Ferroelectric Rhombohedral Research Articles

Observation of a stable fractionalized polar skyrmionlike texture with giant piezoelectric response enhancement

We report the creation of stable fractionalized polar skyrmionlike structures via flexoelectric effect in a prototypical multiferroic ${\mathrm{BiFeO}}_{3}$ thin film, which are directly imaged by angle-resolved piezoresponse force microscopy technique. We also demonstrate an approach to enhance piezoresponse at the nanoscale. Phase-field simulations reveal that a tip-driven flexoelectric effect allows the formation of an ordered polar skyrmionlike configuration that is topologically protected by the converse flexoelectric effect. Our findings open up avenues for designing and controlling spatially localized topological textures in rhombohedral ferroelectrics, and also could contribute to future developments for ferroelectric-based nanoelectronic devices.

Multistep stochastic mechanism of polarization reversal in rhombohedral ferroelectrics

A stochastic model for the field-driven polarization reversal in rhombohedral ferroelectrics is developed, providing a description of their temporal electromechanical response. Application of the model to simultaneous measurements of polarization and strain kinetics in a rhombohedral Pb(Zr,Ti)O3 ceramic over a wide time window allows identification of preferable switching paths, fractions of individual switching processes, and their activation fields. Complementary, the phenomenological Landau-Ginzburg-Devenshire theory is used to analyze the impact of external field and stress on switching barriers showing that residual mechanical stress may promote the fast switching.

In-situ XRD study of actuation mechanisms in BiFeO3-K0.5Bi0.5TiO3-PbTiO3 ceramics

In the present study, we report a nonergodic relaxor ferroelectric composition for high temperature piezoelectric applications, 0.57BiFeO3-0.21K0.5Bi0.5TiO3-0.22PbTiO3, which exhibits Tm around 420 °C. By combining the results of in-situ synchrotron XRD and strain measurements using digital image correlation, a pseudocubic nonergodic relaxor to rhombohedral ferroelectric transformation is identified, accompanied by a volume strain close to zero. A methodology is developed to determine the crystallographic parameters of the transformed rhombohedral ferroelectric phase in a strain-free state, using the invariant intersection for diffraction stress analysis. The phase transformation process was analyzed by methods combining peak profile fitting and full pattern refinement; the results obtained illustrate the strain arising from the phase transformation, together with intrinsic/extrinsic contributions and anisotropy in the field-induced strain. The study reveals unusual microscopic strain behavior, distinguished from that of normal rhombohedral ferroelectrics, showing the combined properties of ergodic and normal ferroelectric materials and leading to a dominant intrinsic lattice strain together with a weaker extrinsic domain switching effect. The elastic coupling between different grain families is also reflected in their similar strain orientation distribution (SOD) functions.

Deterministic Switching in Bismuth Ferrite Nanoislands.

We report deterministic selection of polarization variant in bismuth BiFeO3 nanoislands via a two-step scanning probe microscopy procedure. The polarization orientation in a nanoisland is toggled to the desired variant after a reset operation by scanning a conductive atomic force probe in contact over the surface while a bias is applied. The final polarization variant is determined by the direction of the inhomogeneous in-plane trailing field associated with the moving probe tip. This work provides the framework for better control of switching in rhombohedral ferroelectrics and for a deeper understanding of exchange coupling in multiferroic nanoscale heterostructures toward the realization of magnetoelectric devices.

Out-of-plane three-stable-state ferroelectric switching: Finding the missing middle states

By realizing a nonvolatile third intermediate ferroelectric state through anisotropic misfit strain, we demonstrate electrical switching among three stable out-of-plane polarizations in bismuth ferrite thin films grown on ${(110)}_{\mathrm{pc}}$-oriented gadolinium scandate substrates (where pc stands for pseudocubic) by the use of an asymmetric external electric field at the step edge of a bottom electrode. We employ phenomenological Landau theory, in conjunction with electrical poling experiments using piezoresponse force microscopy, to understand the role of anisotropic misfit strain and an in-plane electric field in stabilization of multiple ferroelectric states and their competition. Our finding provides a useful insight into multistep ferroelectric switching in rhombohedral ferroelectrics.

