefficients begin to saturate. In order to understand our measurements, we have used Mason's model for electrostriction and we have developed a nonlinear macroscopic model for electromechanical materials based on a Taylor's series expansion of the thermodynamic potentials to third and higher order terms in field and stress. The resonance equations for the DC biased length extensional resonator have been obtained and DC biased resonance techniques are shown to be useful in determining the electrostrictive and other higher order coefficients. The saturation at higher bias fields arises from higher fourth order terms (S∞kE4, with k negative) that result from saturation in the dielectric response.

Approximate Green's functions and a boundary element method for electro-elastic analyses of active materials

A boundary element method (BEM) for the analysis of two-dimensional, time independent problems of linear electro-elasticity is presented. Emphasis is given to the derivation of representation formulas and fundamental solutions as well as to the construction of an efficient numerical algorithm. The method is particularly suitable for studying the behavior of active materials such as electrostrictive, ferroelectric and piezoelectric ceramics. Two numerical examples with direct impact on the structural safety and reliability of piezoceramics are provided to demonstrate the virtues of the new BEM.

Investigation of crystallographic and bulk strain in doped lead magnesium niobate

Using an in situ x-ray diffraction (XRD) technique, the electric-field induced change in the d-spacings Δd/d of the individual microcrystals or “crystallographic” strain is measured on lead magnesium niobate—lead titanate—barium titanate electrostrictive ceramics of composition 0.970(0.900PMN−0.100PT)−0.030BT from zero field to saturation. This crystallographic strain is then compared to the bulk longitudinal strain as measured by Δl/l using a photonic sensor. The crystallographic electric-field induced strain behavior for virgin samples could be fit to a constitutive model, where the induced strain is proportional to the square of the polarization with an electrostrictive coefficient Q determined to be 1.4 (×106 cm4/C2). Attempts to fit the bulk strain behavior on the same sample required lower values of the electrostrictive coefficient Q∼1, and generally yielded worse fits where the model predicted greater than the observed strain values at low electric fields. Subsequent in situ XRD measurements on previously electric-field cycled samples yielded much lower crystallographic strain values with a significantly different electric field dependence.