Finite-temperature properties of Pb(Zr1-xTi(x))O3 alloys from first principles

Extrinsic Contribution and Instability Properties in Lead-Based and Lead-Free Piezoceramics

Piezoceramic materials generally exhibit a notable instability of their functional properties when they work under real external conditions. This undesirable effect, known as nonlinear behavior, is mostly associated with the extrinsic contribution to material response. In this article, the role of the ferroelectric domain walls’ motion in the nonlinear response in the most workable lead-based and lead-free piezoceramics is reviewed. Initially, the extrinsic origin of the nonlinear response is discussed in terms of the temperature dependence of material response. The influence of the crystallographic phase and of the phase boundaries on the material response are then reviewed. Subsequently, the impact of the defects created by doping in order to control the extrinsic contribution is discussed as a way of tuning material properties. Finally, some aspects related to the grain-size effect on the nonlinear response of piezoceramics are surveyed.

Discovery of stable skyrmionic state in ferroelectric nanocomposites

Non-coplanar swirling field textures, or skyrmions, are now widely recognized as objects of both fundamental interest and technological relevance. So far, skyrmions were amply investigated in magnets, where due to the presence of chiral interactions, these topological objects were found to be intrinsically stabilized. Ferroelectrics on the other hand, lacking such chiral interactions, were somewhat left aside in this quest. Here we demonstrate, via the use of a first-principles-based framework, that skyrmionic configuration of polarization can be extrinsically stabilized in ferroelectric nanocomposites. The interplay between the considered confined geometry and the dipolar interaction underlying the ferroelectric phase instability induces skyrmionic configurations. The topological structure of the obtained electrical skyrmion can be mapped onto the topology of domain-wall junctions. Furthermore, the stabilized electrical skyrmion can be as small as a few nanometers, thus revealing prospective skyrmion-based applications of ferroelectric nanocomposites.

Critical Thickness for Antiferroelectricity in PbZrO3

Ferroelectrics and antiferroelectrics appear to have just the opposite behavior upon scaling down. Below a critical thickness of just a few nanometers the ferroelectric phase breaks into nanodomains that mimic electric properties of antiferroelectrics very closely. On the other hand, antiferroelectric thin films were found to transition from the antiferroelectric behavior to a ferroelectric one under certain growth conditions. At present, the origin of such a transition is controversial. Here, we use accurate first-principles-based finite-temperature simulations to predict the existence of a critical thickness for antiferroelectricity in the most celebrated antiferroelectric, PbZrO3. The origin of this effect is traced to the intrinsic surface contribution that has been previously overlooked. The existence of a critical thickness below which the antiferroelectric phase is replaced with a ferroelectric one not only complements the discovery of a critical thickness for ferroelectricity, but also suggests that ferroelectricity and antiferroelectricity are just two opposite manifestations of the same phenomenon: the material's tendency to develop a long-range order. Nanoscaling offers the opportunity to manipulate this order.

First-principles-based effective Hamiltonian simulations of bulks and films made of lead-free Ba(Zr,Ti)O3 relaxor ferroelectrics

A review of the recent development and application of a first-principles-derived effective Hamiltonian technique to the study of lead-free Ba(Zr,Ti)O3 (BZT) relaxor ferroelectrics is provided. In addition to the computation and analysis of macroscopic properties (such as different types of dielectric responses and electric polarization) and their connections to previous published works, particular emphasis is given to microscopic insights arising from this atomistic technique. These include (i) the numerically-found determination of the physical origin of the relaxor behavior in BZT; and (ii) the prediction of polar nanoregions and the evolution of their morphology as a response to temperature, electric fields and epitaxial misfit strain. Other striking phenomena that were predicted in BZT compounds, such as Fano resonance and field-driven percolation, are also documented and discussed. Finally, a brief perspective of possible remaining computational studies to be conducted in relaxor ferroelectrics, in order to further understand them, is attempted.

Electronic properties of electrical vortices in ferroelectric nanocomposites from large-scale ab initio computations

An original ab initio procedure is developed and applied to a ferroelectric nanocomposite, in order to reveal the effect of electrical vortices on electronic properties. Such procedure involves the combination of two large-scale numerical schemes, namely, the effective Hamiltonian (to incorporate ionic degrees of freedom) and the linear-scaling three-dimensional fragment method (to treat electronic degrees of freedom). The use of such procedure sheds some light into the origin of the recently observed current that is activated at rather low voltages in systems possessing electrical vortices. It also reveals a novel electronic phenomena that is a systematic control of the type of the band-alignment (i.e., type I versus type II) within the same material via the temperature-driven annihilation/formation of electrical topological defects.

