Barium Titanate Single Crystals Research Articles

Effect of temperature on dislocation-tuned dielectricity and piezoelectricity in single-crystal BaTiO3

The pinning-controlled mobility of ferroelectric/ferroelastic domain walls is an important part of managing polarization switching and determining the final properties of ferroelectric and piezoelectric materials. Here, we assess the impact of temperature on dislocation-induced domain wall pinning as well as on dislocation-tuned dielectric and piezoelectric response in barium titanate single crystals. Our solid-state nuclear magnetic resonance spectroscopy results indicate that the entire sample exclusively permits in-plane domains, with their distribution remaining insensitive to temperature changes below the Curie temperature (TC). The domain wall pinning field monotonically decreases with increasing temperature up to TC, as evidenced by a combination of experimental observations and phase-field simulations. Our work highlights the promising potential of dislocation engineering in controlling domain wall mobility within bulk ferroelectrics.

Modelling needle domains with dislocations: A dislocation pile-up model and comparison with synchrotron experiment

The shape and strain field of a needle domain in a barium titanate single crystal are modelled using a distribution of dislocations and line charges. The arrangement of these dislocations and charges is a result of the balance of modified Peach–Koehler forces acting among the dislocations and a lattice friction assumed to act at each dislocation site. Based on measurements of needle shape by synchrotron X-ray diffraction, dislocation pile-up theory is used to compute the distribution of discrete dislocations along the needle and hence estimate the lattice friction. It is found that the lattice friction in this model is proportional to the opening angle of a wedge-shape needle domain and consistent with the observed magnitude of stress required to mobilize needle domains. The microstrain distribution around an a-a needle domain tip, obtained from X-ray diffraction measurement, is further used to test the dislocation model, with a similar pattern and magnitude of strains identified in the model and the experiment.

Rejuvenation of giant electrostrain in doped barium titanate single crystals

Engineering materials through the introduction of point defects has resulted in significant advances in semiconductor processing and, more recently, the observation of novel phenomena such as large reconfigurable strains in ferroelectrics as a result of defect dipole complexes. Up to 0.8% strain has been demonstrated in BaTiO3 crystals dilutely doped with iron. However, the defect dipole pinning sites and the corresponding achievable strains are found to degrade as the crystal is electrically cycled as part of the measurement process. The strain degradation rate is dependent on the applied field values but shows an exponential change in materials properties regardless of the electric field. This behavior, plus a change in impedance with number of times cycled, suggests these changes are due to electric field induced oxygen migration—similar to the cause of the resistance degradation effect. Despite this, effective piezoelectric coefficients of over 4700 pm/V were recorded with 1.5 kV/cm fields, one of the largest values for a lead-free piezoelectric material thus far. In addition, the defect dipole-aligned state and the high strains can be repeatably recovered by a subsequent heat treatment step after cycling. Potential paths to exploiting the defect dipole induced effects and large piezoelectric coefficient in these dilutely doped systems are proposed.

Fatigue-free dielectric and piezoelectric response in single-crystal BaTiO3 tuned by dislocation imprint

Dislocations have recently been imprinted into barium titanate single crystals to provide local domain wall pinning sites. Here, we assess the cycling stability under unipolar loading for the interaction between dislocations with [001] line vector and engineered ferroelectric domain walls. We find that a high large-signal piezoelectric strain coefficient (∼2100 pm/V) and dielectric permittivity (20 800) can be obtained without degradation if the topological interaction between domain wall and dislocation line is well chosen to utilize transient and permanent pinning sites. Our findings demonstrate the potential of dislocation engineering for the manipulation of the mobility of domain walls in bulk ferroelectrics.

Thermodynamic analysis of electro-optic coefficients of ferroelectrics

The electro-optic coefficients of ferroelectric materials were obtained by Landau thermodynamic theory. It is proved that if the permittivity tensor is diagonal, then some ratios of the electro-optical coefficients are equal to the ratios of its diagonal components. The dependence of electro-optic coefficients on the external electric field for single-crystal barium titanate was studied and discussed. It is shown that electro-optic coefficients are rather high for barium titanate due to a non-linear response of dielectric susceptibility to electric field strength.

