Electrostrictive Coupling Research Articles

Strong variation of electrostrictive coupling near an intermediate temperature of relaxor ferroelectrics

A sudden increase in the electrostrictive coefficient ${Q}_{13}$ when temperature decreases is seen in three different types of ferroelectric relaxors (PLZT 9/65/35, PLZT 22/20/80, and PMN-PT) starting from $\ensuremath{\sim}50\text{ }\text{K}$ above the dielectric permittivity maximum temperature, ${T}_{m}$. The temperature dependence is attributed to the softening of the quasilocal mode occurring near dopants or charge-transfer sites. The steep increase when the temperature decreases could be related to the transition of polar nanoregions from dynamic to quasistatic regime, which introduces an intermediate temperature scale ${T}^{\ensuremath{\ast}}$ [W. Dmowski, S. B. Vakhrushev, I.-K. Jeong, M. P. Hehlen, F. Trouw, and T. Egami, Phys. Rev. Lett. 100, 137602 (2008); B. Dkhil, P. Gemeiner, A. Al-Barakaty, L. Bellaiche, E. Dul'kin, E. Mojaev, and M. Roth, Phys. Rev. B 80, 064103 (2009)], besides Burns temperature ${T}_{B}$ and freezing temperature ${T}_{f}$. Possible consequences for nonequilibrium phenomena, including high-temperature memory found in relaxors, are conjectured.

Pressure effects on relaxor ferroelectricity in disordered Pb(Sc1/2Nb1/2)O3

High-pressure Brillouin and Raman scattering spectroscopy and x-ray diffraction measurements were carried out on disordered Pb(Sc1/2Nb1/2)O3, considered to be a model system for phase transitions in relaxor ferroelectrics and related materials. The observed pressure-dependent Raman spectra are unusual, with the relaxor state distinguished by broad Raman bands. Raman spectra as a function of pressure reveal a new peak at 370 cm−1, with two peaks near 550 cm−1 merge above 2–3 GPa, indicating a structural phase transition in this pressure range consistent with earlier dielectric measurements. A significant softening in the longitudinal acoustic mode is observed by Brillouin scattering. Both the temperature and pressure dependencies of the linewidth reveal that the longitudinal acoustic mode softening arises from electrostrictive coupling between polar nanoregions and acoustic modes. X-ray diffraction indicates that the pressure-volume compression curve changes near 2 GPa.

Elastic softening and central peaks in BaTiO3 single crystals above the cubic-tetragonal phase-transition temperature

A strong relaxation mode was observed in the paraelectric phase of barium titanate (BaTiO3) single crystals by Brillouin scattering study and was found to correlate with the softening of the longitudinal acoustic mode and the increase in the hypersonic damping. These observations support the existence of polar percursors and their electrostrictive coupling with the strain caused by the acoustic waves, consistent with former studies evidencing off-centered Ti ions in the high-symmetry cubic phase. A critical slowing down has been clearly observed in the vicinity of the cubic-tetragonal phase transition, indicating order-disorder component contributes to the phase transition of BaTiO3.

Central peaks, acoustic modes, and the dynamics of polar nanoregions inPb[(Zn1∕3Nb2∕3)xTi1−x]O3single crystals studied by Brillouin spectroscopy