Combining high time and angular resolutions: time-resolved X-ray powder diffraction using a multi-channel analyser detector

The design and testing of the new MAD-STROBO data acquisition system are reported. The system realizes stroboscopic collection of high-resolution X-ray powder diffraction profiles under a dynamically applied electric field. It synchronizes an externally applied stimulus and detected X-ray photons. The feasibility of detecting sub-millidegree shifts of powder diffraction profiles with microsecond time resolution is demonstrated. MAD-STROBO may be applied for the investigation of various macroscopic and domain-related processes induced by an external perturbation, such as elasticity or piezoelectricity.

Time-resolved X-ray diffraction reveals the hidden mechanism of high piezoelectric activity in a uniaxial ferroelectric

High piezoelectric activity of many ferroelectrics has been the focus of numerous recent studies. The structural origin of this activity remains poorly understood due to a lack of appropriate experimental techniques and mixing of different mechanisms related to ferroelectricity and ferroelasticity. Our work reports on the study of a uniaxial Sr_{0.5}Ba_{0.5}Nb_{2}O_{6} ferroelectric where the formation of regions with different spontaneous strains is ruled out by the symmetry and where the interrelation between piezoelectricity and ferroelectricity can be inspected in an isolated fashion. We performed x-ray diffraction experiments on a single crystalline sample under alternating electric field and observed an unknown hidden-in-the-bulk mechanism, which suggests that the highest piezoelectric activity is realized in the volumes where nucleation of small ferroelectric domains takes place. This new mechanism creates a novel roadmap for designing materials with enhanced piezoelectric properties.

Why Sn doping significantly enhances the dielectric properties of Ba(Ti 1-x Snx)O3

Through appropriate doping, the properties of BaTiO₃-based ferroelectrics can be significantly enhanced. To determine the physical process induced by the doping of Sn atoms in Ba(Ti_0.8Sn_0.2)O₃, we performed high-resolution scanning transmission electron microscopy experiments and observed that the regions with low Sn content formed polar nano regions (PNRs) embedded in the matrix in Ba(Ti_0.8Sn_0.2)O₃. The interactions among Sn, Ti, Ba and O atoms were determined using first principles calculations. Based on the characteristics of the electronic structure and crystal lattice strain fields, the effects of doping with Sn were investigated. The Sn doping not only changed the electronic structure of the crystal but also increased the dielectric properties of the PNRs. Moreover, the Sn doping was also responsible for the diffuse phase transition of the Ba(Ti_1-xSn_x)O₃ material. The effects mentioned in this paper are universal in lead-free ferroelectrics, and similar elements such as Sb, Mg, and Zr may have the same functions in other systems. Thus, these results provide guidance for the design of the doping process and new systems of ferroelectric or relaxor materials.

Local structure of Pb(Zr0.53Ti0.47)O3

High-angle annular dark-field (HAADF) and annular bright-field (ABF) images recorded from the Pb(ZrxTi1−x)O3morphotropic phase boundary (PZTmpb) showB-site displacements along the 〈110〉 directions and prominent distortions in the oxygen cages surrounding both theBsites and the Pb environments. The measured range ofB-site displacements is about 0.25–0.4 Å. Oxygen cage distortions appear to be variable in shape and dimensions at the unit-cell level. Comparison of the observed displacements with the structural projections based on the established monoclinic space groupCm(Cs3) shows a good overall agreement. A qualitative match betweenCm(Cs3) and the reported observations is inconclusive because of inaccuracy in the measurements, originating from imprecise identification of atomic column centres inherent in the HAADF and ABF images. In most of the observed cases,B-site displacements in HAADF images, and oxygen cage distortions in ABF images, appear pronounced compared with the structural projections inCm(Cs3). Columnar chemical inhomogeneity has been commonly observed in bothB-site and Pb columns in PZTmpb. Weak 〈110〉 diffuse streaking along the [001], [110] and [111] zone axes has been imaged, suggestive of correlation with the systematic ion disorder along 〈110〉.