Non-Resonant Magnetoelectric Energy Harvesting Utilizing Phase Transformation in Relaxor Ferroelectric Single Crystals

Recent advances in phase transition transduction enabled the design of a non-resonant broadband mechanical energy harvester that is capable of delivering an energy density per cycle up to two orders of magnitude larger than resonant cantilever piezoelectric type generators. This was achieved in a [011] oriented and poled domain engineered relaxor ferroelectric single crystal, mechanically biased to a state just below the ferroelectric rhombohedral (FR)-ferroelectric orthorhombic (FO) phase transformation. Therefore, a small variation in an input parameter, e.g., electrical, mechanical, or thermal will generate a large output due to the significant polarization change associated with the transition. This idea was extended in the present work to design a non-resonant, multi-domain magnetoelectric composite hybrid harvester comprised of highly magnetostrictive alloy, [Fe81.4Ga18.6 (Galfenol) or TbxDy1-xFe2 (Terfenol-D)], and lead indium niobate–lead magnesium niobate–lead titanate (PIN-PMN-PT) domain engineered relaxor ferroelectric single crystal. A small magnetic field applied to the coupled device causes the magnetostrictive element to expand, and the resulting stress forces the phase change in the relaxor ferroelectric single crystal. We have demonstrated high energy conversion in this magnetoelectric device by triggering the FR-FO transition in the single crystal by a small ac magnetic field in a broad frequency range that is important for multi-domain hybrid energy harvesting devices.

Crystallographic Features of the Relaxor State in the Mixed Ferroelectric System Ba(Ti<sub>1-x</sub>Zr<sub>x</sub>)O<sub>3</sub>

The relaxor state has been found in the mixed ferroelectric system Ba (Ti1-xZrx)O3 around x = 0.35. To understand the nature of the relaxor state, the crystallographic features of the paraelectric (PC), ferroelectric, and relaxor states for 0.15 ≤ x ≤ 0.40 have been investigated mainly by transmission electron microscopy. It was found that a microstructure of the ferroelectric state for 0.15 ≤ x ≤ 0.28 consisted of banded structures with boundaries parallel to the {110}PC and {100}PC planes. Based on the Sapriel theory concerning ferroelastic transitions, it was understood that the banded structures were consistent with domain structures in the ferroelectric rhombohedral (FR) state having a polarization vector parallel to one of the <111>PC directions. With the help of the failure of Friedel’s law in diffraction, furthermore, polar regions having <001>PC and <110>PC components of a <111>PC polarization vector were also found to be separately observed in the PC and relaxor states as well as the FR state. Then, in-situ observation for 0.29 ≤ x ≤ 0.40 made in this study indicated that the PC and relaxor states consisted of polar nanometer-sized regions having these two components. Based on this, the relaxor state in BTZ can be identified as an assembly of polar nanometer-sized regions, which were produced by the suppression of the (PC→FR) ferroelectric transition on cooling.

Dynamic In Situ X-Ray Diffraction Study of Antiferroelectric–Ferroelectric Phase Transition in Strontium-Modified Lead Zirconate Titanate Ceramics

The electric field-induced electromechanical properties of strontium-modified lead zirconate titanate (PSZT) ceramics, at the Zr-rich region of the phase diagram, are investigated by a dynamic in situ x-ray diffraction technique. PSZT compositions with different Zr/Ti ratios are prepared using a tape lamination approach. An experimental setup using Bragg-Brentano parafocusing geometry is used for the in situ x-ray diffraction on samples under a dynamic ac electric field up to their saturation polarization at 0.1 mHz frequency. The results indicated that strains for the compositions in the ferroelectric rhombohedral (FR) phase field are mostly due to structural changes and non-180° domain movements after coercive field. As a result the experimental longitudinal strains in these materials are not very high (∼0.4%). On the other hand, for the compositions at the FR-AFT phase field, near the morphotropic phase boundary, dynamic in situ x-ray diffraction showed the continuous field-induced phase transition from the AFT → FR. It is also seen from the changes in the pseudo-cubic (111) diffraction peak that this phase transition is accompanied by movements of non-180o or 90o domains. This resulted in very high field-induced strain of ∼0.8% in these materials. The compositions farther away from the boundary in the AT side showed neither structural changes nor domain movements up to 9 KV/mm. This is commensurate with the low observed strain of 0.03% for these materials.

