Tetragonal Ferroelectrics Research Articles

Double hysteresis loops and large negative and positive electrocaloric effects in tetragonal ferroelectrics.

Phase field modelling and thermodynamic analysis are employed to investigate depolarization and compression induced large negative and positive electrocaloric effects (ECEs) in ferroelectric tetragonal crystalline nanoparticles. The results show that double-hysteresis loops of polarization versus electric field dominate at temperatures below the Curie temperature of the ferroelectric material, when the mechanical compression exceeds a critical value. In addition to the mechanism of pseudo-first-order phase transition (PFOPT), the double-hysteresis loops are also caused by the abrupt rise of macroscopic polarization from the abc phase to the c phase or the sudden fall of macroscopic polarization from the c phase to the abc phase when the temperature increases. This phenomenon is called the electric-field-induced-pseudo-phase transition (EFIPPT) in the present study. Similar to the two types of PFOPTs, the two types of EFIPPTs cause large negative and positive ECEs, respectively, and give the maximum absolute values of negative and positive adiabatic temperature change (ATC ΔT). The temperature associated with the maximum absolute value of negative ATC ΔT is lower than that associated with the maximum positive ATC ΔT. Both maximum absolute values of ATC ΔTs change with the variation in the magnitude of an applied electric field and depend greatly on the compression intensity.

A condensed microelectromechanical constitutive and damage model for tetragonal ferroelectrics

AbstractA condensed model for ferroelectric solids with tetragonal unit cells is presented. The approach is microelectromechanically and physically motivated, considering discrete switching processes on the level of unit cells and quasi‐continuous evolution of inelastic fields on the domain wall level. To calculate multiple grain interactions an interaction tensor is introduced. Hysteresis loops are simulated for pure electric and electromechanical loading, demonstrating e.g. the influence of a compressive preload on the poling process and interaction between statistically arranged crystallits. The residual stresses and the corresponding principle stresses are used to simulate fatigue damage in ferroelectric materials. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

A condensed microelectromechanical approach for modeling tetragonal ferroelectrics

A model for ferroelectric solids with tetragonal unit cells is presented. It is microelectromechanically motivated considering discrete switching on the level of unit cells and quasi-continuous evolution of inelastic fields on the domain wall level. The efficiency of the approach is due to the fact that an implementation within the framework of a numerical discretization scheme is not required to calculate smooth hysteresis loops or residual stresses emanating from strain incompatibilities or charges in a polycrystalline material. The condensed approach, on the other hand, can be combined with the FEM yielding extended elements where each integration point represents a polycrystalline representative volume element. Multiple grain interactions are modeled applying an averaging technique, embedding grains into an effective electromechanical medium. Due to the comparably low implementation effort, the approach is a useful means for the development of a variety of nonlinear constitutive models of functional materials like morphotropic PZT compositions, antiferroelectrics or ferromagnets. The feasibility of the approach is demonstrated by comparison with Finite Element calculations.

Atomic-scale mapping of dipole frustration at 90° charged domain walls in ferroelectric PbTiO3 films.

The atomic-scale structural and electric parameters of the 90° domain-walls in tetragonal ferroelectrics are of technological importance for exploring the ferroelectric switching behaviors and various domain-wall-related novel functions. We have grown epitaxial PbTiO3/SrTiO3 multilayer films in which the electric dipoles at 90° domain-walls of ferroelectric PbTiO3 are characterized by means of aberration-corrected scanning transmission electron microscopy. Besides the well-accepted head-to-tail 90° uncharged domain-walls, we have identified not only head-to-head positively charged but also tail-to-tail negatively charged domain-walls. The widths, polarization distributions, and strains across these charged domain-walls are mapped quantitatively at atomic scale, where remarkable difference between these domain-walls is presented. This study is expected to provide fundamental information for understanding numerous novel domain-wall phenomena in ferroelectrics.