Theoretical Methods of Domain Structures in Ultrathin Ferroelectric Films: A Review

This review covers methods and recent developments of the theoretical study of domain structures in ultrathin ferroelectric films. The review begins with an introduction to some basic concepts and theories (e.g., polarization and its modern theory, ferroelectric phase transition, domain formation, and finite size effects, etc.) that are relevant to the study of domain structures in ultrathin ferroelectric films. Basic techniques and recent progress of a variety of important approaches for domain structure simulation, including first-principles calculation, molecular dynamics, Monte Carlo simulation, effective Hamiltonian approach and phase field modeling, as well as multiscale simulation are then elaborated. For each approach, its important features and relative merits over other approaches for modeling domain structures in ultrathin ferroelectric films are discussed. Finally, we review recent theoretical studies on some important issues of domain structures in ultrathin ferroelectric films, with an emphasis on the effects of interfacial electrostatics, boundary conditions and external loads.

Relaxor-based ferroelectric single crystals: growth, domain engineering, characterization and applications

In the past decade, domain engineered relaxor-PT ferroelectric single crystals, including (1-x)Pb(Mg1/3Nb2/3)O3-xPbTiO3 (PMN-PT), (1-x)Pb(Zn1/3Nb2/3)O3-xPbTiO3 (PZN-PT) and (1-x-y)Pb(In1/2Nb1/2)O3-yPb(Mg1/3Nb2/3)O3-xPbTiO3 (PIN-PMN-PT), with compositions near the morphotropic phase boundary (MPB) have triggered a revolution in electromechanical devices owing to their giant piezoelectric properties and ultra-high electromechanical coupling factors. Compared to traditional PbZr1-x Ti x O3 (PZT) ceramics, the piezoelectric coefficient d33 is increased by a factor of 5 and the electromechanical coupling factor k33 is increased from < 70% to > 90%. Many emerging rich physical phenomena, such as charged domain walls, multi-phase coexistence, domain pattern symmetries, etc., have posed challenging fundamental questions for scientists. The superior electromechanical properties of these domain engineered single crystals have prompted the design of a new generation electromechanical devices, including sensors, transducers, actuators and other electromechanical devices, with greatly improved performance. It took less than 7 years from the discovery of larger size PMN-PT single crystals to the commercial production of the high-end ultrasonic imaging probe "PureWave". The speed of development is unprecedented, and the research collaboration between academia and industrial engineers on this topic is truly intriguing. It is also exciting to see that these relaxor-PT single crystals are being used to replace traditional PZT piezoceramics in many new fields outside of medical imaging. The new ternary PIN-PMN-PT single crystals, particularly the ones with Mn-doping, have laid a solid foundation for innovations in high power acoustic projectors and ultrasonic motors, hinting another revolution in underwater SONARs and miniature actuation devices. This article intends to provide a comprehensive review on the development of relaxor-PT single crystals, spanning material discovery, crystal growth techniques, domain engineering concept, and full-matrix property characterization all the way to device innovations. It outlines a truly encouraging story in materials science in the modern era. All key references are provided and 30 complete sets of material parameters for different types of relaxor-PT single crystals are listed in the Appendix. It is the intension of this review article to serve as a resource for those who are interested in basic research and practical applications of these relaxor-PT single crystals. In addition, possible mechanisms of giant piezoelectric properties in these domain-engineered relaxor-PT systems will be discussed based on contributions from polarization rotation and charged domain walls.

Effects of a rotating electric field on the properties of epitaxial (001) Pb(Zr,Ti)O3 ultrathin film: a first-principles-based study

Pb(Zr,Ti)O3 ultrathin films under open-circuit electrical boundary conditions and subjected to an electric field rotating in the (1¯10) plane are investigated via the use of an effective Hamiltonian, for different magnitudes of this field. Varying the direction and magnitude of the electric field leads to specific reorganization of dipoles into original configuration states, whose microstructures and macroscopic properties are revealed. In particular, a novel (direction of the electric field-versus-magnitude of the electric field) phase diagram is reported here. The field-induced correlation between the polar distortions and the oxygen octahedral tilting is also discussed.

Properties of epitaxial films made of relaxor ferroelectrics

Finite-temperature properties of epitaxial films made of Ba(Zr,Ti)O3 relaxor ferroelectrics are determined as a function of misfit strain, via the use of a first-principles-based effective Hamiltonian. These films are macroscopically paraelectric at any temperature, for any strain ranging between ≃-3% and ≃+3%. However, original temperature-versus-misfit strain phase diagrams are obtained for the Burns temperature (Tb) and for the critical temperatures (Tm,z and Tm,IP) at which the out-of-plane and in-plane dielectric response peak, respectively, which allow the identification of three different regions. These latter differ from their evolution of Tb, Tm,z, and/or Tm,IP with strain, which are the fingerprints of a remarkable strain-induced microscopic change: each of these regions is associated with its own characteristic behavior of polar nanoregions at low temperature, such as strain-induced rotation or strain-driven elongation of their dipoles or even increase in the average size of the polar nanoregions when the strength of the strain grows.

