Role of random electric fields in relaxors

Critical Insight into Pretransitional Behavior and Dielectric Tunability of Relaxor Ceramics

This model discussion focuses on links between the unique properties of relaxor ceramics and the basics of Critical Phenomena Physics and Glass Transition Physics. It indicates the significance of uniaxiality for the appearance of mean-field type features near the paraelectric-to-ferroelectric phase transition. Pretransitional fluctuations, that are increasing up to the size of a grain and leading to inter-grain, random, local electric fields are responsible for relaxor ceramics characteristics. Their impact yields the pseudospinodal behavior associated with "weakly discontinuous" local phase transitions. The emerging model redefines the meaning of the Burns temperature and polar nanoregions (PNRs). It offers a coherent explanation of "dielectric constant" changes with the "diffused maximum" near the paraelectric-to-ferroelectric transition, the sensitivity to moderate electric fields (tunability), and the "glassy" dynamics. These considerations are challenged by the experimental results of complex dielectric permittivity studies in a Ba0.65Sr0.35TiO3 relaxor ceramic, covering ca. 250 K, from the paraelectric to the "deep" ferroelectric phase. The distortion-sensitive and derivative-based analysis in the paraelectric phase and the surrounding paraelectric-to-ferroelectric transition reveal a preference for the exponential scaling pattern for ε(T) changes. This may suggest that Griffith-phase behavior is associated with mean-field criticality disturbed by random local impacts. The preference for the universalistic "critical & activated" evolution of the primary relaxation time is shown for dynamics. The discussion is supplemented by a coupled energy loss analysis. The electric field-related tunability studies lead to scaling relationships describing their temperature changes.

Emergence of high piezoelectricity from competing local polar order-disorder in relaxor ferroelectrics

Relaxor ferroelectrics are known for outstanding piezoelectric properties, finding a broad range of applications in advanced electromechanical devices. Decoding the origins of the enhanced properties, however, have long been complicated by the heterogeneous local structures. Here, we employ the advanced big-box refinement method by fitting neutron-, X-ray-based total scattering, and X-ray absorption spectrum simultaneously, to extract local atomic polar displacements and construct 3D polar configurations in the classical relaxor ferroelectric Pb(Mg_1/3Nb_2/3)O₃-PbTiO₃. Our results demonstrate that prevailing order-disorder character accompanied by the continuous rotation of local polar displacements commands the composition-driven global structure evolution. The omnidirectional local polar disordering appears as an indication of macroscopic relaxor characteristics. Combined with phase-field simulations, it demonstrates that the competing local polar order-disorder between different states with balanced local polar length and direction randomness leads to a flattening free-energy profile over a wide polar length, thus giving rise to high piezoelectricity. Our work clarifies that the critical structural feature required for high piezoelectricity is the competition states of local polar rather than relaxor.

Brillouin Scattering Study of Electro-Optic KTa1-xNbxO3 Crystals

The functionality enhancement of ferroelectrics by local polar clusters called polar nanoregions (PNRs) is one of the current interests in materials science. KTa_1-xNb_xO₃ (KTN) with perovskite structure is a well-known electro-optic crystal with a large Kerr effect. The existence of PNRs in relaxor-like ferroelectric Nb-rich KTN with homovalent B-site cations is controversial. This paper reviews recent progress in understanding precursor dynamics in Nb-rich KTN crystals studied using Brillouin scattering. The intense central peak (CP) and significant softening of sound velocity are observed above the Curie temperature (T_C) due to the polarization fluctuations in PNRs. The effects of Li-doping, defects, and electric fields on the growth and/or creation of PNRs are found using changes in acoustic properties. The electric-field-induced T_C, which is shifted to higher values with increases in applied voltage, including critical endpoint (CEP) and field gradient by trapped electrons, are discussed as well. This new knowledge may give new insight into advanced functionality in perovskite ferroelectrics.

