Tetragonal Ferroelectrics Research Articles

Huge mobility difference between the neutral and charged steps on 180° domain walls of PbTiO3 by first-principles calculations

The microscopic mechanism of ferroelectric switching is the motion of domain walls, which is actually accomplished by the movement of tiny steps on the domain walls. Using first-principles calculations, the detailed polarization structures and the motion barriers of neutral and charged steps on 180° domain walls of prototypical ferroelectrics PbTiO3 are elaborately revealed in this study. While the Bloch components get weakened near all neutral steps, they become weakened/strengthened near the head-to-head/tail-to-tail charged steps. The neutral step possesses a lower formation energy but a higher migration barrier, indicating that the charged step could move faster. Based on these results, the possible motion picture of steps on one 180° domain wall of tetragonal ferroelectrics is proposed, which provides a better understanding of the mechanism of domain wall motion and may shed light on the future development of domain wall–based functional devices.

Pyroelectric Effect in Tetragonal Ferroelectrics BaTiO3 and KNbO3 Studied with Density Functional Theory

Pyroelectric Effect in Tetragonal Ferroelectrics BaTiO₃ and KNbO₃ Studied with Density Functional Theory

The morphologies of twins in tetragonal ferroelectrics

Twins, as a special structure, have been observed in a small number of experiments on ferroelectrics. A good understanding of the morphologies of twins is very important for twin engineering applications in ferroelectric materials. In this work, the morphologies of twins in tetragonal ferroelectrics are investigated using the compatibility analysis of the transformation strains and spontaneous polarization and the energetic analysis. The tetragonal BaTiO3 single crystal is chosen as an example for the material system. The results show that the lamellar twin structures with 111 as the twin plane have been identified by both compatibility analysis and energetic analysis, which is consistent with the experimental observations. In addition to 111 twin structures, 12¯1 and 21¯5 twin structures can also appear in tetragonal ferroelectrics. Furthermore, stable state uncharged twin boundaries and metastable charged twin boundaries are distinguished by energetic analysis, where the spontaneous polarization is compatible across the uncharged twin boundaries, while it is not compatible across the charged twin boundaries. The results predicted by the compatibility analysis and energetic analysis are consistent, thus providing a pathway for understanding the morphologies of twins.

An effective Fourier spectral phase-field approach for ferroelectric materials

In this article, we propose an efficient iterative numerical algorithm applying a Fourier spectral method to accurately compute the coupled elasto–electrostatic equilibrium equations in ferroelectric microstructures. The method is implemented for a phase-field model for domain pattern formation and domain kinetics evolution in tetragonal perovskite ferroelectrics, that uses spontaneous polarization as order parameter and includes the piezoelectric effect in the constitutive equation. The scheme is based on a two-scale homogenization approach, introducing local perturbations for stress and dielectric displacement. Green’s functions are derived in Fourier space for the coupled constitutive equations. Furthermore, using model parameters for BaTiO3 we investigate domain formation in 2D and 3D, and the polarization switching process starting from a critical nucleus subjected to an applied electric field and compressive stress. The simulation results based on the proposed method reveal that for polarization switching under external fields, intermediately appearing domains with 90° rotated polarization are formed, that reduce electrostatic or elastic strain energy.

Examining the Relationship Between Local Polarization and Modulation Variations in a Relaxor Ferroelectric Tetragonal Tungsten Bronze By 4D STEM

Examining the Relationship Between Local Polarization and Modulation Variations in a Relaxor Ferroelectric Tetragonal Tungsten Bronze By 4D STEM

Self-Organized Ferroelastic Superdomains with Enhanced Piezoresponse in (101)-Oriented Pb(Zr0.2,Ti0.8)O3 Thin Films

Thin film engineering, utilizing proper control of crystalline orientation, strain, thickness, and defect density in thin films, has offered tremendous degrees of freedom for researchers to modify the physical properties, phase stability, and domain architectures in a wide spectrum of functional materials. This work unveils a naturally formed superdomain architecture arising from the low-orientation-symmetry-induced energetically degenerate state in a (101)-oriented tetragonal Pb(Zr,Ti)O3 epitaxial film. Different from conventional (101)-oriented/(110)-oriented domains found in (101)-oriented tetragonal Pb(Zr,Ti)O3 epitaxial heterostructures, these superdomains are composed of (101)-oriented domains with an alternative arrangement of opposite out-of-plane polarizations. Additionally, the conjunction between these superdomains has been found as another variant of the 90° domain wall that can exist in the low-symmetric preferred crystallographic orientation. The superdomains simultaneously exhibit an atypical piezoresponse hysteresis loop with additional metastable states, corresponding to the multistate ferroelastic domain switching process. This work gives distinct insight into the correlation between the domain pattern, lattice symmetry, and polarity switching, offering an effective way for exploring and engineering ultrafine domain features in tetragonal ferroelectrics.