Mediating the contradiction of d33 and TC in potassium-sodium niobate lead-free piezoceramics

For potassium-sodium niobate, the piezoelectric constant (d33) was usually improved by sacrificing the Curie temperature (TC). In this work, a material system of 0.992(K0.46Na0.54)0.965Li0.035Nb(1-x)Sb(x)O3-0.008BiScO3 has been designed and prepared with the aim of achieving both a large d33 and a high TC at the same time. The chemical compositions are found to be homogeneously distributed in the ceramics. The introduction of Sc is found to be responsible for different grain sizes. The rhombohedral-tetragonal phase coexistence zone lies in the composition range of 0.02<x ≤ 0.06. The ceramic is thermally stable in terms of ferroelectric properties. The change in the domain-wall activities induced by the configuration variation of defect dipoles upon annealing is believed to be responsible for the variation in the d33 at different temperatures. The ceramic with x = 0.025 shows a good comprehensive performance of d33 ≈ 325 pC/N and k(p) ≈ 48%, together with a high T(C) of ~358 °C, demonstrating that this material system is a promising candidate for high-temperature piezoelectric applications.

First-principles model potentials for lattice-dynamical studies: general methodology and example of application to ferroic perovskite oxides

We present a scheme to construct model potentials, with parameters computed from first principles, for large-scale lattice-dynamical simulations of materials. We mimic the traditional solid-state approach to the investigation of vibrational spectra, i.e., we start from a suitably chosen reference configuration of the compound and describe its energy as a function of arbitrary atomic distortions by means of a Taylor series. Such a form of the potential-energy surface is general, trivial to formulate for any material, and physically transparent. Further, such models involve clear-cut approximations, their precision can be improved in a systematic fashion, and their simplicity allows for convenient and practical strategies to compute/fit the potential parameters. We illustrate our scheme with two challenging cases in which the model potential is strongly anharmonic, namely, the ferroic perovskite oxides PbTiO3 and SrTiO3. Studying these compounds allows us to better describe the connection between the so-called effective-Hamiltonian method and ours (which may be seen as an extension of the former), and to show the physical insight and predictive power provided by our approach-e.g., we present new results regarding the factors controlling phase-transition temperatures, novel phase transitions under elastic constraints, an improved treatment of thermal expansion, etc.

Effect of central mode on the dielectric tunability of ferroelectrics near room temperature: a first-principle-based study

First-principles-based effective Hamiltonian molecular dynamics simulations are performed to investigate GHz-THz dynamical properties of bulk and epitaxially strained film made of SrTiO3 near room temperature. Our simulations confirm the huge dielectric tunability recently observed in films. Moreover, universal phenomenological laws, with bulk-like parameters, are found to describe reasonably well the dielectric tunability-versus-dc electric field curves in both systems at low and high electric fields, except for the sole case of the STO film in the low-field regime. Such deviation originates from the presence of a central mode in this low-dimensional system. A revised equation, arising from an original analysis of the simulations, is proposed for modeling this latter situation.

Field-induced percolation of polar nanoregions in relaxor ferroelectrics

A first-principles-based effective Hamiltonian is used to investigate low-temperature properties of Ba(Zr,Ti)O(3) relaxor ferroelectrics under an increasing dc electric field. This system progressively develops an electric polarization that is highly nonlinear with the dc field. This development leads to a maximum of the static dielectric response at a critical field, E(th), and involves four different field regimes. Each of these regimes is associated with its own behavior of polar nanoregions, such as shrinking, flipping, and elongation of dipoles or change in morphology. The clusters propagating inside the whole sample, with dipoles being parallel to the field direction, begin to form at precisely the E(th) critical field. Such a result, and further analysis we perform, therefore, reveal that field-induced percolation of polar nanoregions is the driving mechanism for the transition from the relaxor to ferroelectric state.