An active straight waveguide polarization rotator in single crystal thin film barium titanate-on-insulator

Electro-optic materials play an essential role in telecommunications. In active devices like Mach–Zehnder modulators, typically the diagonal Pockels coefficients are employed to induce an optical phase shift through electrical tuning of the refractive index along an optic axis. On the other hand, waveguide polarization rotators are usually passive devices where asymmetric structures or specially designed couplers are used. In this Letter, we exploit off diagonal Pockels coefficients to demonstrate an active straight waveguide polarization rotator using a c-axis single crystal thin film barium titanate (BTO)-on-insulator, with a maximum power conversion of ∼30% from the input TE (or TM) mode into its orthogonal mode observed. The device is switched on or off through an applied voltage and is demonstrated in a simple straight waveguide. A TM output extinction ratio of 26.1 dB is achieved in the device with a TE input. The r51 value in the BTO thin film is estimated to be around 600 pm/V. This work adds a different polarization rotation scheme to the active photonics family.

History dependence of avalanche dynamics of ferroelectric phase transition in BaTiO3 under external bias field

A ferroelectric phase transition under an external bias electric field after field cooling and zero field cooling in barium titanate single crystals shows scale invariant nucleation and growth of complex domain structures. The avalanche energy exponents vary with the external bias, depending on the cooling history of the sample under applied field or zero field cooling. After field cooling, resulting in a single domain sample, the energy exponent is near the integrated mean field value of 5/3, namely, 1.68 ± 0.022. The sample after field cooling shows the same exponent with an external bias electric field range of up to 4.5 kV/cm. The exponent of a multi-domain sample, after zero field cooling, decreases from ε = 1.85 to the fixed point of 1.66 under high fields. The different behavior is attributed to the greater complexity of domain patterns in the multi-domain sample, which reduces to a single domain state under strong applied fields. Compared with the single-domain state, the multi-domain state has more domain boundaries and the intersections formed by these domain boundaries. These domain boundaries and their intersections will hinder the movement of the phase boundary and act as a pinning effect on the front of the phase interface. The effect is to generate more small energy signals, making the critical exponent high. At the same time, the aftershock time distribution (Omori law) remains the same for all switching conditions with an Omori exponent near −1 and switching time correlations of −1 ± 0.05 for short times (<1 s) and −2 ± 0.10 for long times (>1 s).

Improved description of the potential energy surface in BaTiO3 by anharmonic phonon coupling

Barium titanate (BT) based materials are at the forefront of materials being searched as possible candidates for the replacement of lead-based compositions in applications ranging from piezoelectrics to energy storage devices. Computational methods are very promising to increase the efficiency of materials discovery, provided that finite temperature properties can be realistically computed using, for example, molecular dynamics (MD). In this work, we present a systematic increase of the quality of MD simulations via an alternative way to calculate anharmonic contributions to the potential energy surface (PES) of barium titanate. A large number of first-principles calculations are performed, which are subsequently used to parametrize an effective Hamiltonian. To test the effects on various physical properties, MD simulations for the determination of transition temperatures, hysteresis, and permittivity of BT are shown. Furthermore, measurements were performed on BT single crystals to compare them directly with the MD simulations. It is observed that by incorporating a large number of anharmonic couplings, the description of the local minima in the PES becomes more accurate than in previous simulations. This leads to a better prediction of phase transition temperatures and shows the importance of anharmonic couplings in barium titanate. The presented approach can be directly adapted for other perovskite structures.

