Barium Titanate Single Crystals Research Articles

Influence of uniaxial stress on the ferroelectric-to-paraelectric phase change in barium titanate

The dielectric behavior near the ferroelectric-to-paraelectric phase transition of 〈001〉C-oriented single crystal and polycrystalline barium titanate (BaTiO3) was investigated as a function of uniaxial compressive stress in the temperature range from 25 to 200 °C. An increase in the Curie point (TC) and decrease in the Curie-Weiss temperature (θ) were observed with increasing stress for both single crystal and polycrystalline samples, resulting in an increase in the first order nature of the phase transition as measured by the temperature difference (TC – θ). With increasing applied stress levels, the permittivity versus temperature curves of polycrystalline samples were found to broaden and flatten near the Curie point, which was not observed for the single crystals. The experimental results were analyzed using a classical 2-4-6 Landau polynomial. The observed increase in the first order nature of the ferroelectric-to-paraelectric phase transition with uniaxial stress was explained by a linear dependence of the quartic coefficient of the Landau series on stress.

Evolution of compatible laminate domain structures in ferroelectric single crystals

The electromechanical properties and behaviour of ferroelectric single crystals are dominated by their domain structures. The domain structure can evolve according to the applied electrical and mechanical boundary conditions, but typically maintains a low energy state by adopting compatible configurations of microstructure in the form of multi-rank laminates. In this work, a model of domain structure evolution is developed, using a variational method to capture the dissipative nature of domain wall motion. The model describes the evolution of domain patterns with the constraint that they remain in low energy, compatible configurations. The electromechanical behaviour, such as microstructure evolution and hysteresis response, of periodic compatible laminate domain patterns in the tetragonal crystal system is studied. Estimates of the material response based on uniform field approximations are developed, and compared with a numerical model in which finite element analysis is used for accurate computation of the free energy. Microstructural transitions from one type of laminate domain pattern to another are included in the model by considering “pivot states”, which are the limiting states shared by more than one laminate pattern. The transition between distinct microstructural patterns at a pivot state is modelled as a bifurcation in which a material element notionally evolves along multiple paths simultaneously, representing sub-regions of the element evolving in different ways. The model is applied to study the hysteresis responses, such as dielectric hysteresis loops and butterfly strain loops, and switching mechanism of barium titanate (BaTiO3) single crystals subjected to a variety of loads. The relationship between domain patterns and the behaviour of ferroelectric switching is discussed. The results show good general agreement with experimental data in the literature, reproducing several features such as the effect of stress on electrical hysteresis.

In-situ observation of needle domain evolution in barium titanate single crystals

Abstract We report in-situ optical observations of the ferroelastic switching in a barium titanate single crystal under compressive stress. Optical micrographs were captured in two regions showing distinct arrangements of domains. Coarsely spaced needle domains in a matrix consisting of a differently oriented large single domain were found to retreat under the application of compressive stress of around 1–2 MPa. However, a comb of closely spaced needle domains was found to be more stable, retreating only slightly under a similar magnitude of applied load. The observations show that the pattern of needle domains influences the ferroelastic switching process and the observed coercive stress can depend strongly on domain arrangement.

Precursor dynamics in rhodium-doped barium titanate single crystals studied by Brillouin light scattering and birefringence measurements

The dynamics of precursor polar clusters in rhodium(Rh)-doped barium titanate single crystals were examined in the paraelectric phase by Brillouin light scattering and birefringence measurements in a wide temperature range. The longitudinal acoustic (LA) mode and central peaks in the inelastic light scattering spectrum were investigated by Brillouin scattering, while the temperature dependence of the birefringence was accurately determined by means of a birefringence imaging system. In a specific temperature range above the ferroelectric phase transition temperature, the LA mode frequency exhibited a significant softening concomitant with the substantial increase in the hypersonic damping, which was attributed to the formation of polar clusters and their interactions with acoustic waves. In this temperature range where acoustic anomalies were brought about, the birefringence showed non-zero values, indicating the existence of local non-centrosymmetric regions. All these results clearly indicated that the off-centered motions of Ti ions in the oxygen octahedra in Rh-doped BaTiO3 are correlated in the paraelectric phase inducing slowing down of the precursor dynamics and anomalous birefringence, similar to pure BaTiO3 (Ko et al., Phys. Rev. B 84, 094123 (2011)). The effect of rhodium doping in BaTiO3 enhanced the first-order character of the ferroelectric phase transition.