Development of a bond-valence based interatomic potential for BiFeO3 for accurate molecular dynamics simulations

We present an atomistic potential for BiFeO(3) based on the principles of bond-valence (BV) and bond-valence vector (BVV) conservation. The validity of this model potential is tested for both canonical ensemble (NVT) and isobaric-isothermal ensemble (NPT) molecular dynamics (MD) simulations. The model reproduces the ferroelectric-to-paraelectric phase transition in both NVT and NPT MD simulations and the temperature dependence of the local structure in BiFeO(3). The calculated domain wall energies for 71°, 109°and 180° walls agree well with density functional theory results. The success of our simple model potential for BiFeO(3) indicates that BV and BVV conservation provides a firm basis for the development of accurate atomistic potentials for complex oxides.

Collective dipole behavior and unusual morphotropic phase boundary in ferroelectric Pb(Zr(0.5)Ti(0.5))O3 nanowires

Dipole collective behavior and phase transition in ferroelectric (FE) Pb(Zr(0.5)Ti(0.5))O(3) nanowires, caused by modulated electric fields, are reported. Our result also leads to the finding of a rather outstanding electromechanical d(31) response in a 8.4 nm diameter PZT wire, which may potentially outperform bulk PMN-PT and PZN-PT. Moreover, we further demonstrate the existence of a new type of morphotropic phase boundary (MPB) that bridges two dissimilar structure phases of different order parameters. Microscopic insights for understanding the collective behavior and the structural phase within the new MPB are provided.

Terahertz sensing using ferroelectric nanowires

Molecular dynamics simulations are used to study the interaction of ferroelectric nanowires with terahertz (THz) Gaussian-shaped pulses of electric field. The computational data indicate the existence of two interaction scenarios that are associated with 'lossless' and dissipative, or 'lossy', interaction mechanisms. A thermodynamical approach is used to analyze the computational data for a wide range of THz pulses. The analysis establishes the foundation for understanding the nanowires' response to the THz pulses and reveals the potential of ferroelectric nanowires to function as nanoscale sensors of THz radiation. Various aspects of this THz nanosensing are analyzed and discussed.

Finite-temperature properties of Ba(Zr,Ti)O3 relaxors from first principles

A first-principles-based technique is developed to investigate the properties of Ba(Zr,Ti)O(3) relaxor ferroelectrics as a function of temperature. The use of this scheme provides answers to important, unresolved and/or controversial questions such as the following. What do the different critical temperatures usually found in relaxors correspond to? Do polar nanoregions really exist in relaxors? If yes, do they only form inside chemically ordered regions? Is it necessary that antiferroelectricity develop in order for the relaxor behavior to occur? Are random fields and random strains really the mechanisms responsible for relaxor behavior? If not, what are these mechanisms? These ab initio based calculations also lead to deep microscopic insight into relaxors.

Interplay of couplings between antiferrodistortive, ferroelectric, and strain degrees of freedom in monodomain PbTiO3/SrTiO3 superlattices

We report first-principles calculations on the coupling between epitaxial strain, polarization, and oxygen octahedra rotations in monodomain (PbTiO(3))(n)/(SrTiO(3))(n) superlattices. We show how the interplay between (i) the epitaxial strain and (ii) the electrostatic conditions can be used to control the orientation of the main axis of the system. The electrostatic constrains at the interface facilitate the polarization rotation and, as a consequence, we predict large piezoelectric responses at epitaxial strains smaller than those required considering only strain effects. In addition, ferroelectric (FE) and antiferrodistortive (AFD) modes are strongly coupled. Usual steric arguments cannot explain this coupling and a covalent model is proposed to account for it. The energy gain due to the FE-AFD coupling decreases with the periodicity of the superlattice, becoming negligible for n ≥ 3.

Nanodynamics of ferroelectric ultrathin films

The nanodynamics of ferroelectric ultrathin films made of PbTi(0.6)Zr(0.4)TiO(3) alloy is explored via the use of a first-principles-based technique. Our atomistic simulations predict that the nanostripe domains which constitute the ground state of ferroelectric ultrathin films under most electric boundary conditions oscillate under a driving ac field. Furthermore, we find that the atomically thin wall, or nanowall, that separates the nanodomains with different polarization directions behaves as an elastic object and has a mass associated with it. The nanowall mass is size-dependent and gives rise to a unique size-driven transition from resonance to relaxational dynamics in ultrathin films. A general theory of nanodynamics in such films is developed and used to explain all computational findings. In addition, we find an unusual dynamical coupling between nanodomains and mechanical deformations that could potentially be used in ultrasensitive electromechanical nanosensors.