Self-Similar Nested Flux Closure Structures in a Tetragonal Ferroelectric

In specific solid-state materials, under the right conditions, collections of magnetic dipoles are known to spontaneously form into a variety of rather complex geometrical patterns, exemplified by vortex and skyrmion structures. While theoretically, similar patterns should be expected to form from electrical dipoles, they have not been clearly observed to date: the need for continued experimental exploration is therefore clear. In this Letter we report the discovery of a rather complex domain arrangement that has spontaneously formed along the edges of a thin single crystal ferroelectric sheet, due to surface-related depolarizing fields. Polarization patterns are such that nanoscale "flux-closure" loops are nested within a larger mesoscale flux closure object. Despite the orders of magnitude differences in size, the geometric forms of the dual-scale flux closure entities are rather similar.

Double-hysteresis-like loops in Cr2Ti3O9-doped BaTiO3 ceramics

Barium titanate (BaTiO3) ceramics doped with different content of Cr2Ti3O9 were obtained by sintering in a temperature rang from 1300 to 1350 °C in air for 2 h. The phase composition, perovskite structural parameters and ferroelectric properties have been obtained by X-ray diffraction and ferroelectric measurements as a function of chemical composition and temperature. At low doping levels the peculiar double-hysteresis-like loops were found to have striking similarities to aging tetragonal ferroelectrics, besides following random local strains mechanism driven by the displacement of oxygen octahedral in shrunk crystals caused by phase transition. The polar moments surrounding the shrunk crystal cells were partially aligned and disrupted the long-range polar order due to the different final polarization direction by coupling between spontaneous polarization in original lattice. With temperature rising, the double-hysteresis-like loops can transform into a normal one because of the increase of long-range polar order.

Dynamic hysteresis of tetragonal ferroelectrics: The resonance of 90°-domain switching

The dynamic hysteresis of ferroelectric lattice with 90°-domain structure in response to time-varying electric field of frequency ω and amplitude E0 is investigated using Monte Carlo simulation based on the Ginzburg-Landau phenomenological theory. A resonance mode of the polarization switching at low frequency range, associated with cluster dipole switching, beside the dipole switching resonance mode, is revealed, characterized by two separate peaks in the hysteresis area spectrum A(ω). It is indicated that the power law scaling behaviors A(ω) ∼ ωα for ω → 0 and A(ω) ∼ ω−β for ω → ∞ remain applicable.

Impact of Strain Effects on the Stability of Ising Walls in Ferroelectrics

The stability of Ising 180-degree domain walls with respect to appearance of chirality is analytically studied in tetragonal perovskite-type ferroelectrics taking into account electro-mechanical coupling. It is shown that the widely used approximation neglecting the elastic effects may lead to qualitatively wrong results. Sufficient condition for the stability of Ising walls is formulated only in terms of elastic and electrostrictive properties, regardless the correlation energy. We demonstrate that elasticity stabilizes Ising walls in tetragonal Pb(Zr1-cTic)O3 and makes chiral walls unfavorable for any composition of the material (factor c), while nonelastic model predicts chirality of 180-degree walls near the morphotropic boundary.

A ferroelectric and ferroelastic microscopic switching criterion for tetragonal ferroelectrics

AbstractThe present contribution addresses the continuum mechanical modeling of ferroelectric/ferroelastic material behavior from a microscopic point of view. An electric enthalpy function for the representation of tetragonal ferroelectrics will be introduced and combined with an energy based ferroelectric/ferroelastic switching criterion. The result is a microscopically motivated material model for the description of ferroelectric and ferroelastic switching effects in electro‐mechanically coupled solids. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

A novel criterion for nonuniform domain switching of tetragonal ferroelectrics

This paper issues a simple criterion to characterize nonuniform domain switching. The criterion is obtained by minimizing switch-induced system energy change computationally. Combining the numerical result and experimental observations, we propose a quasi-analytic criterion defined by a piecewise function. The piecewise criterion is observed to coincide with the accurate solution very well. As examples, we apply the criterion to: (1) portray a nonhomogeneous switching zone near a stationary crack tip; (2) quantify the switch zone size; (3) predict the volume fractions of ferroelastic and ferroelectric switchings. These predictions all agree with experimental measurements.