Logarithmic temperature variations of the elastic constant of barium titanate near the ferroelectric phase transition

The temperature variations of the elastic constant C11 and the corresponding acoustic attenuation coefficient of barium titanate single crystals grown by two different methods in the paraelectric phase were obtained in a wide temperature by means of Brillouin light scattering. Two phenomenological approaches were adopted to attempt to explain the anomalous change in C11 (denoted as ΔC11) in the paraelectric phase. ΔC11 exhibited a logarithmic variation as log[(T−T0)/T0] in a certain temperature range from Tc to about Tc+80°C instead of the other variation of (T−T0)ζ predicted by the mean-field approach. This temperature range was almost the same as the range where precursor dynamics were theoretically predicted to set in. The fact that the logarithmic variation was proposed for uniaxial systems might indicate that the correlated deformation of precursor polar clusters is tetragonal, as was suggested from nuclear magnetic resonance study [7].

Highly piezoelectric biocompatible and soft composite fibers

We report the fabrication of highly piezoelectric biocompatible soft fibers containing barium titanate ferroelectric ceramic particles dispersed in electrospun poly lactic acid (PLA). These fibers form mats that have two orders of magnitude larger piezoelectric constant per weight than single crystal barium titanate films. We propose that the observed apparent piezoelectricity results from the electrospinning induced polar alignment of the ferroelectric particles that pole the fibers similar to ferroelectret polymer foams that are poled by corona discharge. Due to the biocompatibility of PLA that encases the ferroelectric particles, these mats can be used in biological applications such as bio-sensors, artificial muscles, and energy harvesting devices.

Scanning electro-optic microscopy of ferroelectric domain structure with a near-field fiber probe

Ferroelectric domain structure of barium titanate single crystals has been visualized using a fiber probe near-field microscope, combined with temporal modulation of optical signal provided by a sinusoidal electric field applied to the sample. We find that electro-optic contrast between the adjacent domains depends on the polarization of incident light not as strongly as in case of confocal microscopy. This fact is ascribed to presence of additional optical aberrations caused by the near-field arrangement confirmed by complicated approaching curve observed for the electro-optic signal. Surprising improvement in spatial resolution of the near-field electro-optic image comparing to the optical one has been observed in some cases, supporting the idea of surface-confined electro-optic modulation in qualitative agreement with the observed phenomenon.

Precursor dynamics in the ferroelectric phase transition of barium titanate single crystals studied by Brillouin light scattering

The acoustic anomalies and precursor dynamics of high-quality barium titanate single crystals were investigated by Brillouin light scattering and the birefringence measurements in the paraelectric phase above the cubic-to-tetragonal ferroelectric phase transition temperature (${T}_{c}$). Two elastic stiffness coefficients ${C}_{11}$ and ${C}_{44}$, the related sound velocities, and their absorption coefficients were determined from ${T}_{c}$ to 400${\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{\circ}}$C for the first time. The longitudinal acoustic (LA) mode showed a substantial softening over a wide temperature range above ${T}_{c}$ which was accompanied by a remarkable increase in the acoustic damping as well as growth of central peaks. The broad central peak (CP) exhibited a two-mode and one-mode behavior in the paraelectric and ferroelectric phase, respectively, which was consistent with recent far-infrared reflectivity measurements and first-principle-based calculations [Ponomareva et al., Phys. Rev. B 77, 012102 (2008)]. The acoustic anomalies and CP behavior were correlated with the anomalous birefringence, piezoelectric effect, and the deviation of the Curie-Weiss law observed from the same crystal. This strongly indicates similarity between the dynamics of polar clusters in typical ferroelectrics and the dynamics of polar nanoregions in relaxors, consistent with recent acoustic emission measurements [Dul'kin et al., Appl. Phys. Lett. 97, 032903 (2010)]. The relaxation times estimated from the central peak and the LA mode anomalies exhibited similar temperature dependences with comparable orders of magnitude, indicating that the polarization fluctuations due to the precursor polar clusters couples to the LA mode through density fluctuations. All these anomalies share common microscopic origin, correlated Ti off-centered motions forming polar clusters having local symmetry breaking in the paraelectric phase. The existence of the polar clusters were directly evidenced by the temperature evolution of the precise birefringence map. The narrow central peak within $\ifmmode\pm\else\textpm\fi{}$5 GHz proposed before was not confirmed to exist in the present study.