Flexoelectric rotation of polarization in ferroelectric thin films

Strain engineering enables modification of the properties of thin films using the stress from the substrates on which they are grown. Strain may be relaxed, however, and this can also modify the properties thanks to the coupling between strain gradient and polarization known as flexoelectricity. Here we have studied the strain distribution inside epitaxial films of the archetypal ferroelectric PbTiO(3), where the mismatch with the substrate is relaxed through the formation of domains (twins). Synchrotron X-ray diffraction and high-resolution scanning transmission electron microscopy reveal an intricate strain distribution, with gradients in both the vertical and, unexpectedly, the horizontal direction. These gradients generate a horizontal flexoelectricity that forces the spontaneous polarization to rotate away from the normal. Polar rotations are a characteristic of compositionally engineered morphotropic phase boundary ferroelectrics with high piezoelectricity; flexoelectricity provides an alternative route for generating such rotations in standard ferroelectrics using purely physical means.

First-principles investigation of morphotropic transitions and phase-change functional responses in BiFeO3-BiCoO3 multiferroic solid solutions

We present an ab initio study of the BFCO solid solution formed by multiferroics BiFeO(3) (BFO) and BiFeO(3) (BCO). We find that BFCO presents a strongly discontinuous morphotropic transition between BFO-like and BCO-like ferroelectric phases. Further, for all compositions such phases remain (meta)stable and retain well-differentiated properties. Our results thus suggest that an electric field can be used to switch between these structures and show that such a switching involves large phase-change effects of various types, including piezoelectric, electric, and magnetoelectric ones.

Epitaxial Pb(Zr,Ti)O3 ultrathin films under open-circuit electrical boundary conditions

The temperature-versus-misfit-strain phase diagram of Pb(Zr,Ti)O3 ultrathin films under open-circuit electrical boundary conditions is simulated via the use of an effective Hamiltonian. Two novel phases, both exhibiting dipolar nanodomains and oxygen octahedral tilting, are discovered. The interplay between dipolar, antiferrodistortive, alloying, and strain degrees of freedom induces several striking features in these two phases, such as the chemical pinning of domain walls, the enhancement of oxygen octahedral tilting near the domain walls, and the existence of dipolar waves and cylindrical dipolar chiral bubbles.

Probing the Nanodomain Origin and Phase Transition Mechanisms in (Un)Poled PMN-PT Single Crystals and Textured Ceramics

Outstanding electrical properties of solids are often due to the composition heterogeneity and/or the competition between two or more sublattices. This is true for superionic and superprotonic conductors and supraconductors, as well as for many ferroelectric materials. As in PLZT ferroelectric materials, the exceptional ferro- and piezoelectric properties of the PMN-PT ((1-x)PbMg1/3Nb2/3O₃-xPbTiO₃) solid solutions arise from the coexistence of different symmetries with long and short scales in the morphotropic phase boundary (MPB) region. This complex physical behavior requires the use of experimental techniques able to probe the local structure at the nanoregion scale. Since both Raman signature and thermal expansion behavior depend on the chemical bond anharmonicity, these techniques are very efficient to detect and then to analyze the subtitle structural modifications with an efficiency comparable to neutron scattering. Using the example of poled (field cooling or room temperature) and unpoled PMN-PT single crystal and textured ceramic, we show how the competition between the different sublattices with competing degrees of freedom, namely the Pb-Pb dominated by the Coulombian interactions and those built of covalent bonded entities (NbO₆ and TiO₆), determine the short range arrangement and the outstanding ferro- and piezoelectric properties.

Single crystal study of competing rhombohedral and monoclinic order in lead zirconate titanate

Neutron diffraction data obtained on single crystals of PbZr(1-x)Ti(x)O3 with x=0.325 and x=0.460, which lie on the pseudorhombohedral side of the morphotropic phase boundary, suggest a coexistence of rhombohedral (R3m/R3c) and monoclinic (Cm) domains and that monoclinic order is enhanced by Ti substitution. A monoclinic phase with a doubled unit cell (Cc) is ruled out as the ground state.

An efficient computational method for use in structural studies of crystals with substitutional disorder

We present a computationally efficient semi-empirical method, based on standard first-principles techniques and the so-called virtual crystal approximation, for determining the average atomic structure of crystals with substitutional disorder. We show that, making use of a minimal amount of experimental information, it is possible to define convenient figures of merit that allow us to recast the determination of the average atomic ordering within the unit cell as a minimization problem. We have tested our approach by applying it to a wide variety of materials, ranging from oxynitrides to borocarbides and transition-metal perovskite oxides. In all the cases we were able to reproduce the experimental solution, when it exists, or the first-principles result obtained by means of much more computationally intensive approaches.