Near‐Room‐Temperature Large Electrocaloric Effect in Barium Titanate Single Crystal Based on the Electric Field–Temperature Phase Diagram

Phase transition plays a key role in the electrocaloric effect, but the first‐order ferroelectric–paraelectric phase transition always occurs far above room temperature, which heavily limits the practical application. Herein, the focus is on the orthorhombic–tetragonal first‐order ferroelectric–ferroelectric phase transition (@288 K) in <011>‐oriented barium titanate single crystal. Ferroelectric properties under a high electric field indicate a reversible field‐induced tetragonal–orthorhombic phase transition, based on which the electric field–temperature phase diagram is established. It is strongly related to the enhanced electrocaloric effect, and a large adiabatic temperature change of 1.33 K is obtained at 288 K under 15 kV cm−1, that is, a high electrocaloric strength of 88.7 mK cm kV−1. The large electrocaloric effect near room temperature makes lead‐free BaTiO3 a promising candidate for next‐generation solid‐state refrigeration.

Piezoresponse in Ferroelectric Materials under Uniform Electric Field of Electrodes.

The analytical solution for the displacements of an anisotropic piezoelectric material in the uniform electric field is presented for practical use in the “global excitation mode” of piezoresponse force microscopy. The solution is given in the Wolfram Mathematica interactive program code, allowing the derivation of the expression of the piezoresponse both in cases of the anisotropic and isotropic elastic properties. The piezoresponse’s angular dependencies are analyzed using model lithium niobate and barium titanate single crystals as examples. The validity of the isotropic approximation is verified in comparison to the fully anisotropic solution. The approach developed in the paper is important for the quantitative measurements of the piezoelectric response in nanomaterials as well as for the development of novel piezoelectric materials for the sensors/actuators applications.

Boundary influence on the fields and arrangement of the needle domains in barium titanate single crystals

The superposition theory is adopted to study the boundary value problem of needle domains in barium titanate single crystals, which decomposes into an infinite-medium solution and a complementary solution. The model of an equivalent edge dislocation and line charge is adopted to calculate the fields due to the discrete needle domains in an infinite medium. The complementary solutions are obtained from a linear elastic boundary value problem using the finite element method. The influence of boundaries on the fields and arrangement of the needles in thin barium titanate single crystals is analysed, by considering traction-free boundaries and using the plane stress approximation. According to the principle of minimum potential energy, it is found that pairs of parallel needle domains can be stabilized if the effective charge associated with the needle tips is reduced to 48% of the material’s full polarization charge. The evolution of comb-like arrays of needle domains under compressive mechanical load is simulated, and the results are found to be qualitatively similar to experimental observations which have not previously been explained theoretically.

Local polarization reversal in barium titanate single crystals and ceramics

Ex-situ local switching is a useful method for studying the domain structure evolution during polarization reversal in the individual grains of the ferroelectric ceramics. In this paper, the local switching by a biased tip of atomic force microscope was studied in the single crystals and ceramics of barium titanate BaTiO3 (BTO). The initial domain structure in BTO crystal was also studied. The domain growth during local switching in the crystal and individual grains of ceramics was characterized in terms of the parameters of the domain wall motion.

Thermal and electric field stability of square-net domain patterns in barium titanate

We use polarized light microscopy in situ with an externally applied electric field to induce square-net birefringence patterns in top-seeded single crystals of barium titanate above the Curie temperature (${T}_{C}$). The patterns occur under a wide range of electric field magnitudes larger than $\ensuremath{\sim}0.2$ kV/mm and at temperatures up to $6{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{\circ}}\mathrm{C}$ above ${T}_{C}$. We mapped this behavior on a pseudophase diagram showing the region in electric field and temperature space where this domain configuration is stable. We observed the electric field induced transformation into the periodically ordered structure from both the cubic structure above ${T}_{C}$ and the tetragonal structure below ${T}_{C}$. Synchrotron x-ray reciprocal space maps indicate the presence of ferroelastic domains perpendicular to the electric field direction at a range of electric field magnitudes similar to those required to induce the periodic domain ordering we observe using polarized light microscopy. Combined with a simple model of the optical retardation, we show that the periodic domain ordering responsible for the square-net birefringence occurs only at the surfaces of the crystals and that these domain structures are unexpectedly invariant with respect to the electric field that induces them.