Ferroelectric phase transitions studied by dielectric and light scattering spectroscopies on Ba 1− xCa xTiO 3 single crystals ( x = 0.12, 0.20)

The ferroelectric phase transition of Ca-substituted barium titanate single crystals, Ba 1− x Ca x TiO 3 (BCTO- x), with x = 0.12 and 0.20 grown by optical floating zone method were studied by dielectric and Brillouin scattering methods. The X-ray diffraction investigation confirmed the structural phase transition from cubic to tetragonal phase in BCTO- x. The dielectric constant exhibited a sharp peak at the ferroelectric phase transition temperature ( T c ) and a deviation from the Curie–Weiss law on approaching T c from the high-temperature side. Brillouin scattering results showed that, similar to the acoustic properties of BCTO-0.20, dynamic precursor polar clusters are formed in the paraelectric phase of BCTO-0.12 single crystals which interact with acoustic waves via electrostrictive coupling resulting in large acoustic anomalies near T c . However, the temperature dependence of the dielectric constant indicated that diffuseness of the ferroelectric phase transition of BCTO- x became enhanced with Ca content, which was attributed to compositional disorder induced by random substitution of Ba cations by Ca ions.

Synchrotron Mapping of Laminate Microstructures in Barium Titanate Single Crystals

Imaging of domains is a key step in understanding the microstructure and hence the properties of ferroelectric single crystals. In this paper, single crystals of Barium Titanate are observed by reflection topography using unfocussed monochromatic synchrotron X-ray light. The resulting composite images are spatial maps showing regions of distinct microstructure, the proportions of the domain types present, and their orientations. The results are interpreted in the context of models of compatible microstructure in tetragonal crystals; optical microscopy of etched crystals and AFM imaging assist the interpretation. The method shows promise for mapping ferroelectric microstructure.

Oxygen-vacancy-induced memory effect and large recoverable strain in a barium titanate single crystal

A phase field model is developed in this paper to study the influences of oxygen vacancies on domain evolutions under electric field in ${\text{BaTiO}}_{3}$ single crystal. The oxygen vacancies are modeled as defect dipoles, enabling the capture of domain memory effect. Three different domain structures are studied, and the distributions of defect density and the electromechanical responses under electric loading are simulated. The simulations reproduce well the reversible domain switching and large recoverable electric-field-induced strain observed in experiments on both engineered domain structure and single domain structure. It is also discovered that double hysteresis loop, stepwise hysteresis loop and shifted hysteresis loop can emerge due to vacancy induced depolarization field, which explains well the previous experimental observations. The results also indicate that domain memory effect and non-$180\ifmmode^\circ\else\textdegree\fi{}$ domain switching are the mechanisms for large recoverable electric-field-induced strain in ferroelectrics with oxygen vacancies.

Web-like domain structure formation in barium titanate single crystals

The evolution of ferroelectric domain structure in Remeika-grown BaTiO3 crystals under an inhomogeneous electric field has been investigated using piezoresponse force microscopy. The ac imaging bias was found to affect the metastable polarization state and lead to the formation of a web-like domain structure. It is suggested that this behavior is due to the existence of subsurface domains arising in single crystals with a layered structure.

Piezoelectric properties of domain engineered barium titanate single crystals with different volume fractions of domain walls.

A piezoelectric domain wall model has been developed to analyze the effective piezoelectric properties of domain engineered BaTiO(3) (BT) single crystals with different volume fractions of 90 degrees domain walls. The model takes into account the nonuniform deformation in the domain wall region, which can create additional anisotropy to enhanced functional properties of multidomain single crystals. Our theoretical results indicate that a larger volume fraction of domain walls will produce larger effective piezoelectric coefficients. In addition, with the increase in domain wall volume fraction, [011](c) poled BT single crystals will have a much larger piezoelectric property enhancement than [111](c) poled BT single crystals.