Study of phase transitions in ternary lead indium niobate-lead magnesium niobate-lead titanate relaxor ferroelectric morphotropic single crystals

In this work we report on the elastic hysteretic behavior observed in ferroelectric lead indium niobate-lead magnesium niobate-lead titanate (PIN-PMN-PT) relaxor single crystals under conditions of cooperative stress, temperature, and electric field. Room temperature elastic response displays strong and sharp discontinuity associated with stress induced phase transition. Quasistatic elastic response and ultrasonic wave propagation measurements demonstrated that this strain discontinuity in PIN-PMN-PT single crystal is associated with a ferroelectric rhombohedral (FR)—ferroelectric orthorhombic (FO) phase transition. The temperature dependent elastic response and transition strain were modeled by Devonshire theory. The crystal instability under compression is significantly improved by application of a dc bias electric field.

Electromechanical properties of high- coupling (1-ξ)Pb(Zn1/3Nb2/3)O3-(ξ)PbTiO3 single crystals for sound projectors

Isothermal weak field frequency sweeps were conducted over the temperature range 30 to 140 degrees C on multidomain, oriented, and poled (1-x)Pb(Zn(1/3)Nb(2/3))O(3)-xPbTiO(3) (PZN-PT) single crystals with x = 0.045, 0.06, 0.07, and 0.08 near the ferroelectric rhombohedral (FR)-ferroelectric tetragonal (F(T)) morphotropic phase boundary (MPB). The temperature dependencies of the small-signal 33-mode electromechanical properties were derived from the isothermal frequency sweeps. Morphotropic compositions with x = 0.06 and 0.07 PT were found to exhibit the largest electromechanical coupling and piezoelectric coefficient, with k(33) > 0.90 and d(33) approximately 2300 pC/N, and the lowest short-circuit Young's modulus of approximately 9 GPa. Reversible zero-field elastic instability attributable to a F(R)- F(O) transition was observed under isothermal compression-decompression of a 0.94PZN-0.06PT single crystal. The application of a dc bias field enhanced the F(R) stability under compression. The large-signal, dc biased, 33-mode electromechanical response was measured under mechanical compressions similar to those used in sound projectors. The remarkable small-signal electromechanical properties are in a good agreement with the large-signal response. The crystal response to thermal, electrical, and mechanical variable is discussed in terms of high-coupling single crystal models.

Processing, Electro-Mechanical Behavior and Microstructure of Strontium Modified Lead Zirconate Titanate Ceramics

Dense (Pb0.9Sr0.1)(Zr1−xTix)O3 (PSZT) ceramics, across the morphotropic phase boundary, are made by a modified oxide precursor route and tape lamination approach. The ferroelectric rhombohedral (FR) phase changed to antiferroelectric tetragonal (AFT) phase below the tolerance factor (t) of about 0.97 as the composition is systematically varied. Scanning electron micrograph showed a systematic decrease in grain size from the FR to AFT and a change in domain structure from 180° water mark to herringbone type pattern. The influence of electric field-induced AF to F phase transition on piezoelectric and strain behaviors is also studied. Polarization over 41 μC/cm2 for FR compositions and strain as high as 0.8% for certain composition on F-AF phase boundary are observed.

Dc field effect on stability of piezoelectric PZN-0.06PT single crystals under compressive stress

A reversible elastic instability was observed in PZN-0.06PT high coupling single crystals when subjected to uniaxial compressions similar to those used in sound projectors. The strain magnitude at the onset of the instability supported a free energy prediction of a ferroelectric rhombohedral (FR)-ferroelectric orthorhombic (FO) phase transition. The thermal response of the normalized phase transition strain is in a good agreement with model calculation. A dc bias field drastically enhanced the crystal stability under compression. dc bias and compressive stress levels that are required for their stable operation in sound projectors have been deduced and will be presented.

Dielectric Properties of Pb0.97La0.02(Zr0.87−xSnxTi0.13)O3Thin Films with Compositions near the Morphotropic Phase Boundary

Pb0.97La0.02(Zr0.87−xSnxTi0.13)O3(PLZST,x=0.27, 0.17, 0.07)) thin films with the compositions in ferroelectric rhombohedral (FER) region, near the morphotropic phase boundary (MPB), were deposited on the Pt‐electroded silicon (PtSi) substrates by the sol–gel process. The phase structure and surface morphology of PLZST thin films were analyzed by XRD and SEM, respectively. The dc electric field and temperature‐dependent dielectric properties of the PLZST thin films were investigated in detail. The results indicated that the dielectric constant, remnant polarization, and the Curie temperature (Tc) of PLZST films were elevated with the decrease of Sn content. Hence, the larger dielectric tunability (τ) was obtained for PLZST thin films withx=0.07, and the maximum τ value was 78.1%.

