Electrostrictive Strain Research Articles

Design of a Mach - Zehnder interferometer for the measurement of electrostrictive strains

The investigation of quadratic electrostriction of non-ferroelectric crystals is interesting from a fundamental point of view, because this phenomenon of electromechanical interaction has not yet been completely elucidated. The extreme smallness of the dilatations that have to be measured ( m) has made the development of advanced interferometric systems necessary. Here, a new design concept of a double Mach - Zehnder interferometer is presented that allows one to apply a null method.

Reliability of ceramic multilayer actuators: A nonlinear finite element simulation

In a ceramic multilayer actuator, the abrupt end of an internal electrode concentrates the electric field, inducing stresses in the ceramic. Crack nucleation and growth have been observed experimentally, but have not been well modeled due to the complex material behaviors. We write a finite element program to solve this coupled electromechanical problem. The material is taken to be nonlinearly dielectric with electrostrictive strain quadratic in electric displacement. The program solves field distributions in a multilayer actuator, which are combined with fracture mechanics to obtain cracking condition. The calculations are compared with the existing analytical solution under the small-scale saturation conditions, and then extended to the large-scale saturation conditions. We show that the cracking condition established under the small-scale saturation conditions gives useful estimate even when the saturation zone is comparable to the actuator layer thickness.

Electromechanical Properties of Relaxor Ferroelectric Lead Magnesium Niobate-Lead Titanate Ceramics

In this paper, the results of a recent investigation of the dependence of the induced piezoelectric activity on temperature, electric bias field, and frequency and the electrostrictive response in the relaxor ferroelectric lead magnesium niobate-lead titanate ceramics ( (1- x)(Pb(Mg1/3Nb2/3)O3)- x(PbTiO3)) at compositions below 30% PT are presented. It was observed that the electrostrictive strain at temperatures near the dielectric constant maximum T max increases monotonically with increased PT content. For PMN:PT at compositions near 30% PT, the electrostrictive strain under a 10 kV/cm electric field can reach about 0.15% with very little hysteresis. An exceptionally large piezoelectric response with an effective piezoelectric d33 coefficient in the electric field induced state of over 1,800 pC/N could be achieved for selected PMN:PT compositions and electric bias fields.

Dielectric and electrostrictive properties of (1 – x) Pb(Mg1/3Nb2/3)O3−xPb(Mn2/3W1/3)O3 ceramics

The dielectric and electrostrictive properties of (1 - x) PMN−xPMW (x ⋚ 0.2) using chloride salts were investigated as a function of x. When the PMN-PMW powders were calcined at 700 °C for 1 h, the perovskite phase formed was 92%–97% at any given PMW composition (x ⋚ 0.2). With the increase of PMW content up to 0.2, the relative density of the specimens increased slightly, and the electrostrictive coefficient Q11 of the 0.8 PMN−0.2 PMW specimen increased about 6 × 10−2 m4/C2. However, the dielectric constant and electrostrictive strain of the specimens decreased despite the improved sinterability.

Boundary Conditions for Shape Memory in Ceramic Material Systems

Piezoelectric ceramics have excellent transduction capability in elastoelectric conversion and are widely used as both sensors and actuators for smart materials and systems. The very high authority in actuation (tons/in2) is limited in application by the very short throw (strains = 10-3) and there is urgent need to improve this strain capability. Since the polarization related piezoelectric and electrostriction constants in perovskites have a very limited range, to improve strain it is necessary to switch larger values of polarization. In this paper, phase change and domain switching systems which mimic the high strain of the metallic martensite shape memory alloys will be reviewed. Characteristic features necessary to ensure electrical control of the shape will be discussed and illustrated by three different families of perovskites. It is speculated that at very high switching speeds the electrostrictive domain strain may become 'uncoupled' from the polarization and evidence that this occurs in bismuth titanate is presented.