Spontaneous electric polarization of high-valance-ion-doped lead-free ferroelectric KSr2Nb5O15 by first-principles calculations

The polarizability and spontaneous polarization of high-valent cations (La3+, Bi3+, Y3+, Ti4+, Ta5+ and W6+) doped KSr2Nb5O15 lead-free tetragonal tungsten bronze ferroelectrics are calculated by using the first principles and experimental results. The cation dopants give different results, mainly due to the shortage of the additivity rule that ignores the ion polarizability of the missing atoms and the polarizability caused by the interaction of the atoms. The polarizability based on the dielectric constants is in good agreement with experimental values, especially for the structures with trivalent cation doping. And the spontaneous polarization calculated by the polar moment by using first principles result is consistent with that based on the polar moment from experiment. This shows the reliability of the prediction, and the spontaneous polarization of high-valent cations doped KSr2Nb5O15 are confirmed. This work paves a way for the spontaneous polarization of the ferroelectric materials with tetragonal tungsten bronze structure.

Local Structure and Order–Disorder Transitions in “Empty” Ferroelectric Tetragonal Tungsten Bronzes

The “empty” tetragonal tungsten bronze Ba4La0.67□1.33Nb10O30 displays both relaxor-like and normal dielectric anomalies as a function of temperature; the former is associated with loss of ferroelec...

Photo-Hall, photorefractive and photomagnetoelectric effects in tungsten bronzes and related tetragonal ferroelectrics

We present, at the phenomenological point of view, the responses of tetragonal ferroelectrics under linearly polarized light illumination, using a new theory based on the intertwining of the symmetries of both the material and the incident wave. Photopolarization, photomagnetic, photovoltaic, and phototoroidal vector responses are worked out as functions of the wave vector and wave polarization directions. Second-order response tensors associated with photoelastic, photomagnetoelectric, photorefractive, photoconductivity, and photo-Hall effects are also described in detail. We focus attention on the tetragonal and orthorhombic phases in crystals of the family of tungsten bronzes, and we discuss related tetragonal materials.

Frequency-switchable polarity-inverted BAW resonators based on electric-field-induced piezoelectric PMN-PT/PZT epitaxial film stacks

Spontaneous polarization of tetragonal ferroelectrics cannot be inverted unless the applied electric field is greater than the coercive field. In the case of the cubic phase, on the other hand, polarization and piezoelectricity can be induced merely by applying an electric field. In this study, we proposed polarity-inverted cubic/tetragonal multilayer film resonators which allow switching between the fundamental and high-order mode resonances through the independent control of the polarization of the cubic layer. Frequency switching in bulk acoustic wave (BAW) resonators based on all-epitaxial cubic 0.95Pb(Mg1/3Nb2/3)O3 (PMN)-0.05PbTiO3 (PTO)/tetragonal Pb(Zr,Ti)O3 (PZT) bilayer film stacks is demonstrated theoretically and experimentally. Under a negative voltage application, which is less than the coercive field of the tetragonal PZT layers, a fundamental mode resonance (327 MHz) is observed, whereas a second-mode resonance (779 MHz) is observed under a positive voltage application in BAW resonators. A theoretical simulation based on Mason’s equivalent circuit model, taking account of the polarity-inverted bilayer structure, shows good agreement with the experimental results.

Effects of B-Site Substitution on Up-Conversion Luminescence and Ferroelectric Properties in Er3+-Doped Strontium Barium Niobate

An effective route to regulate up-conversion luminescence (UCL) and polarization properties has been developed in tetragonal tungsten bronze ferroelectrics (TTBs). In this work, we have synthesized a series of (Sr0.29Er0.01)Ba0.7Nb2−xMoxO6 (SBN-Ax, 0 ≤ x ≤ 0.1) and Sr0.3Ba0.7(Nb1.99−xMoxEr0.01)O6 (SBN-Bx, 0 ≤ x ≤ 0.1) ceramics. Through investigating the UCL spectra of SBN-Ax and SBN-Bx ceramics, markedly different enhancement effects of UCL intensity have been revealed which can be attributed to the peculiar structural feature of TTBs. Furthermore, temperature sensing, dielectric and ferroelectric properties have also confirmed to display B-site substitution-dependent intriguing behaviors.