Novel room temperature multiferroics for random access memory elements

We have fabricated a variety of PZT-PFW (P bZr₀.₅₂Ti₀.₄₈O₃)1-x(PbFe₂/₃W₁/₃O₃)x [PZTFWx; 0.2 < x <0.4] single-phase tetragonal ferroelectrics via chemical solution deposition [polycrystalline] and pulsed laser deposition [epitaxial] onto Pt/Ti/SiO2/Si(100) and SrTiO₃/Si substrates. These exhibit ferroelectricity and (weak) ferromagnetism above room temperature with strain coupling via electrostriction and magnetostriction. Application of modest magnetic field strength (μ₀H < 1.0 T) destabilizes the long-range ferroelectric ordering and switches the polarization from approximately 22 μC/cm² (0.22 C/m²) to zero (relaxor state). This offers the possibility of three-state logic (+P, 0, -P) and magnetically switched polarizations. Because the switching is of large magnitude (unlike the very small nanocoulomb per centimeter squared values in terbium manganites) and at room-temperature, commercial devices should be possible.

Phase diagrams, dielectric response, and piezoelectric properties of epitaxial ultrathin (001) lead zirconate titanate films under anisotropic misfit strains

We develop a nonlinear thermodynamic model to predict the phase stability of ultrathin epitaxial (001)-oriented ferroelectric PbZr1−xTixO3 (PZT) films with x=1.0, 0.9, 0.8, and 0.7 on substrates which induce anisotropic in-plane strains. The theoretical formalism incorporates the relaxation by misfit dislocations at the film deposition temperature, the possibility of formation of ferroelectric polydomain structures, and the effect of the internal electric field that is generated due to incomplete charge screening at the film-electrode interfaces and the termination of the ferroelectric layer. This analysis allows the development of misfit strain phase diagrams that provide the regions of stability of monodomain and polydomain structures at a given temperature, film thickness, and composition. It is shown that the range of stability for rotational monodomain phase is markedly increased in comparison to the same ferroelectric films on isotropic substrates. Furthermore, the model finds a strong similarity between ultrathin PbTiO3 and relatively thicker PZT films in terms of phase stability. The combinations of the in-plane misfit strains that yield a phase transition sequence that results in a polarization rotation from the c-phase (polarization parallel to the [001] direction in the film) to the r-phase, and eventually to an in-plane polarization parallel to the [110] direction (the aa-phase) is determined to be the path with the most attractive dielectric and piezoelectric coefficients resulting in enhancements of 10 to 100 times in the dielectric permittivity and piezoresponse compared to bulk tetragonal ferroelectrics of the same PZT composition.

Dispersion of the permittivity of a uniaxial ferroelectric solid solution in the morphotropic region

A phenomenologic al theory of the permittivity dispersion fk(ω) in tetragonal ferroelectrics with polarization directed normally to a selected axis was developed for the first time. The permittivity dispersion was calculated for single-domain single crystals in both symmetry-allowed low-symmetry phases. A simple model is proposed for calculating the permittivity dispersion of solid solutions belonging to the morphotropic region of T-c phase diagrams. This model includes the results obtained for single-domain crystals, which in combination with the special averaging method yield the equality (fk(ω)) = ((fk-1 (ω)))-1.

Crystallographic Features of Ferroelectric States around the Tetragonal /Rhombohedral Phase Boundary in Pb&lt;sub&gt;1-x&lt;/sub&gt;La&lt;sub&gt;x&lt;/sub&gt;(Zr&lt;sub&gt;1-y&lt;/sub&gt;Ti&lt;sub&gt;y&lt;/sub&gt;)O&lt;sub&gt;3&lt;/sub&gt;