Temperature dependence of acoustic behaviors and quasielastic central peaks (CPs) of $\mathrm{Pb}[{({\mathrm{Zn}}_{1∕3}{\mathrm{Nb}}_{2∕3})}_{x}{\mathrm{Ti}}_{1\ensuremath{-}x}]{\mathrm{O}}_{3}$ $(\mathrm{PZN}\text{\ensuremath{-}}x\mathrm{PT})$ single crystals with $x=4.5%$ and 9% have been investigated in a temperature range of $300\char21{}900\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ by using the Brillouin light scattering. The temperature dependence of the ${C}_{11}$ elastic constant of both crystals showed a deviation from normal lattice anharmonicity at the Burns temperature $({T}_{B})$ of about $730\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ upon cooling, indicating the onset of the electrostrictive coupling between the polar nanoregions (PNRs) and the longitudinal acoustic (LA) waves. Upon further cooling, depolarized CP began to appear at a certain temperature $({T}_{d})$ located in $500\char21{}550\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, which was accompanied by substantial softening of the ${C}_{44}$ elastic constant below this temperature suggesting anisotropic electrostrictive coupling between PNRs and the two acoustic waves. In addition, the onset of significant increase in the acoustic damping of both acoustic waves at ${T}_{d}$ could be seen from the temperature dependence of the linewidth of Brillouin doublets. These results suggested that electrostrictive coupling of the strain to the square of the local polarization of PNRs and the resultant order-parameter fluctuations are enhanced not at ${T}_{B}$ but at a much lower temperature of ${T}_{d}$, which may be ascribed to a local structural transformation occurring in PNRs at ${T}_{d}$. This suggestion is consistent with recent studies on $\mathrm{PZN}\text{\ensuremath{-}}x\mathrm{PT}$ single crystals reporting the appearance of strong acoustic emission signals [M. Roth et al., Phys. Rev. Lett. 98, 265701 (2007)] and substantial changes in the Raman spectrum [O. Svitelskiy, Phys. Rev. B 72, 172106 (2005)] at almost the same temperature. From the comparison of the present results to those of two typical relaxors, $\mathrm{Pb}({\mathrm{Mg}}_{1∕3}{\mathrm{Nb}}_{2∕3}){\mathrm{O}}_{3}$ and $\mathrm{Pb}({\mathrm{Mg}}_{1∕3}{\mathrm{Ta}}_{2∕3}){\mathrm{O}}_{3}$, it was suggested that the existence of an intermediate characteristic temperature ${T}_{d}$ below ${T}_{B}$ may be considered as a more common characteristic in the temperature evolution of PNRs of relaxor ferroelectrics.

Optical Heterodyne Detected Accumulated Acoustic Grating Responses in Near Supercritical Fluids

A novel third-order polarization effect due to an accumulated optical heterodyne detected (OHD) transient acoustic grating response in near critical fluids was observed and experimentally characterized. Femtosecond pump-probe responses in near critical CO2 and CHF3 illustrate this phenomenon. This large optically generated acoustic response due to electrostrictive coupling appears only when pump and probe pulses are temporally overlapped and is pi out-of-phase with the normal optical Kerr effect (OKE) birefringent signal. The local oscillator, the laser intensity, and the modeled experimental repetition rate dependence identify the accumulated heterodyne origin of these responses. The observed OHD accumulated acoustic birefringent signal is inversely dependent on sound velocity to the fifth power. A corresponding sound velocity dependent dichroic (in-phase) response was also observed for these electronically nonresonant samples. The accumulated effect described here may have applications for the design of efficient modulators and as a simple and sensitive experimental technique for the measurement of near critical fluid thermodynamic and acoustic parameters.

Elastic Stabilization of a Single-Domain Ferroelectric State in Nanoscale Capacitors and Tunnel Junctions

Taking into account the electrostrictive coupling between inhomogeneous polarization fluctuations and lattice strains in ferroelectric films, we show that, in heterostructures involving strained epitaxial films and metal electrodes, the single-domain state may remain stable against the transformation into a polydomain state down to the nanometer scale. This result indicates that the ferroelectric states with opposite remanent polarizations can be stabilized even in nanoscale capacitors and tunnel junctions, which opens the possibility of their application for memory storage.

Brillouin scattering study on ferroelectric single crystal Sr 2Ta 2O 7

Acoustic properties of strontium tantalite (Sr 2Ta 2O 7) single crystals with perovskite-slab structure were investigated by micro-Brillouin scattering. The two elastic stiffness constants c 22 and c 33 were determined in the temperature range between −140 °C and 300 °C. The elastic constant c 22 shows marked continuous softening on approaching phase transition temperature T o around 167 °C from both sides, indicating ferroelastic and nearly second-order nature of this phase transition. The values of c 22 can be well reproduced by the Landau theory including bilinear coupling (linear in strain, quadratic in order parameter) between order parameter and the strain. Hypersonic attenuation increases markedly around T o, which seems to reflect not only bilinear coupling between the order parameter and the strain in the ferroelastic phase, but also electrostrictive coupling in the paraelectric phase.

Electrostrictive and Piezoelectric Effect in BaTiO3 and PbZrO3

Order-disorder mechanism is a part of phase transition nature in the ABO3 perovskites. It is related with the existence of polar regions, which dynamics in the electric field determines the dielectric response near T c. Temperature dependence of mechanical strain connected with polarisation change in the paraelectric phase has been investigated for the BaTiO3 and PbZrO3 single crystals. Existence of polar regions influences the electrostrictive properties and induces the piezoelectric effect in the paraelectric phase. A non-linear temperature dependence of the electrostrictive coupling between the macroscopic strain and macroscopic polarisation has been found above T c.