Periodic boundary conditions for the simulation of 3D domain patterns in tetragonal ferroelectric material

Periodic domain patterns in tetragonal ferroelectrics are explored using a phase field model calibrated for barium titanate. In this context, we discuss the standard periodic boundary condition and introduce the concept of reverse periodic boundary conditions. Both concepts allow the assembly of cubic cells in accordance with mechanical and electrical conditions. However, application of the reverse periodic boundary condition is due to an increased size of the RVE and enforces more complex structures compared to the standard condition. This may be of particular interest for other multiphysics simulations. Additionally, we formulate mechanical side conditions with minimal spherical (hydrostatic) stress, or conditions with controlled average strain. It is found that in sufficiently small periodic cells, only a uniform single domain, or the simplest stripe domains constitute equilibrium states. However, once the periodic cells are of order 20 domain wall widths in size, more complex, 3-dimensional patterns emerge. Some of these patterns are known from prior studies, but we also identify other domain patterns with long, ribbon-like domains threaded through them and some vortex-like structures.

Phase-field modeling and electronic structural analysis of flexoelectric effect at 180° domain walls in ferroelectric PbTiO3

The flexoelectric effect is the coupling between strain, polarization, and their gradients, which are prominent at the nanoscale. Although this effect is important to understand nanostructures, such as domain walls in ferroelectrics, its electronic mechanism is not clear. In this work, we combined phase-field simulations and first-principles calculations to study the 180° domain walls in tetragonal ferroelectric PbTiO3 and found that the source of Néel components is the gradient of the square of spontaneous polarization. Electronic structural analysis reveals that there is a redistribution of electronic charge density and potential around domain walls, which produces the electric field and Néel components. This work thus sheds light on the electronic mechanism of the flexoelectric effect around 180° domain walls in tetragonal ferroelectrics.

Domain Wall Architecture in Tetragonal Ferroelectric Thin Films.

Non-Ising-like 180° ferroelectric domain wall architecture and domain distribution in tetragonal PbZrx Ti1-x O3 thin films are probed using a combination of optical second harmonic generation and scanning transmission electron microscopy. In the remnant state, a specific nonlinear optical signature of tilted 180° domain walls corresponding to a mixed Ising-Néel-type rotation of polarization across the wall is shown.

In situ X-ray diffraction of lead zirconate titanate piezoMEMS cantilever during actuation

Synchrotron X-ray diffraction (XRD) was used to probe the electric-field-induced response of a 500nm lead zirconate titanate (52/48, Zr/Ti) (PZT) based piezoelectric microelectromechanical system (piezoMEMS) device. 90° ferroelectric/ferroelastic domain reorientation was observed in a cantilever comprised of a 500nm thick PZT film on a 3μm thick elastic layer composite of SiO2 and Si3N4. Diffraction data from sectors both parallel- and perpendicular-to-field showed the presence of ferroelastic texture, which is typically seen in in situ electric field diffraction studies of bulk tetragonal perovskite ferroelectrics. The fraction of domains reoriented into the field direction was quantified through the intensity changes of the 002 and 200 diffraction profiles. The maximum induced volume fraction calculated from the results was 20%, which is comparable to values seen in previous bulk and thin film ferroelectric diffraction studies. The novelty of the present work is that a fully released ferroelectric thin film device of micron scale dimensions (down to 60,000μm3) was interrogated in situ with an applied electric field using synchrotron XRD. Furthermore, the experiment demonstrates that 90° ferroelectric/ferroelastic domain reorientation can be characterized in samples of such small dimensions.