Striking similarity of ferroelectric aging effect in tetragonal, orthorhombic and rhombohedral crystal structures

A series of Mn-doped alkaline niobate-based and lead zirconic titanate ferroelectrics that possess tetragonal, orthorhombic, and rhombohedral perovskite structures was fabricated, and the aging behavior of their hysteresis loop and electrostrain was studied. We found that after aging, all the samples showed a similar double hysteresis loop and large recoverable electrostrain behavior, regardless of their crystal structure and of their ionic species. The striking similarity of the aging effect in different ferroelectric phases suggests that there exists a common physical origin of aging in ferroelectric perovskites. Based on a symmetry-conforming short-range ordering mechanism of point defects, we provided a unified microscopic explanation for the aging effect in the tetragonal, orthorhombic, and rhombohedral ferroelectrics.

Constrained modeling of domain patterns in rhombohedral ferroelectrics

A nonconventional phase-field model is developed to predict ferroelectric domain structures. It employs a set of field variables motivated by multirank laminates to represent energy-minimizing domain configurations, giving rise to an explicit expression of the energy-well structure. The framework is applied to domain simulation in the rhombohedral phase assuming that polarization is close to the ground states. An electromechanical self-accommodation pattern consisting of eight rhombohedral variants and an engineered domain configuration are predicted and found in good agreement with those observed in experiment.

Effect of acceptor and donor dopants on ferroelectric and piezoelectric properties of lead zirconate titanate ceramics

AbstractDielectric, ferroelectric and piezoelectric properties of Pb1−x Lax (Zry Ti1−y )1−(x /4)−(3/4)z Fez O3 ceramics for z = 0 to 6 mol% prepared by a mixed oxide method were investigated. Fe substitution in lead lanthanum zirconate titanate (PLZT) compositions resulted in a phase transformation from coexisting phases (ferroelectric rhombohedral (FERH) and ferroelectric tetragonal (FETET)) to intensified tetragonal phase. Grain size and apparent density increased with increasing acceptor (Fe) content up to 3 mol% in the PLZT system. The optimum dielectric properties (ϵ RT, ϵ Tc and tan δ) were observed in 3 mol% Fe‐doped PLZT composition and then decreased thereafter. Acceptor (Fe) substitution in the PLZT system influenced the ferroelectric remanent polarization (P r) and spontaneous (P s) polarization, reaching saturation at 6 mol% Fe, while the coercive field (E c) increased up to 3 mol% Fe‐doped PLZT composition. The piezoelectric properties are sensitive to acceptor (Fe) modification in the PLZT system which was proved by the decreasing trend of piezoelectric charge coefficient (d 33) up to 3 mol% Fe and then increasing to 6 mol% Fe while the piezoelectric planar coupling coefficient (k p) showed a continuous decreasing trend throughout the series. Dielectric, ferroelectric and piezoelectric properties were characterized as a function of acceptor (Fe) concentration in the PLZT system for possible sensor and actuator applications. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Elasticity of high coupling relaxor-ferroelectric lead zinc niobate-lead titanate crystals

The elastic response of a [001]-oriented and -poled ferroelectric rhombohedral lead zinc niobate-lead titanate single crystal close to the morphotropic phase region is examined under thermal, electrical, and mechanical boundaries similar to those used in sound projectors. Resonance measurements yielded a monotonically decreasing Young’s modulus as a function of temperature in the ferroelectric rhombohedral state with a sudden stiffening near the ferroelectric rhombohedral (FR)-ferroelectric tetragonal (FT) transition. The quasistatic, zero-field stress-strain response revealed a FR instability under uniaxial compression. A dc bias field stabilized the FR state under compressive stress. Young’s modulus derived from the linear elastic response below instability agrees well with resonance data for FR. A larger modulus than expected for FT was observed above instabilities. The elastic response is analyzed in terms of ferroelectric-ferroelectric transitions as predicted by a high-order Devonshire theory. Implications for sound projectors are discussed.