Effect of mechanical stresses on the domain structure of barium titanate single crystals

This review article summarizes the material of years of research on the impact of mechanical stresses on the domain structure of multiaxhetoelectrics using the example of barium titanium monocrystals. Since the discovery of the ferroelectric properties of barium titanate in 1944, this material has been the subject of comprehensive investigation as the first practically important and perhaps the most famous ferroelectric. The domain structure of barium titanate is sensitive to mechanical stresses arising both from simple uniaxial compression and from point impacts by local mechanical loading. Mechanical stress applied to a ferroelectric crystal may have a significant effect on dielectric and piezoelectric properties. In particular, 90-degree domain switching is possible under the influence of stresses. The most interesting experimental results are obtained in the study of elastoplastic processes in BaTiO 3 originating from local mechanical stresses. The following features are found and studied: development of strained region around the point of application of the load; “internal” 90-degree domain that does not extend to the crystal surfaces and does not close upon other domains; the growth of 90-degree domains under the influence of residual mechanical stresses; growth of cracks along charged 90-degree domain walls. The notions of “ferroplastic effect” (crystal deformation due to the formation of 90-degree ferroelectric domains) and “ferromechanical effect” (crack formation and growth along charged 90-degree domain walls) are introduced. The hypothesis of a significant role of oxygen vacancies in the processes of 90-degree domain reorientation was put forward and experimentally confirmed. In particular, an increase in the concentration of oxygen vacancies by reducing annealing of barium titanate single crystals creates more favorable conditions for the appearance of an "internal" 90-degree domain under local mechanical load. The study of the mechanisms governing the formation of a domain structure in ferroelectric crystals remains an important problem of modern materials science.

Hydrostatic pressure mapping of barium titanate phase transitions with quenched FeRh

We report a pressure study of the metamagnetic/ferroelectric hybrid heterostructure of a quenched FeRh thin film (25 nm) grown on single crystal barium titanate (BTO). It has been previously reported that when the BTO undergoes a crystal transition a massive magnetization and coercivity change is triggered in the highly strain sensitive quenched FeRh thin film. Therefore quenched FeRh makes for an ideal probe for mapping a materials structural phase transitions. In this work we demonstrate this effect as a function of both temperature and hydrostatic pressure. As a result, we present the pressure dependence of the hybrid material which aligns identically with the BTO substrates pressure dependence reported in literature. The concept of combining a structural phase transitional (SPT) material with a magnetostrictive magnetic metal has been shown with vanadium oxides and our findings here prove that this methodology can be extended to strain sensitive metamagnetic materials systems in thin film, and possibly in bulk, heterostructures.

Modelling and interaction of needle domains in barium titanate single crystals

Needle domains are thin, lamellar domains that can appear as fine lines or stripes in a ferroelectric crystal. They affect the poling, switching, and other properties of ferroelectrics. A model is established to study the stress and electric fields caused by needle domains and their interaction. Considering the electrical and mechanical compatibility conditions at the tip of a needle domain, the fields are represented using equivalent edge dislocations and line charges. Accordingly, the dislocation fields derived by Barnett and Lothe for anisotropic piezoelectric media are employed. A modified Peach–Koehler force and calculations of the total energy due to the needle domains are used to study the formation, interaction and stability of needle patterns, taking full account of the strong anisotropy and electromechanical coupling present.The interaction of pairs of needle domains in an infinite piezoelectric with properties of barium titanate is found to be dominated by the electrostatic terms. This makes comb-like arrays of needle domains unstable if perfectly insulating properties are assumed. By considering redistribution of charge, stable equilibrium states for arrays of needle domains are found; these agree well with experimental observations. The model explains the stability of various observed needle patterns and also how unstable patterns evolve.