Control of Tetragonal Distortion and Ferroelectricity in Bi(Zn1/2Ti1/2)O3-Based Lead-Free Ferroelectric Thin Films

Lead-free ferroelectric materials with superior property have been demanded, yet a few lead-free ferroelectrics such as alkali-based (K,Na)NbO3 family and bismath-based (Bi,Na)TiO3 family have been reported. Pb(Zr,Ti)O3[PZT] is one of very famous ferroelectric because their ferroelectric and piezoelectric properties can be controlled by their composition and domain structure. And almost of all for application use, PZT having tetragonal and morphotropic phase boundary[MPB] composition have been used. From a view point of material design in PZT case, mother material of tetragonal PbTiO3 is very important for designing MPB. However, it is know that there are only BaTiO3 and (Bi,K)TiO3 in the field of tetragonal perovskite materials. Novel lead-free tetragonal ferroelectric materials are really wanted. Recently, novel metastable phase materials prepared by high pressure synthesis have been reported. Among them, BiCoO3 1 and Bi(Zn0.5Ti0.5)O3 2 are promising ferroelectric materials due to their high tetragonality, c/a, of over 1.2. Large spontaneous polarization is expected by first principal calculation. BiCoO3 is a one of multiferroic, but unfortunately it is very leaky because of containing Co3+(d 6). On the other hand, Bi(Zn0.5Ti0.5)O3 is constructed by only d 0 and d 10 ions. Unfortunately, nobody reported their ferroelectricity. We can expect that leakage property will be better than that of BiCoO3. Therefore, we have focused on Bi(Zn0.5Ti0.5)O3 and prepare novel ferroelectric materials. Epitaxial Bi(Zn0.5Ti0.5)O3-BiFeO3 thin films with about 300 nm thickness were grown at 700oC on (100)cSrRuO3//(100)SrTiO3 by pulsed metalorganic chemical vapor deposition using Bi[(CH3)2(2-(CH3)2NCH2C6H4)] (Tosoh Co. Ltd), Zn(C14H25O2)2, Ti(O∙i-C3H7)4, Fe(C2H5C5H4)2 and oxygen gas as the source materials. SrRuO3 films were grown by RF magnetron sputtering method. Film thickness and composition were confirmed by surface profilometry and X-ray fluorescence (XRF) calibrated using standard samples. Crystal structure of the deposited films was characterized by X-ray diffraction (XRD) analysis using a four-axis diffractometer with CuKa radiation. Atomic microstructures of the films were observed by high angle annular dark field scanning transmission electron microscopy (HAADF-STEM). Pt/[Bi(Zn1/2Ti1/2)O3- BiFeO3]/SrRuO3 capacitor structure was used for the electrical measurements after making circular Pt top electrodes of 100 mm in diameter, which were deposited by e-beam evaporation. Piezoresponse mappings and longitudinal piezoelectric coefficient (d 33) was measured using piezoresponse force microscopy. High resolution Advanced X-ray reciprocal space mapping leads us to know all diffractions from the films, suggesting that crystal structure and domain structure could be investigated easily. This mapping reveals d-spacing information along both the substrate surface normal and off-normal directions. It is observed that all diffraction peaks from the films can be identified to tetragonal P4mm symmetry as same as Bi(Zn1/2Ti1/2)O3, and a single perovskite phase is achieved to fabricate. The out-of-plane (c-axis) and in-plane (a-axis) lattice parameters calculated from diffractions are 0.465 nm and 0.381 nm, respectively, resulting in a giant tetragonal distortion of (c/a)-1 = 22%. This value is 3.5 times larger than the 6.3% of PbTiO3. In addition, this [(c/a)-1] is larger than the reported one for pure Bi(Zn1/2Ti1/2)O3, [(c/a)-1] = 21%. Similar enlargement of the [(c/a)-1] by the substitution with BiFeO3 has been reported in PbTiO3-BiFeO3, even if the substituted BiFeO3 has rhombohedral symmetry. We have also conducted cross sectional high resolution HAADF-STEM for visualization of the crystal structure directly. The “90o domain boundary” has a 51o/39o angle due to the large tetragonality, which is in good agreement with 50.7o/40.3 o value based on the crystal structure information obtained by XRD measurement. Z-contrast image to perovskite unit cell shows that the B-site ions are also displaced along [001] significantly away from the center. There are in good agreement with structure analysis of the Bi(Zn1/2Ti1/2)O3 prepared by high pressure synthesis. In addition, as XRD results showed no super lattice peaks, B-site cations in perovskite are not ordered. These results clearly indicate that this material is characterized as displacive-type ferroelectric, and unusual angle of the 90o domain is originated from large tetragonal distortion. We will also perform to measure ferroelectricity for discussing relationship between ferroelectricity/piezoelectricity and tetragonality in these materials. 1A. A. Belik, S. Iikubo, K. Kodama, N. Igawa, S. Shamoto, S. Niitaka, M. Azuma, Y. Shimakawa, M. Takano, F. Izumi, and E. Takayama-Muromachi, Chem. Mater. 18 (2006) 798. 2M. R. Suchomel, A. M. Fogg, M. Allix, H. Niu, J. B. Claridge, M. J. Ro sseinsky, Chem. Mater. 18 (2006) 4987.