The influence of strain on the polarization of epitaxial (Ba(0.70)Sr(0.30))TiO(3) ultrathin film obtained from first principles

A first-principles-derived approach is used to investigate the temperature-versus-misfit strain phase diagram of (Ba(0.70)Sr(0.30))TiO(3) ultrathin film. Our predicted phase diagram is qualitatively similar to those developed by Shirokov et al (2009 Phys. Rev. B 79 144118) and Ban and Alpay (2002 J. Appl. Phys. 91 9288). However, there are some quantitative differences that are microscopically revealed and explained. The results also indicate that the electrical polarization is very sensitive to the applied strain. Moreover, the polarization components show a strong dependence on the surface/interface, thickness, and electrical boundary conditions.

Low-symmetry phases in ferroelectric nanowires

Ferroelectric nanostructures have recently attracted much attention due to the quest of miniaturizing devices and discovering novel phenomena. In particular, studies conducted on two-dimensional and zero-dimensional ferroelectrics have revealed original properties and their dependences on mechanical and electrical boundary conditions. Meanwhile, researches aimed at discovering and understanding properties of one-dimensional ferroelectric nanostructures are scarce. The determination of the structural phase and of the direction of the polarization in one-dimensional ferroelectrics is of technological importance, since, e.g., a low-symmetry phase in which the polarization lies away from a highly symmetric direction typically generates phenomenal dielectric and electromechanical responses. Here, we investigate the phase transition sequence of nanowires made of KNbO(3) and BaTiO(3) perovskites, by combining X-ray diffraction, Raman spectroscopy, and first-principles-based calculations. We provide evidence of a previously unreported ferroelectric ground state of monoclinic symmetry and the tuning of the polarization's direction by varying factors inherent to the nanoscale.

Contributions of domain wall motion to complex electromechanical coefficients of 0.62Pb(Mg(13)Nb(23))O(3)-0.38PbTiO(3) crystals

The loss behavior of 0.62Pb(Mg(13)Nb(23))O(3)-0.38PbTiO(3) (PMN-38%PT) ferroelectric single crystal poled along [001](c) was investigated. It was found that the complex electromechanical coefficients and loss factors change dramatically at the coercive field E(c) around 250 Vmm, representing the intrinsic switching barrier. Since the energy loss is related to the domain wall motion, the imaginary parts of the electromechanical coefficients can be used to study the degree of domain wall motions in relaxor-based ferroelectric single crystals. Experimental results indicate that for this system, domain wall motion contributes significantly to the imaginary parts of electromechanical coefficients. In addition, [001](c) poled PMN-38%PT single crystals have much larger mechanical loss factor compared to that of conventional single crystal like LiNbO(3). This phenomenon is proved to be closely related to 90 degrees domain wall motion in this crystal system.

Large piezoelectric effect in Pb-free ceramics

We report a non-Pb piezoelectric ceramic system Ba(Ti(0.8)Zr(0.2))O(3)-(Ba(0.7)Ca(0.3))TiO(3) which shows a surprisingly high piezoelectric coefficient of d(33) approximately 620 pC/N at optimal composition. Its phase diagram shows a morphotropic phase boundary (MPB) starting from a tricritical triple point of a cubic paraelectric phase (C), ferroelectric rhombohedral (R), and tetragonal (T) phases. The high piezoelectricity of the MPB compositions stems from the composition proximity of the MPB to the tricritical triple point, which leads to a nearly vanishing polarization anisotropy and thus facilitates polarization rotation between 001T and 111R states. We predict that the single-crystal form of the MPB composition of the present system may reach a giant d(33) = 1500-2000 pC/N. Our work may provide a new recipe for designing highly piezoelectric materials (both Pb-free and Pb-containing) by searching MPBs starting from a TCP.

On the discovery of new low temperature monoclinic phases with Cm and Cc space groups in Pb(Zr0.52Ti0.48)O3: an overview

The decades old phase diagram of the technologically important Pb(Zr x Ti1– x )O3 (PZT) ceramics in the vicinity of the morphotropic phase boundary has been under review during the last few years. This article summarises the results of the discoveries of two new mono clinic phases (F M HT) and (F M LT) with Cm and Cc space group by the Brookhaven group and our group, respectively, in the PZT ceramics.