Effects of Ca doping on the Curie temperature, structural, dielectric, and elastic properties of Ba0.4Sr0.6−xCaxTiO3 (0⩽x⩽0.3) perovskites

The effects of Ca doping on the Curie temperature, structural, dielectric, and elastic properties of Ba0.4Sr0.6−xCaxTiO3 (0⩽x⩽0.3) has been studied. Powder x-ray diffraction revealed that the cubic lattice constant a decreases linearly with increasing x from 0 to 0.15, while showing an anomalous expansion between x=0.15 and x=0.18. This, together with the anomalies in the dielectric constants, Curie temperature TC, and elastic constants observed for 0.15<x<0.18, suggests that a small amount of Ca ions substituted for Ti ions. Correlated with the evolution of a with x, TC increases linearly with increasing x from 0 to 0.15; while deviating from linear behavior for x>0.15, TC increases persistently up to x=0.25 and thereafter shows a decrease. These variations of TC with x have been interpreted in terms of Ca-doping-induced A-site cation size variance, a substitution of a small amount of Ca ions for Ti ions, and structural phase separation. Upon cooling the longitudinal elastic constant CL shows drastic softening near TC, arising from the electrostrictive coupling between the polarization fluctuations and the elastic strains. Moreover, it was found that Ca doping induces the hardening of CL just below TC, and the magnitude of the relative hardening of CL (i.e., ΔCL∕CL) increases with increasing x, implying that the tetragonal ferroelectric phase was increasingly stabilized by Ca doping.

A micro-Brillouin scattering study of the acoustic properties of PLZT relaxorceramics

Acoustic properties of the transparent relaxor ferroelectric ceramics of PLZT-10/65/35 andPLZT-7.6/72/28 were studied by the high-resolution micro-Brillouin scattering technique.The ceramics showed significant softening in the elastic constant and velocity of thelongitudinal acoustic (LA) phonon mode, a broad anomaly in the attenuation of the LAmode, and a frequency-dependent dielectric maximum. The temperature dependences ofthe acoustic anomalies could be explained qualitatively by using electrostrictive coupling,quadratic in order parameter and linear in strain. The interaction between the polar microregions is more pronounced at some percolation limit below the Burns temperatureTB,where the shear deformation develops due to polarization fluctuations, local electrostrictivestrain fields and tilting of the oxygen octahedra.

Acoustic anomalies and central peak in SrBi2Ta2O9 single crystals studied by micro-Brillouin scattering

Acoustic properties of layered perovskite SrBi2Ta2O9 (SBT) single crystals were investigated by micro-Brillouin scattering. Two elastic stiffness coefficients, c33 and c44, defined within the pseudotetragonal crystallographic axes, and the corresponding sound velocities were determined in the temperature range between 290 and 773 K. The longitudinal sound velocity propagating along the pseudotetragonal c axis was found to be very small, which can be related to the weak interlayer bonding of SBT. The corresponding c33 shows marked softening on approaching the ferroelectric phase transition temperature Tc around 600 K from both high- and low-temperature sides. The hypersonic attenuation increases markedly around Tc, which seems to reflect not only the bilinear coupling between the order parameter and the strain in the ferroelectric phase, but also the electrostrictive coupling in the paraelectric phase. Furthermore, a quasielastic central component was observed near Tc, which is believed to be partly responsible for the change of the low-frequency dielectric permittivity at Tc, besides the contributions from the soft mode and the low-frequency dielectric dispersion.

Nonlinear electrostriction in the mixed ferroelectricKTa1−xNbxO3

The dielectric resonance previously reported in the paraelectric phase of the mixed ferroelectric ${\mathrm{KTa}}_{1\ensuremath{-}x}{\mathrm{Nb}}_{x}{\mathrm{O}}_{3}$ is studied quantitatively. A theoretical model is developed that incorporates a field-induced electrostrictive coupling mediated by polar nanoregions appearing above the transition, and their orientational relaxation. Theoretical expressions for the dielectric dispersion and absorption are calculated, fitted to the experimental data, and values are obtained for the electrostriction coefficient and the relaxation time of the polar regions. Starting approximately 5 K above the transition, and upon repetitive excitation, a remarkable growth in the resonance is observed, ending in a singular behavior where the resonance splits into two very sharp spikes. This observation is described in the framework of the model as a nonlinear electrostrictive effect.