An unconventional phase field modeling of domains formation and evolution in tetragonal ferroelectrics

Based on characteristic functions of variants, we developed an unconventional phase field modeling for investigating domains formation and evolution in tetragonal ferroelectrics. In order to develop this computational approach, we constructed the anisotropy energy of tetragonal variants, which is used instead of Landau-Devonshire potential in the conventional phase field method, resulting in that much fewer parameters are needed for simulations. This approach is advantageous in simulations of emerging ferroelectric materials. We employ it to study the formation and evolution of domains in tetragonal barium titanate single crystal, as well as the nonlinear behaviors under cyclical stress and electric field loading. A multi-rank laminated ferroelectric domain pattern, 90° domain switching accompanied by polarization rotation, and 180° domain switching accompanied by move of domain wall are predicted. It is found that the speed of 90° domain switching is slower than that of 180° domain switching, due to both polarization and transformation strain changed in 90° domain switching. It also suggests that large strain actuation can be generated in single crystal ferroelectrics via combined electromechanical loading inducing 90° domain switching. The good agreement between simulation results and experimental measurements is observed.

High cycle fatigue damage and life time prediction for tetragonal ferroelectrics under electromechanical loading

High cycle fatigue is one of the most crucial problems in designing reliable ferroelectric actuators and sensors. On the micro- and mesoscales, fatigue crack growth determines the life time of the smart ceramic devices, being controlled by both mechanical and electric loads. Giving rise to residual stresses, ferroelectric domain switching and domain wall motion mediate between crack tip and external loading. Thus, two dissipative processes have to be modeled on the microscale, finally leading to evolutions of damage as well as macroscopic piezoelectric, dielectric and stiffness properties. A condensed approach is used to solve the nonlinear constitutive problem of a polycrystalline representative volume and an accumulation model is applied to efficiently handle predictions of high cycle loading. Numerical examples help investigating measures to foster the life time of ferroelectric devices, always keeping an eye on the actuating performance of the system.

A constitutive and damage model for high cycle fatigue of tetragonal ferroelectrics

AbstractReliability and life time of smart materials are crucial features for the development and design of actuator and sensor devices. Being widely used and exhibiting brittle failure characteristics, ceramic ferroelectrics are of particular interest in this field. Due to manifold interactions of the complex nonlinear constitutive behavior on the one hand and the damage evolution in terms of microcrack growth on the other, modeling and simulation are inevitable to investigate influence parameters on strength, reliability and life time. A condensed approach is used for the simulations considering just one characteristic point in the material, nonetheless accounting for polycrystalline grain interactions. On this basis, a model to predict the life time in terms of high cycle fatigue under electromechanical loading conditions is introduced. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Scale effects and the formation of polarization vortices in tetragonal ferroelectrics

Vortices consisting of 90° quadrant domains are rarely observed in ferroelectrics. Although experiments show polarization flux closures with stripe domains, it is as yet unclear why pure single vortices are not commonly observed. Here, we model and explore the energy of polarization patterns with vortex and stripe domains, formed on the square cross-section of a barium titanate nanowire. Using phase-field simulations, we calculate the associated energy of polarization patterns as a function of nanowire width. Further, we demonstrate the effects of surface energy and electrical boundary conditions on equilibrium polarization patterns. The minimum energy equilibrium polarization pattern for each combination of surface energy and nanowire width is mapped for both open- and short-circuit boundary conditions. The results indicate a narrow range of conditions where single vortices are energetically favorable: nanowire widths less than about 30 nm, open-circuit boundary condition, and surface energy of less than 4 N/m. Short-circuit boundary conditions tend to favor the formation of a monodomain, while surface energy greater than 4 N/m can lead to the formation of complex domain patterns or loss of ferroelectricity. The length scale at which a polarization vortex is energetically favorable is smaller than the typical size of nanoparticle in recent experimental studies. The present work provides insight into the effects of scaling, surface energy, and electrical boundary conditions on the formation of polarization patterns.