First-principle study of materials involved in incommensurate transitions

We discuss the applicability of the density functional theory to the study of incommensurate crystals. After a brief introduction to these aperiodic but ordered materials we present several types of ab initio methodologies that are adequate in the context of incommensurate transitions and phases. We also give a survey of the corresponding applications, while providing two case studies: Pb2MgTeO6 and K2SeO4.

Comments on origins of enhanced piezoelectric properties in ferroelectrics

This review discusses recent advances in understanding origins of large piezoelectric properties in some ferroelectric materials. In particular, it addresses the role of polarization rotation and monoclinic phases. It is suggested that the polarization rotation is an old concept that was proposed more than 30 years ago to explain enhanced properties of Pb(Zr,Ti) O3 in the morphotropic phase boundary region. It is further demonstrated that in addition to polarization rotation, polarization extension can also lead to large electro-mechanical properties. In fact, the largest piezoelectric coefficient has been reported in KH2PO4, which exhibits structural instability involving polarization extension and no monoclinic phases. It is also shown that substantial theoretical and experimental evidence exists to show that the highest piezoelectric response is often not observed in monoclinic phases but in the phase transition regions where polarization either changes direction or appears from the nonpolar state. Finally, it is proposed that the concept of free energy instability, which emerged from phenomenological and first principle calculations, is the most general approach that can be used to consistently interpret many experimental observations and underlies many theoretical results on enhancement of piezoelectric properties.

Critical behavior in ferroelectrics from first principles

We report first-principles-based calculations, combined with an efficient Monte Carlo technique, that undoubtedly show that Pb(Zr0.5Ti0.5)O3, one of the most important ferroelectrics to date, adopts critical behavior that strongly deviates from the classical mean-field approach while being, in fact, consistent with the 3D-random Ising universality class.

Pressure induced phase transitions in PbTiO(3)

Recent theoretical simulations using density functional theory (DFT) and novel low temperature high energy x-ray diffraction experiments clearly show the existence of a high pressure morphotropic phase boundary (MPB) in pure PbTiO(3). The experiments show a richer phase diagram than the simulations, with multiple monoclinic phases (Pm and Cm) in the MPB region. In this paper we examine the MPB region in more detail using high precision DFT calculations within the local-density approximation (LDA) and the Wu-Cohen generalized gradient approximation. Our results support the polarization rotation theory and open up fresh possibilities for applying chemical pressure to engineer novel electromechanical materials. We also explain why the zone-boundary mode is more likely to be stable only at higher pressures above ∼25 GPa and not at moderate pressures of ∼10 GPa, using the LDA.

Cooperative response of Pb(ZrTi)O3 nanoparticles to curled electric fields

We investigate cooperative responses, as well as a microscopic mechanism for vortex switching, in Pb(Zr0.5Ti0.5)O3 nanoparticles under curled electric fields. We find that the domain coexistence mechanism is not valid for toroid switching. Instead dipoles display unusual collective behavior by forming a new vortex with a perpendicular (not opposite) toroid moment. The correlation between the new and original vortices is revealed to be critical for reversing the toroid moment. We further describe a technological approach that is able to drastically reduce the curled electric field needed for vortex switching.

Nature of dynamical coupling between polarization and strain in nanoscale ferroelectrics from first principles

A first-principle-based technique is used to investigate dynamical coupling between polarization and picosecond time-scale strain pulses in ferroelectric nanolayers. Two different dynamical mechanisms are found. The first mechanism concerns homogeneous dipole patterns, is governed by the ultrafast soft-mode dynamics, mostly consists in the modification of the dipoles' magnitude, and leads to a polarization only weakly changing and following the strain pulse via an "usual" coupling law. On the other hand, the second mechanism occurs in highly inhomogeneous dipole patterns, is characterized by a large change in polarization and by a time delay between polarization and strain, and is governed by the "slower breathing" of dipolar inhomogeneities. This second mechanism provides a successful explanation of puzzling experimental data.

Unusual polarization patterns in flat epitaxial ferroelectric nanoparticles

We investigate the effects of a lattice misfit strain on a ground state and polarization patterns in flat perovskite nanoparticles (nanoislands of BaTiO3 and PZT) with the use of an ab initio derived effective Hamiltonian. We show that the strain strongly controls the balance between the depolarizing field and the polarization anizotropy in determining the equilibrium polarization patterns. Compressive strain favors 180 degrees stripe or tweed domains while a tensile strain leads to in-plane vortex formation, with the unusual intermediate phase(s) where both ordering motifs coexist. The results may allow us to explain contradictions in recent experimental data for ferroelectric nanoparticles.