Brillouin scattering study of elastic properties in ferroelectric copolymer single-crystalline films

The in-plane elastic properties of as-grown random copolymer poly (vinylidene fluoride-trifluoroethylene) single-crystalline films with 75/25 molecular ratio have been studied by Brillouin light scattering up to approximately 140 degrees C from room temperature, covering the D6h-C2v ferroelectric phase transition at approximately 126 degrees C. The in-plane longitudinal acoustic (LA) phonons propagating parallel and perpendicular to the polymer chains were examined. In spite of the strongly first-order nature of the phase transition, both LA velocities exhibit only a broad down step in the temperature range between approximately 100 degrees C and approximately 130 degrees C, depending on the propagation direction, with increasing temperature. The LA phonon width perpendicular to the polymer chains increases with increasing temperature, and exhibits a broad maximum centered at approximately 120 degrees C. On the other hand, the LA phonon width along the polymer-chain axis is much wider than the width perpendicular to the polymer chains, and continues to increase even in the paraelectric phase. Treating the E(u) symmetry electric polarizations (Px,P(y)) of the D6h point group as the macroscopic order parameter, a Laudau free energy was developed to discuss the elastic properties. Using the free energy, we found that the elastic anomalies expected through the electrostrictive couplings between the order parameter and the elastic strains are strongly suppressed by the intrinsic electrical nature of the ferroelectric polymer. For both LA phonons, the temperature development of the phonon frequency and width can be reasonably reproduced by the Cole-Davidson relaxation model for the velocity dispersion with an exponent of betaCD=0.4. The relaxation time was found to obey the Arrhenius law tau=tau(0) exp(DeltaE/k(B)T) with DeltaE=0.55+/-0.01 eV and tau(0)=(4.0+/-0.6)x10(-18) s. At 24.0 degrees C in the ferroelectric phase, the in-plane phonon width anisotropy can be reasonably described by gammaB(straight theta)/2pi=0.18+0.72 sin4 straight theta for the LA phonon and gammaB(straight theta)/2pi=0.02+0.095 sin2 2straight theta for the transverse acoustic phonon, where the phonon propagation angle straight theta is measured from the perpendicular direction with respect to the polymer-chain axis. The straight theta dependence is strongly related to the one-dimensional freedom constrained in each copolymer chain.

Evidence for another low-temperature phase transition in tetragonalPb(ZrxTi1−x)O3(x=0.515,0.520)

Results of dielectric and resonance frequency (f r ) measurements below room temperature are presented for Pb(Zr x Ti 1-x )O 3 , x=0.515 and 0.520. It is shown that the temperature coefficient of f r changes sign from negative to positive around 210 and 265 K for x=0.520 and 200 and 260 K for x=0.515. Anomalies in the real part of the dielectric constant (e') are observed around the same temperatures at which the temperature coefficient of f r changes sign because of the electrostrictive coupling between the elastic and dielectric responses. Low-temperature powder x-ray-diffraction (XRD) data, however, reveal only one transition from the tetragonal to monoclinic phase similar to that reported by Noheda et al. [Phys. Rev. B, 61, 8687 (2000)]. Electron-diffraction data, on the other hand, reveal yet another structural transition at lower temperatures corresponding to the second anomaly in the e' vs T and f r vs T curves. This second transition is shown to be a cell-doubling transition not observed by Noheda et al. in their XRD studies. The observation of superlattice reflections raises doubts about the correctness of the Cm space group proposed by Noheda et al. for the monoclinic phase of Pb(Zr x Ti 1-x )O 3 below the second transition temperature.

High electrostrictive strain under high mechanical stress in electron-irradiated poly(vinylidene fluoride-trifluoroethylene) copolymer

In this letter, we show that the electric field induced strain in the electron irradiated poly(vinylidene fluoride-trifluoroethylene) copolymer can generate high strain even under a high mechanical stress. The observed change in strain with stress is due to the electrostrictive coupling of the local polarization with stress, and can be directly related to the change of the induced strain with temperature. The results indicate that the field induced strain observed in the films investigated is indeed from the local polarization regions in the material, and is electrostrictive in nature.