High field electrostrictive response of polymers

AbstractIt is well known that electrostrictive strains are proportional to the square of the applied electric field. It therefore appeared reasonable to assume that for some polymeric materials, a large acoustic thickness response, dT, \[ \left( {d_T = \frac{{dS}}{{dE}}} \right) \] might be obtained by application of high dc bias fields, ∼ 20 MV/m, to a film while driving the film with an ac signal to access the high slope region of the electrostrictive strain vs. applied field curve. Previous studies of crystallizing poly(vinylidene fluoride) (PVF2) from solution under high electric fields have demonstrated that gel‐like samples of PVF2 with high content of the plasticizer tricresyl phosphate (TCP) could be subjected to electric fields as high as ∼ 100 MV/m. Using this type of heavily plasticized PVF2 dT values ∼ 4 Å/V were obtained. Values of 9 Å/V were obtained for a certain class of thermoplastic elastomer (i.e., a polyurethane). These dT values are considerably greater than those obtained from conventional piezoelectric ceramic materials. In addition, large elastic strains (> 3%) were observed as a function of applied dc field. © 1994 John Wiley & Sons, Inc.

Electric field-induced antiferroelectric-to-ferroelectric phase transition in lead zirconate titanate stannate ceramics modified with lanthanum

Results of measurements in situ of electrostrictive strain, dielectric polarization, dielectric constant, and crystallographic parameters as functions of applied electric field in the temperature range 20–200 °C of Pb0.97La0.02(Zr0.66Ti0.11Sn0.23)O3 composition are reported. The antiferroelectric to ferroelectric phase transition with large volume change ΔV=0.35 Å3 is shown to be the dominant mechanism of the field-induced strain. The microscopic nature of the switching mechanism and the variation of the strain versus polarization squared at various temperatures are discussed.

Influence of processing methods on dielectric properties of 0.9Pb(Mg1/3Nb2/3)o3-0.1PbTio3with V2O5

Abstract 0.9PMN-0.1PT ceramics with V2O5 were prepared by both columbite precursor method and molten salt synthesis method. The V2O5 additive was incorporated as a mill addition to the calcined columbite precursor and a batch addition in the molten salt synthesis method, respectively. Microstructure and dielectric properties were investigated as a function of the amount of V2O5 and the sintering temperature. Dielectric constant and sinterability increased with increase of V2O5 addition up to 0.25 wt% and these properties were degraded by the further addition of V2O5. The level of phase transition diffuseness was enhanced with the increase of V2O5 content. The dielectric constant and the electrostrictive strain were found to be lower in the specimens prepared by the columbite method than in those prepared by the molten salt synthesis. These results were explained by the micro structure and phase analysis.

Synthesis and properties of lead zinc niobate: Pb(Zn1/3Nb2/3)O3based relaxor ferroelectrics

Abstract Lead zinc niobate [PZN: Pb(Zn1/3Nb2/3)O3] and compositions in the PZN-PbTiO3 system are promising materials for capacitors and actuators because of their high dielectric constant and excellent electrostrictive properties in single crystal form. PZN is one of the few relaxor ferroelectrics with high Curie temperature of about 140°C. The ceramic preparation of PZN or compositions near the morphotropic phase boundary in the PZN-PbTiO3 system still remains a challenge as the ceramics result in a mixture of perovskite and pyrochlore phases with poor properties. The perovskite structure in PZN can be stabilized by adding additives such as BaTiO3 or SrTiO3. During the last several years extensive work has been done to investigate the perovskite structure and the properties of several compositions in the PZN-BaTiO3 (SrTiO3)-PbTiO3, PZN-PbZrO3-PbTiO3, PZN-Pb(Ni1/3Nb2/3)O3-PbTiO3, and PZN-Pb(Mg1/3Nb2/3)O3-BaTiO3. In this paper the recent work done on synthesis and properties of PZN based ceramics in the above systems is reviewed. Many of these compositions offer the advantages of wide Curie temperature range, large dielectric constant, large piezoelectric coefficients and electrostrictive strains and low sintering temperature.