Thin-Film Ferroelectrics

Over the last 30 years, the study of ferroelectric oxides has been revolutionized by the implementation of epitaxial-thin-film-based studies, which have driven many advances in the understanding of ferroelectric physics and the realization of novel polar structures and functionalities. New questions have motivated the development of advanced synthesis, characterization, and simulations of epitaxial thin films and, in turn, have provided new insights and applications across the micro-, meso-, and macroscopic length scales. This review traces the evolution of ferroelectric thin-film research through the early days developing understanding of the roles of size and strain on ferroelectrics to the present day, where such understanding is used to create complex hierarchical domain structures, novel polar topologies, and controlled chemical and defect profiles. The extension of epitaxial techniques, coupled with advances in high-throughput simulations, now stands to accelerate the discovery and study of new ferroelectric materials. Coming hand-in-hand with these new materials is new understanding and control of ferroelectric functionalities. Today, researchers are actively working to apply these lessons in a number of applications, including novel memory and logic architectures, as well as a host of energy conversion devices.

Spontaneous helielectric nematic liquid crystals: Electric analog to helimagnets

Recently, a type of ferroelectric nematic fluid has been discovered in liquid crystals in which the molecular polar nature at molecule level is amplified to macroscopic scales through a ferroelectric packing of rod-shaped molecules. Here, we report on the experimental proof of a polar chiral liquid matter state, dubbed helielectric nematic, stabilized by the local polar ordering coupled to the chiral helicity. This helielectric structure carries the polar vector rotating helically, analogous to the magnetic counterpart of helimagnet. The helielectric state can be retained down to room temperature and demonstrates gigantic dielectric and nonlinear optical responses. This matter state opens a new chapter for developing the diverse polar liquid crystal devices.

Surfactant-Free Synthesis of Three-Dimensional Perovskite Titania-Based Micron-Scale Motifs Used as Catalytic Supports for the Methanol Oxidation Reaction

We synthesized and subsequently rationalized the formation of a series of 3D hierarchical metal oxide spherical motifs. Specifically, we varied the chemical composition within a family of ATiO3 (wherein "A" = Ca, Sr, and Ba) perovskites, using a two-step, surfactant-free synthesis procedure to generate structures with average diameters of ~3 microns. In terms of demonstrating the practicality of these perovskite materials, we have explored their use as supports for the methanol oxidation reaction (MOR) as a function of their size, morphology, and chemical composition. The MOR activity of our target systems was found to increase with decreasing ionic radius of the "A" site cation, in order of Pt/CaTiO3 (CTO) > Pt/SrTiO3 (STO) > Pt/BaTiO3 (BTO). With respect to morphology, we observed an MOR enhancement of our 3D spherical motifs, as compared with either ultra-small or cubic control samples. Moreover, the Pt/CTO sample yielded not only improved mass and specific activity values but also a greater stability and durability, as compared with both commercial TiO2 nanoparticle standards and precursor TiO2 templates.

The Effect of Intensity Fluctuations on Sequential X-ray Photon Correlation Spectroscopy at the X-ray Free Electron Laser Facilities

How materials evolve at thermal equilibrium and under external excitations at small length and time scales is crucial to the understanding and control of material properties. X-ray photon correlation spectroscopy (XPCS) at X-ray free electron laser (XFEL) facilities can in principle capture dynamics of materials that are substantially faster than a millisecond. However, the analysis and interpretation of XPCS data is hindered by the strongly fluctuating X-ray intensity from XFELs. Here we examine the impact of pulse-to-pulse intensity fluctuations on sequential XPCS analysis. We show that the conventional XPCS analysis can still faithfully capture the characteristic time scales, but with substantial decrease in the signal-to-noise ratio of the g2 function and increase in the uncertainties of the extracted time constants. We also demonstrate protocols for improving the signal-to-noise ratio and reducing the uncertainties.

Polarization Spinodal at Ferroelectric Morphotropic Phase Boundary

Here, we report a new phenomenon of uniform and continuous transformation of a single polarization domain into alternating nanodomains of two polarization vectors with the same magnitude but different directions at ferroelectric morphotropic phase Boundary (MPB). The transformation is fully reversible and could enhance the piezoelectric coefficient d_{33}. Further free energy calculations illustrate that such a polarization "decomposition" process occurs within the region on the Landau free energy curve with respect to the polarization direction where the second derivative becomes negative, which is similar to spinodal instability in phase transformations such as spinodal ordering or isostructural phase separation (e.g., spinodal decomposition). This "polarization spinodal" uncovers a new mechanism of polarization switching that may account for the ultrahigh ahysterestic piezoelectric strain at the MPB. This work could shed light on the development of phase transition theory and the design of novel ferroelectric memory materials.