Dielectric relaxation and resonance in relaxor ferroelectricK1−xLixTaO3

Polar regions are shown to mediate a strong coupling between polarization and strain in the paraelectric phase of the mixed ferroelectric K12xLixTaO3 ~KLT! and KTa12xNbxO3 resulting in a field-induced piezoelectric response. The coupling is shown to result in a resonance in the dielectric spectrum of the crystals. In KLT, polar nanoregions can reorient via 180° ~p relaxation! or 90° ~p/2 relaxation! rotations. While the p relaxation is of no consequence, the p/2 relaxation has a strong influence on the overall character of the resonance. In addition to providing a mechanism for loss and degradation of the quality factor, this relaxation alters the character of the resonance as the two cross. Experimental results from dielectric spectroscopy above and below this crossover are presented and discussed. A simple theoretical Debye model involving the electrostrictive polarization-strain coupling is presented and the calculated spectrum is shown to reproduce the experimental spectrum. The parameters derived from the model are discussed. Most significantly, the electrostrictive coefficient of KLT is found to be 100 times larger than that of BaTiO3, and is due to the presence of polar nanoregions. @S0163-1829~99!13833-5#

A dynamics model for nonlinear electrostrictive actuators

This paper examines the nonlinear vibration of an electrostrictive ceramic rod actuator excited by a harmonic voltage source. A frequency-domain model was developed using the nonlinear constitutive law for electrostriction. The results predict harmonic distortion of the device's displacement due to the ceramic's nonlinear behavior. AC voltage signal and DC voltage bias were studied to determine the optimum power source parameters for minimizing distortion. The calculations show that the rod's resonance frequency and amplitude depend on the electromechanical coupling strength and differ greatly for large AC voltages from the equivalent linear piezoelectric results. The nonlinear analysis relates the device's electromechanical coupling coefficient to the computed resonance and antiresonance frequencies. This important result could provide the basis for future measurement of the electrostrictive coupling coefficient using resonance techniques.

DISTRIBUTED STRUCTURAL ACTUATION WITH ELECTROSTRICTORS

In this paper a non-linear framework is developed of the dynamic behaviour of a system with distributed electrostrictive coupling. A framework for the derivation of the governing equations is presented which is sufficiently general to model the dynamics of a broad range of non-linear systems. The constitutive relations for electrostrictors are developed in terms of the standard quadratic function and the hyperbolic tangent squared function of the applied electric field. Non-linear coupled equations of motion are derived by introducing the constitutive relations into Hamilton's Principle. Approximate system equations are derived using the assumed mode method. Experimental validation of the equations is accomplished by examining the static and dynamic response of a cantilevered beam actuated with a distributed electrostrictive actuator.

Methods of calculating coupling coefficients for electrostrictive materials

The definition of the coupling constant for piezoelectric ceramics is straightforward and depends directly on the square of the piezoelectric constant and inversely on the compliance and dielectric constants appropriate for the boundary conditions. However, these definitions are not directly applicable to electrostrictive materials because the material is nonlinear and therefore the equivalent piezoelectric and dielectric constants are not universally defined. Also, the presence of bias voltages about which the material would operate complicates the situation dramatically. In this presentation, energy methods [Hom et al., IEEE Trans. Sonics Ultrason. and Freq. Cont. UFFC-41, 541–545 (1994)] are used to calculate k33 for electrostrictive materials using several different constitutive models for the material. Experimental data on PMN taken at NUWC will be used to characterize the materials. The behavior of the electrostrictive coupling constants in the limit of small drive amplitudes about the bias voltage will be discussed. The effects of prestress, bias voltage, and drive level on the coupling coefficient will be examined for each model. The results will be compared with the equivalent piezoelectric definitions for k33.

Polarization switching mechanisms and electromechanical properties of La-modified lead zirconate titanate ceramics

The electromechanical properties of (Pb1−xLax)(ZryTi1−y)O3 [PLZT x/y/(1 - y)] have been investigated in the compositional range 0 < x < 0.10 for y = 0.65 (rhombohedral PLZT) and 0 < x < 0.18 for y = 0.40 (tetragonal PLZT). Both field-induced strains (∊-E) associated with polarization switching and piezoelectric responses (d33) were studied. Transmission electron microscopy (TEM) and dielectric investigations were also performed. Room temperature TEM investigations revealed common trends in the domain structure with increasing La content for both PLZT x/65/35 and x/40/60, including a micron-sized domain structure, a subdomain tweed-like structure, and a nanopolar domain state. Changes in the field-induced strains and piezoelectric properties were then related to these microstructural trends. The dominant electromechanical coupling mechanism in the micron-sized domain state was found to be piezoelectricity. However, an electrostrictive coupling became apparent with the appearance of the subdomain tweed-like structures, and became stronger in the nanopolar domain state. It is believed that polarization switching can-occur through 70°or 110°domains, the subdomain tweed-like structure, or nanopolar domains depending on La content.