Cracking in ceramic actuators caused by electrostriction

Many perosvskite-type ceramics deform appreciably under electric fields; they make good actuators which deliver motions upon receiving electrical signals. High electric fields are usually applied to induce large strains. Fracture has been observed in the actuators under electrical loading. In this theoretical study, the phenomenon is examined on the basis of electrostriction and fracture mechanics. Attention is focused on a crack emanating from an internal electrode or a conducting damage path. At the edge of the conducting path, the electric field is intense and nonuniform, inducing incompatible electrostrictive strains. Consequently, a stress field is set up in the ceramic, localized around the edge of the conducting path. The condition for the stress to extend a crack is estimated by two models, using either quadratic or step-like electrostriction law. It is found that, under a given electric field, cracking is suppressed in a multilayer actuator if the ceramic layers are sufficiently thin.

Electrostrictive Properties of Pb(Mg1/3Nb2/3)O3-Based Relaxor Ferroelectric Ceramics

Perovskite-type Pb(Mg1/3Nb2/3)O3 (PMN)-based ceramics were prepared by modifying La(Mg2/3Nb1/3)O3 and PbTiO3. Dielectric and electrostrictive properties of modified PMN-based ceramics were investigated from the viewpoint of actuator materials. The temperature dependence of the dielectric constant, εs, shows a broader peak compared with that of pure PMN in the vicinity of room temperature. Transverse electrostrictive strain, S=-3.0×10-4, was induced under an applied electric field of 10 kV/cm.

Temperature-stable high electrostrictive strain relaxer ferroelectric ceramics for servo-actuator applications

For servo-type actuator applications, temperature-stable high electric-field-induced-strain electrostrictive lead magnesium niobate (PMN)-based relaxer ferroelectric materials are needed. The synthesis technique of the PMN-based composition with 100% perovskite phase is described. The effects of dopants and processing technology on the dielectric properties and electrostrictive properties are discussed in detail.

Electrostriction and polarization

Abstract Electrostriction, the mechanical strain x resulting from electric polarization P, is a second order effect: x = QP 2. In this paper, the phenomenological and physical origins of the Q coefficients are discussed from a qualitative point of view. As pointed out by von Hippel, the mechanisms of electric polarization are space charge effects, dipole reorientation, ionic displacements and electronic polarizability. Not all of these mechanisms are equally effective in producing electrostriction. We have examined the Q coefficients reported for a number of solids in order to understand the relationships between the polarization mechanisms and electrostrictive strain. Trends were identified in the structure-property relationships but several important questions remain unanswered.

PmC6. Giant electrostriction of ferroelectrics with diffuse phase transition - physics and applications

Abstract Giant Electrostriction (GE) of disordered ferroelectrics such as Ferroelectrics with Diffuse Phase Transition (FDPT) is noteworthy for application and basic researches. We present experimental data on the electrostrictive strain in FDPT. The description of the peculiarities of the electrostrictive strain is given. Some possible applications of the materials with GE are reviewed.

Electromechanical Determination of the High‐Field Phase Transition of Pb(Mg1/3Nb2/3)O3–PbTiO3–(Ba,Sr)TiO3 Relaxor Ferroelectrics

Ceramics in the (1 –x)[(1 –y)Pb(Mg1/3Nb2/3)O3·yPbTiO3] ·xMeTiO3 system, where Me is Sr or Ba, exhibit very large electrostrictive strains at reasonable drive fields. However, the optimum use temperature and frequency vary with the particular composition used. As relaxor ceramics, each composition has a broad transition from electrostrictive to partially piezoelectric behavior. The transition temperature (Tt) can be roughly determined from strain or polarization properties; however, it can be more quantitatively determined from the effective electro‐mechanical Q. A plot of induced transverse strain/induced polarization squared (effective Q12) as a function of temperature shows a sharp and unmistakable change in slope—this defines Tt. The slope of induced transverse strain/polarization (effective g31) also shows a change in slope at Tt, although this is more gradual than that of effective Q. The indicated Tt correlates with those found from measurement of strain and polarization.

Stress induced shift of the Curie point in epitaxial PbTiO3 thin films

A 50 °C shift in Curie temperature has been observed for c-axis oriented PbTiO3 thin films using x-ray diffraction. An analysis of the electrostrictive strain based on the Devonshire thermodynamic formalism showed that the shift in the Curie point for these films can be plausibly explained by an effective two-dimensional compressive stress of ≊400 MPa. The single-domain, single-crystal dielectric susceptibility (η33) and piezoelectric coefficient (d33) were calculated and found to be relatively unaffected, at room temperature, by a compressive stress of this magnitude.