Morphotropic Relaxor Boundary in a Relaxor System Showing Enhancement of Electrostrain and Dielectric Permittivity

In ferroelectric and relaxor-ferroelectric materials, piezoelectric and dielectric properties are significantly enhanced at the morphotropic phase boundary (MPB), a boundary between different ferroelectric phases with different macroscopic symmetries. By contrast, in relaxor systems, such an MPB does not exist because relaxors of different compositions possess the same macroscopic symmetry. Here, we report the existence of a morphotropic relaxor boundary (MRB) in the single phase relaxor region of a K_{0.5}Na_{0.5}NbO_{3}-xBaTiO_{3} system, which is a composition-induced boundary between two relaxors with different local polar symmetries (tetragonal versus rhombohedral) but with the same macroscopic cubic symmetry. At the MRB the electrostrain increases by ∼3 times and the permittivity increases by ∼1.5 times over a wide temperature range of more than 100 K, as compared with off-MRB compositions. Our Letter demonstrates that the MRB may become an effective mechanism to enhance the dielectric and electrostrictive properties of relaxors.

Giant piezoelectricity of Sm-doped Pb(Mg1/3Nb2/3)O3-PbTiO3 single crystals

High-performance piezoelectrics benefit transducers and sensors in a variety of electromechanical applications. The materials with the highest piezoelectric charge coefficients (d ₃₃) are relaxor-PbTiO₃ crystals, which were discovered two decades ago. We successfully grew Sm-doped Pb(Mg_1/3Nb_2/3)O₃-PbTiO₃ (Sm-PMN-PT) single crystals with even higher d ₃₃ values ranging from 3400 to 4100 picocoulombs per newton, with variation below 20% over the as-grown crystal boule, exhibiting good property uniformity. We characterized the Sm-PMN-PT on the atomic scale with scanning transmission electron microscopy and made first-principles calculations to determine that the giant piezoelectric properties arise from the enhanced local structural heterogeneity introduced by Sm³⁺ dopants. Rare-earth doping is thus identified as a general strategy for introducing local structural heterogeneity in order to enhance the piezoelectricity of relaxor ferroelectric crystals.

The relation of local order to material properties in relaxor ferroelectrics

Correlating electromechanical and dielectric properties with nanometre-scale order is the defining challenge for the development of piezoelectric oxides. Current lead (Pb)-based relaxor ferroelectrics can serve as model systems with which to unravel these correlations, but the nature of the local order and its relation to material properties remains controversial. Here we employ recent advances in diffuse scattering instrumentation to investigate crystals that span the phase diagram of PbMg_1/3Nb_2/3O₃-xPbTiO₃ (PMN-xPT) and identify four forms of local order. From the compositional dependence, we resolve the coupling of each form to the dielectric and electromechanical properties observed. We show that relaxor behaviour does not correlate simply with ferroic diffuse scattering; instead, it results from a competition between local antiferroelectric correlations, seeded by chemical short-range order, and local ferroic order. The ferroic diffuse scattering is strongest where piezoelectricity is maximal and displays previously unrecognized modulations caused by anion displacements. Our observations provide new guidelines for evaluating displacive models and hence the piezoelectric properties of environmentally friendly next-generation materials.

Ultrahigh piezoelectricity in ferroelectric ceramics by design

Piezoelectric materials, which respond mechanically to applied electric field and vice versa, are essential for electromechanical transducers. Previous theoretical analyses have shown that high piezoelectricity in perovskite oxides is associated with a flat thermodynamic energy landscape connecting two or more ferroelectric phases. Here, guided by phenomenological theories and phase-field simulations, we propose an alternative design strategy to commonly used morphotropic phase boundaries to further flatten the energy landscape, by judiciously introducing local structural heterogeneity to manipulate interfacial energies (that is, extra interaction energies, such as electrostatic and elastic energies associated with the interfaces). To validate this, we synthesize rare-earth-doped Pb(Mg_1/3Nb_2/3)O₃-PbTiO₃ (PMN-PT), as rare-earth dopants tend to change the local structure of Pb-based perovskite ferroelectrics. We achieve ultrahigh piezoelectric coefficients d₃₃ of up to 1,500 pC N^-1 and dielectric permittivity ε₃₃/ε₀ above 13,000 in a Sm-doped PMN-PT ceramic with a Curie temperature of 89 °C. Our research provides a new paradigm for designing material properties through engineering local structural heterogeneity, expected to benefit a wide range of functional materials.