NMR study of ionic shifts and polar ordering in the relaxor ferroelectricPb(Sc1/2Nb1/2)O3

${}^{207}\mathrm{Pb},$ ${}^{45}\mathrm{Sc},$ and ${}^{93}\mathrm{Nb}$ nuclear-magnetic-resonance (NMR) spectra of partially ordered relaxor ferroelectric ${\mathrm{PbSc}}_{1/2}{\mathrm{Nb}}_{1/2}{\mathrm{O}}_{3}$ (PSN) have been studied at temperatures between 77 K and 420 K. The relatively narrow ${}^{45}\mathrm{Sc}$ and ${}^{207}\mathrm{Pb}$ NMR spectral components, arising from chemically ordered regions of the crystal, show marked anomalies at ${T}_{c}\ensuremath{\simeq}$ 360 K, where ${T}_{c}$ is the temperature of the dielectric susceptibility maximum. The abrupt frequency shifts of these components below ${T}_{c}$ are related to the first-order structural phase transition. In the coexisting broad spectral components, originating from compositionally disordered regions, such anomalies are barely detectable; they were not observed at all in the ${}^{93}\mathrm{Nb}$ NMR spectra. Our NMR data are compatible with an assumption of large, up to 0.04 nm, displacements of lead ions and smaller, $\ensuremath{\sim}0.01\mathrm{nm},$ displacements of scandium ions along the four polar rhombohedral axes, while Nb ions remain in the centers of oxygen octahedra. ${}^{207}\mathrm{Pb}$ NMR measurements in poled crystals reveal that long-range polar ordering is established solely in the chemically ordered parts of the crystal, whereas in the disordered regions a mixed ferro-glass order sets in. At low temperatures, both ${}^{207}\mathrm{Pb}$ and ${}^{93}\mathrm{Nb}$ resonances detect, in addition to the ferroelectric rhombohedral, a tetragonal distortion of the PSN lattice. This distortion appears at ${T}_{c}$ and increases smoothly on decreasing temperature, possessing a second-order phase-transition character. The effective local symmetry of PSN at $T<250\mathrm{K}$ thus lowers from the axial rhombohedral to the nonaxial orthorhombic with lead atom shifts deviating considerably from the [111] polar axes. Structural data, obtained via NMR, are compared with similar data obtained from neutron and x-ray-diffraction experiments.

Domain configuration and crystal structure of Pb(Zn1/3Nb2/3)O3–5%PbTiO3 crystals as a function of the electric-field direction

The domain configuration of 0.95Pb(Zn1/3Nb2/3)O3–0.05PbTiO3 single crystals was investigated as a function of the applied electric-field direction with respect to the crystallographic orientation. A normal ferroelectric domain structure, which was not observable in virgin crystals (not exposed to electric field), appeared upon the electric-field (E-field) induced transition from the relaxor state to the normal ferroelectric state. After E-field was applied along the polar 〈111〉 direction and removed, a band-shaped domain configuration appeared as a result of subsequent depolarization. The depoled 〈111〉 crystal consisted of predominantly (110) domain boundaries, which represents the minimum energy domain state in rhombohedral ferroelectrics. In contrast, crystals must transform into the phase with the symmetry lower than rhombohedral, i.e., monoclinic structure, by an E-field application along 〈001〉. Domain boundaries in 〈001〉 poled crystals were indexed to be (001), being a favorable state for monoclinic ferroelectrics. The dependence of the domain configuration upon the E-field application direction could be explained using the relationship between the mechanical compatibility with respect to the ferroelectric strain and the crystal symmetry of a domain. The residual strain on domain boundaries in 〈001〉 crystals may inhibit crystals to recover the rhombohedral structure, resulting in a monoclinic ferroelectric crystal even upon the removal of the E-field.

Commonalties of the influence of lower valent A-site and B-site modifications on lead zirconate titanate ferroelectrics and antiferroelectrics

Studies of the structure-property relations of lead zirconate titanate (PZT) modified with lower valent substitutions on the A- and B-sites have been performed as a function of substituent concentration. These investigations have yielded common changes induced by these substitutions on ferroelectric phases. The commonalties are the presence of fine domains and polarization pinning effects. Differences in domain morphologies were observed between the rhombohedral and tetragonal ferroelectric phases. Rhombohedral ferroelectrics were found to exhibit “wavy” domain patterns with increasing dopant concentrations, whereas a lenticular domain shape was preserved as the domain size was decreased for tetragonal ferroelectrics. These differences were explained in terms of different pinning mechanisms based on the differences in local elastic strain accommodations. Investigations of high Zr-content PZT have revealed that the ferroelectric rhombohedral phase becomes stabilized over the antiferroelectric orthorhombic with increasing concentrations of lower valent modifications. This change was explained in terms of the enhanced coupling between oxygen octahedra due to the bonding of oxygen-vacancy dipoles.