To understand dielectric properties around the ferroelectric tetragonal (FT)/rhombohedral (FR) phase boundary in Pb1-xLax(Zr1-yTiy)O3, the crystallographic features of ferroelectric states around the boundary have been investigated by transmission electron microscopy. It was found that, when the Ti content approached to the phase boundary in the FT-phase area, a dielectric property became the relaxor behavior. The corresponding change in the crystallographic features is that the usual FT state is converted into the nanometer-sized coexisting state of the ferroelectric monoclinic (FM) and FR phases. Because the crystal structure of FR-phase regions in the coexisting state involves the R25-type rotational displacement of oxygen octahedra, the FR phase can be identified as the low-temperature ferroelectric rhombohedral phase that is present in Pb(Zr1-yTiy)O3. It is thus understood that the relaxor behavior found in Pb1-xLax(Zr1-yTiy)O3 should be associated with the presence of the nanometer-sized coexisting state that consists of two ferroelectric phases.

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.

Ferroelectric Domain Structures and their Morphology Evolution in Pb(Ni1/3Nb2/3)O3–PbZrO3–PbTiO3 Piezoelectric Ceramics Modified by Bismuth and Zinc Substitutions

Ferroelectric domain structures and their morphology evolution in the Bi‐ and Zn‐modified (Pb0.985Bi0.01)(Ni1/4Zn1/12Nb2/3)x(ZrσTi1−σ)1−xO3 piezoelectric ceramics (0.20≤x≤0.60 and 0.10≤σ≤0.60) are investigated as a function of the relaxor Pb(Ni1/3Nb2/3)O3 content and the Zr/(Zr+Ti) ratio (σ) by transmission electron microscopy and selected area electron diffraction, and followed by a complete analysis of the nature of the domain walls based on the predicated twinning planes for the formation of domains in these piezoelectric ceramic systems. A systematic variation in the domain morphology was observed as the compositions move from the ferroelectric tetragonal (FT) to pseudocubic (Fpc) phases, and then to the rhombohedral (FR) phase. Wedged‐shaped domains with misoriented {110} domain walls and mixed with herringbone‐like configuration are the main features of the ferroelectric domains in the FT and Fpc phases, whereas in the compositions near the morphotropic phase boundary (MPB) between the Fpc and FR phases, the characteristic feature of the ferroelectric domains is an intricate domain structure exhibiting a fluctuating mottled contrast. However, the domain boundaries in the FR phase exhibit a wavy character. The domain feature for the compositions at/near the MPB between the FT and FR phases with high property coefficients is a 90° domain texture mixed with an intricate domain structure. The different domain configurations observed in the FT and FR phases are due to their different accommodations of local elastic strain fields. The piezoelectric soft behavior and a normal‐relaxor ferroelectric behavior transition observed in this piezoelectric ceramic system are closely related to the above domain morphology evolution as increasing the PNN content or the Zr/(Zr+Ti) ratio.

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 &amp; Co. KGaA, Weinheim)

Materials contrast in piezoresponse force microscopy

Piezoresponse force microscopy (PFM) contrast in transversally isotropic material corresponding to the case of c+-c− domains in tetragonal ferroelectrics is analyzed using Green’s function theory by Felten et al. [J. Appl. Phys. 96, 563 (2004)]. A simplified expression for PFM signal as a linear combination of relevant piezoelectric constant is obtained. This analysis is extended to piezoelectric material of arbitrary symmetry with weak elastic and dielectric anisotropies. These results provide a framework for interpretation of PFM signals for systems with unknown or poorly known local elastic and dielectric properties, including nanocrystalline materials, ferroelectric polymers, and biopolymers.

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.

Study of new rare earth family Pb1.6K1.2R0.2Nb5O15 (R=La, Nd, Sm, Eu and Gd) of tetragonal tungsten bronze-type ferroelectrics

A new ferroelectric rare earth family Pb 1.6 K 1.2 R 0.2 Nb 5 O 15 with R=La, Nd, Sm, Eu and Gd (PKRN) of tetragonal tungsten bronze type ferroelectrics was synthesized. The ferroelectric transition with nonuniform distribution of critical temperature over a ceramic sample was found from dielectric measurements. According to X-ray diffraction measurements, the ferroelectric phase has an orthorhombic symmetry. The transition temperature was shown to decrease weakly with increasing radius of the rare earth ion R.