Magnetic ordering and dielectric relaxation in the double perovskite YBaCuFeO5

Using magnetization, dielectric constant, and neutron diffraction measurements on a high quality single crystal of YBaCuFeO₅ (YBCFO), we demonstrate that the crystal shows two antiferromagnetic transitions at [Formula: see text] K and [Formula: see text] K, and displays a giant dielectric constant with a characteristic of the dielectric relaxation at T _N2. It does not show the evidence of the electric polarization for the crystal used for this study. The transition at T _N1 corresponds with a paramagnetic to antiferromagnetic transition with a magnetic propagation vector doubling the unit cell along three crystallographic axes. Upon cooling, at T _N2, the commensurate spin ordering transforms to a spiral magnetic structure with a propagation vector of ([Formula: see text] [Formula: see text] [Formula: see text]), where [Formula: see text], [Formula: see text], and [Formula: see text] are odd, and the incommensurability δ is temperature dependent. Around the transition boundary at T _N2, both commensurate and incommensurate spin ordering coexist.

Compositional phase diagram and microscopic mechanism of Ba1−xCaxZryTi1−yO3 relaxor ferroelectrics

A model of a multiphase with coexisting cubic structures is proposed to provide an atomic-scale mechanism for the relaxor behavior of lead-free BCZT relaxor ferroelectrics.

The origin of ultrahigh piezoelectricity in relaxor-ferroelectric solid solution crystals

The discovery of ultrahigh piezoelectricity in relaxor-ferroelectric solid solution single crystals is a breakthrough in ferroelectric materials. A key signature of relaxor-ferroelectric solid solutions is the existence of polar nanoregions, a nanoscale inhomogeneity, that coexist with normal ferroelectric domains. Despite two decades of extensive studies, the contribution of polar nanoregions to the underlying piezoelectric properties of relaxor ferroelectrics has yet to be established. Here we quantitatively characterize the contribution of polar nanoregions to the dielectric/piezoelectric responses of relaxor-ferroelectric crystals using a combination of cryogenic experiments and phase-field simulations. The contribution of polar nanoregions to the room-temperature dielectric and piezoelectric properties is in the range of 50–80%. A mesoscale mechanism is proposed to reveal the origin of the high piezoelectricity in relaxor ferroelectrics, where the polar nanoregions aligned in a ferroelectric matrix can facilitate polarization rotation. This mechanism emphasizes the critical role of local structure on the macroscopic properties of ferroelectric materials.

Combining a perovskite ferroelectric with moderate piezoelectric properties and a nonpiezoelectric pervoskite relaxor can create a highly piezoelectric material. Here, the authors help explain this unusual result by quantifying how polar nanoregions in the material contribute to its piezoelectric response.

Giant electromechanical coupling of relaxor ferroelectrics controlled by polar nanoregion vibrations

Relaxor-based ferroelectrics are prized for their giant electromechanical coupling and have revolutionized sensor and ultrasound applications. A long-standing challenge for piezoelectric materials has been to understand how these ultrahigh electromechanical responses occur when the polar atomic displacements underlying the response are partially broken into polar nanoregions (PNRs) in relaxor-based ferroelectrics. Given the complex inhomogeneous nanostructure of these materials, it has generally been assumed that this enhanced response must involve complicated interactions. By using neutron scattering measurements of lattice dynamics and local structure, we show that the vibrational modes of the PNRs enable giant coupling by softening the underlying macrodomain polarization rotations in relaxor-based ferroelectric PMN-xPT {(1 - x)[Pb(Mg1/3Nb2/3)O3] - xPbTiO3} (x = 30%). The mechanism involves the collective motion of the PNRs with transverse acoustic phonons and results in two hybrid modes, one softer and one stiffer than the bare acoustic phonon. The softer mode is the origin of macroscopic shear softening. Furthermore, a PNR mode and a component of the local structure align in an electric field; this further enhances shear softening, revealing a way to tune the ultrahigh piezoelectric response by engineering elastic shear softening.