Elastic Anisotropy and Slowness Curves of BaTiO3 Single Crystals in the Paraelectric Phase Studied by Brillouin Spectroscopy

Elastic anisotropy and slowness curves of barium titanate (BaTiO3) single crystal in the paraelectric phase were investigated by using Brillouin spectroscopy. The directional dependence of sound velocities of the longitudinal and the transverse acoustic waves in the (001) plane showed a four-fold symmetry typical in the cubic phase. Especially, one of the two transverse modes exhibited a substantial softening along the directions. The sound velocity of this mode decreased significantly as temperature decreased toward the transition temperature, which corresponded to the elastic stiffness coefficient (C11 – C12)/2. This result suggests the tetragonal instability caused by the precursor polar clusters in the paraelectric phase of BaTiO3.

Precursor Phenomena of Barium Titanate Single Crystals Grown Using a Solid-State Single Crystal Growth Method Studied with Inelastic Brillouin Light Scattering and Birefringence Measurements.

The nature of precursor phenomena in the paraelectric phase of ferroelectrics is one of the main questions to be resolved from a fundamental point of view. Barium titanate (BaTiO3) is one of the most representative perovskite-structured ferroelectrics intensively studied until now. The pretransitional behavior of BaTiO3 single crystal grown using a solid-state crystal growth (SSCG) method was investigated for the first time and compared to previous results. There is no melting process in the SSCG method, thus the crystal grown using a SSCG method have inherent higher levels of impurity and defect concentrations, which is a good candidate for investigating the effect of crystal quality on the precursor phenomena. The acoustic, dielectric, and piezoelectric properties, as well as birefringence, of the SSCG-grown BaTiO3 were examined over a wide temperature range. Especially, the acoustic phonon behavior was investigated in terms of Brillouin spectroscopy, which is a complementary technique to Raman spectroscopy. The obtained precursor anomalies of the SSCG-grown BaTiO3 in the cubic phase were similar to those of other single crystals, in particular, of high-quality single crystal grown by top-seeded solution growth method. These results clearly indicate that the observed precursor phenomena are common and intrinsic effect irrespective of the crystal quality.

Thermally stimulated depolarization current study on barium titanate single crystals

Thermally stimulated depolarization current (TSDC) measurements were applied to investigate BaTiO3 single crystals with <100>, <110>, and <111> orientations, and annealed under different atmospheres, respectively. The TSDC peaks related to ferroelectric domain, ferroelectric–paraelectric phase transition, TiTi′−VÖ dipole relaxation and oxygen vacancy migration were observed from the TSDC spectra. The formation of oxygen vacancy clusters in BaTiO3 single crystals leads to a high dipole activation energy. The <111> crystalline face of BaTiO3 is more stable under external field than others.

Effects of oxygen deficiency on the acoustic anomalies and phase transition behaviors of barium titanate single crystals

The acoustic behaviors of oxygen-reduced barium titanate (BaTiO3-δ) single crystals with δ∼0.04 were investigated as a function of temperature by using Brillouin spectroscopy. The longitudinal acoustic mode of the moderately-reduced BaTiO3 (BTO) showed two pronounced anomalies at approximately 112 °C and −11 °C, which correspond to the cubic-tetragonal and tetragonal-orthorhombic phase transition temperature, respectively. These temperatures were lower by more than 10 °C compared to those of the pure BaTiO3 suggesting that the disorder introduced by oxygen vacancies lowers the phase transition temperatures. The paraelectric phase of the reduced BaTiO3 were characterized by substantial softening of the longitudinal acoustic mode and the growth of central peaks centered at zero frequency. These anomalies were observed in a certain temperature range above the Curie temperature, indicating that pretransitional precursor polar clusters exist in the cubic phase and that their dynamics are responsible for the acoustic anomalies caused by electrostrictive coupling between the strain and the polarization. The relaxation time of the precursor polar clusters derived from the central peak exhibited a critical slowing-down behavior showing that their dynamics becomes more sluggish as temperature approaches the Curie point.