Anelastic relaxation and internal strain in lead magnesium niobate relaxors

Abstract Non-linear internal friction measurements have been carried out on lead magnesium niobate with 10 at.% lead titanate. The purpose of these measurements was to investigate the field dependence of the elastic and anelastic responses, and to determine how the response depends on the amplitude of an applied stress. The linear elastic response was found to stiffen at all bias levels with the maximum electroelastic coupling occurring near the Vogel—Fulcher freezing temperature. A strong frequency dependence of the kinetics of the anelastic relaxation was found at low measurement frequencies. These data are compared with recent high-frequency results. The existence of an inhomogeneous internal strain has been found from the line broadening of the (220) and (321) diffraction peaks. On application of an electrical field the internal strain is relieved by the development of a macrostrain which is shown to be the electrostrictive strain. It is proposed that the local electrostrictive strains are dynamic in nature and are at the origin of the anelastic relaxation. Strong elastic non-linearities, both an elastic softening and hardening under stress, have also been observed. These results are interpreted as a stress activation of the internal deformation process.

Pb(Zn1/3Nb2/3)O3-Based Piezoelectric and Electrostrictive Ceramics

Perovskite-type Pb(Zn1/3Nb2/3)O3 (PZN)-based ceramics were prepared by a modification of 0∼10 mol% La(Ni1/2Ti1/2)O3 (LNT) or La(Co1/2Ti1/2)O3 (LCT). Effects on suppression of the pyrochlore phase in these ceramics were studied on the dielectric and electrostrictive properties. The ratios of the perovskite phase to the pyrochlore phase were more than 75% at 5∼10 mol% LNT or LCT modification. The temperature dependence of the dielectric constant, εs, shows a broad peak in the vicinity of room temperature. The transverse electrostrictive strain, S1=-2.5×10-5, of PZN ceramics with 5 mol% LNT modification was obtained under an applied electric field of 20 kV/cm.

X-ray and phenomenological study of lanthanum-modified lead zirconate-titanates in the vicinity of the relaxor phase transition region

X-ray diffraction analyses of chemically derived Pb1−xLax(Zr0.65Ti0.35)1−x/4O3 powders were combined with a phenomenological theory to investigate the corresponding single-crystal thermodynamic properties of compositions approaching the relaxor ferroelectric phase transition region (x=0–0.04). The temperature dependence of the electrostrictive strain component, x4, could be described by the Landau–Ginsburg–Devonshire phenomenological theory taking Tc = 357 °C independent of La content (x). The single-domain, single-crystal elastic Gibbs free-energy density was calculated as a function of temperature and composition. The calculated results were discussed in relation to a simple superparaelectric model of relaxor behavior involving the temperature stabilization of noninteracting polar microregions.

Internal strain relaxation and the glassy behavior of La-modified lead zirconate titanate relaxors

Nonlinear internal friction measurements have been carried out on La-modified lead zirconate titanate relaxors with a Zr/Ti ratio of 65/35. Measurements have been made as a function of La content and dc bias. The elastic softening is believed to have a ferroelastic contribution due to the tilting of the oxygen octahedra, in addition to the expected electrostrictive effects. The temperatures of the maximum softening form a plausible extension to the rhombohedral-rhombohedral phase boundary [Proc. IEEE 61, 959 (1973)]. A frequency dependence of the softening has also been found which was interpreted as the existence of fluctuations in the orientations of the tilts. These fluctuations are proposed to arise in an attempt to partially relieve an inhomogeneity in the electrostrictive strains associated with the polarization fluctuations. The results are discussed in context with previously reported transmission electron microscopy work [C. Randall, Ph. D. dissertation, University of Essex (1987)]. Dielectric measurements have also been done as a function of La content and bias, and the freezing temperature of the polarization fluctuations determined as a function of composition. A revised phase diagram has been proposed using this data base which shows different phase fields having various combinations of freezing mechanisms.