Simulating the Radio-Frequency Dielectric Response of Relaxor Ferroelectrics: Combination of Coarse-Grained Hamiltonians and Kinetic Monte Carlo Simulations

The radio-frequency dielectric response of the lead-free Ba(Zr_{0.5}Ti_{0.5})O_{3} relaxor ferroelectric is simulated using a coarse-grained Hamiltonian. This concept, taken from real-space renormalization group theories, allows us to depict the collective behavior of correlated local modes gathered in blocks. Free-energy barriers for their thermally activated collective hopping are deduced from this ab initio-based approach, and used as input data for kinetic Monte Carlo simulations. The resulting numerical scheme allows us to simulate the dielectric response for external field frequencies ranging from kHz up to a few tens of MHz for the first time and to demonstrate, e.g., that local (electric or elastic) random fields lead to the dielectric relaxation in the radio-frequency range that has been observed in relaxors.

Super-crystals in composite ferroelectrics

As atoms and molecules condense to form solids, a crystalline state can emerge with its highly ordered geometry and subnanometric lattice constant. In some physical systems, such as ferroelectric perovskites, a perfect crystalline structure forms even when the condensing substances are non-stoichiometric. The resulting solids have compositional disorder and complex macroscopic properties, such as giant susceptibilities and non-ergodicity. Here, we observe the spontaneous formation of a cubic structure in composite ferroelectric potassium-lithium-tantalate-niobate with micrometric lattice constant, 10(4) times larger than that of the underlying perovskite lattice. The 3D effect is observed in specifically designed samples in which the substitutional mixture varies periodically along one specific crystal axis. Laser propagation indicates a coherent polarization super-crystal that produces an optical X-ray diffractometry, an ordered mesoscopic state of matter with important implications for critical phenomena and applications in miniaturized 3D optical technologies.

Phase transition of chemically doped uniaxial relaxor ferroelectric

We report a neutron scattering study of the ferroelectric phase transition in Sr0.585Ce0.025Ba0.39Nb2O6 (SBN-61:Ce). We find no evidence for a soft transverse optic phonon. We do, however, observe anisotropic diffuse scattering. This scattering has inelastic and elastic contributions. In the paraelectric phase the susceptibility associated with the elastic diffuse scattering from SBN-61:Ce increases on approaching the transition temperature. In the ferroelectric phase the lineshape of the elastic scattering is consistent with the form expected for the ferroelectric domain walls. In contrast to the macroscopic observations, the scattering properties of Ce-doped crystal do not exhibit important changes with respect to those of pure Sr0.61Ba0.39Nb2O6.

Piezoelectric activity in Perovskite ferroelectric crystals

Perovskite ferroelectrics (PFs) have been the dominant piezoelectric materials for various electromechanical applications, such as ultrasonic transducers, sensors, and actuators, to name a few. In this review article, the development of PF crystals is introduced, focusing on the crystal growth and piezoelectric activity. The critical factors responsible for the high piezoelectric activity of PFs (i.e., phase transition, monoclinic phase, domain size, relaxor component, dopants, and piezoelectric anisotropy) are surveyed and discussed. A general picture of the present understanding on the high piezoelectricity of PFs is described. At the end of this review, potential approaches to further improve the piezoelectricity of PFs are proposed.

Frustration of ferroelectricity in epitaxial film of relaxor ferroelectric PbSc1/2Nb1/2O3

Relaxor-to-ferroelectric transformations induced by varying electric fields and temperatures are studied experimentally in acube-on-cubetype epitaxial PbSc(1/2)Nb(1/2)O3 film grown on La(1/2)Sr(1/2)CoO3/MgO(001). Dielectric response, quasi-static and dynamic polarization, and dynamic current-voltage characteristics evidence the absence of spontaneous relaxor-to-ferroelectric transition. The electricfield-induced transformation from a glass-like relaxor state to a new dynamic polar state is detected at low temperatures below 100 K only. The frustration of ferroelectricity is discussed in relation to orientational anisotropy of the dipolar system in the epitaxial (001) film.