A temperature-dependent study on the polarization-free straining of barium titanate singlecrystals

Previous studies by the authors have shown that, when subjected to combined uniaxialstress and electric field at room temperature, a (001)-oriented barium titanate (BaTiO3) single crystal may display incomplete switching characteristics and a severe disproportionof slope gradients at zero electric field for its polarization and strain hysteresis curves. It isproposed that the likely causes for the observed ‘decoupling’ of switching strain andswitching polarization at room temperature are the cooperative operation of multiple90° switching systems, by which ‘polarization-free’ strain changes could be induced, and the presenceof depolarization fields generated from the unshielded boundaries and/or incompatible domainswithin the crystal. In the present study, the evolution of polarization and strain hystereses ofBaTiO3 single crystals under various electromechanical loading combinations are investigated again at55 °C. When compared to the hysteresis measurements at room temperature,the degree of discrepancy between the slope gradients at zero electricfield for the polarization and strain hysteresis curves measured at55 °C is significantly reduced. This is due to the increase in domain wall mobility at a highertemperature, lowering the extent of incomplete switching at maximum electric field. At55 °C, domainswith 180° relative orientation are less likely to exist at maximum electric field; hence, the criticalprerequisite for polarization-free straining is no longer available. The experimental dataobtained in the present study are expected to assist the development of reliable constitutivemodels for single-crystal ferroelectrics.

Domain Wall Engineering in Lead-free Piezoelectric Materials

For [111] poled barium titanate (BaTiO3) single crystals, piezoelectric properties increased with decreasing domain sizes. To explain the phenomenon, the multidomain crystals were regarded as composite of (a) a distorted 90° domain wall region with ultrahigh piezoelectric property and (b) a normal tetragonal domain region. This model suggested that the d 31 of the lead-free piezoelectric crystals with domain sizes below 1 μ m can be over 1,000 pC/N. Thus, to induce the finer engineered domain configurations, a patterning electrode was used. As the results, the domain size of 3 μm was successfully induced, and the d31 was obtained at −243.2 pC/N.

Defect-mediated adsorption of methanol and carbon dioxide on BaTiO3(001)

The surface chemistry of single crystal barium titanate (BaTiO3) has been studied using temperature programmed desorption (TPD). TPD measurements were performed with several probe molecules, including methanol and carbon dioxide. The role of oxygen vacancies in the adsorption and reaction of these molecules was examined by annealing the crystal under oxidizing or reducing conditions prior to performing TPD. It is shown that the adsorption and reaction of methanol and carbon dioxide are enhanced on BaTiO3(001) by annealing the crystal under reducing conditions.

Spherical nanoindentation and Vickers microhardness study of the deformation of poled BaTiO3 single crystals

In this work, Vickers microhardness and spherical nanoindentation (NI) experiments—with hemispherical radii, R, of 13.5, 5, and 1.4μm—were used to explore the room temperature deformation behavior of poled barium titanate (BaTiO3) single crystals with two orientations: (001) and (110). At 209±11 and 193±11GPa, Young’s moduli of the (001) and (110) surfaces, respectively, were comparable. The (001) surface deforms elastically, before a pop-in event, followed by a strain-hardening regime. The pop-in stresses are stochastic in nature and can be described by Weibull statistics. The (110) surface deforms elastically, then plastically at lower stresses, before cracks are initiated, beyond which the strain-hardening regime is almost identical to that of the (001) surface. This three-regime behavior of the (110) surface was confirmed by postindentation scanning electron microscope micrographs. This work confirms that the room temperature deformation of single crystal BaTiO3 occurs by glide on the {110} slip planes that are also the cleavage planes. Furthermore fully reversible reproducible stress/strain loops were observed and attributed to the formation and annihilation of fully reversible dislocation loops, whose threshold stresses were a function of the domain size that forms under the various indenters. The domain sizes appear to scale with R and are believed to be responsible for the NI size effect observed.

Hysteresis behaviors of barium titanate single crystals based on the operation of multiple 90° switching systems

Large strain actuation in barium titanate (BaTiO 3) single crystals subjected to combined uniaxial stress and electric field is examined. A maximum strain of about 0.45% is measured under a combined loading of 2.7 MPa compressive stress and ±1.25 MV m −1 cyclic electric field. Above 2.7 MPa, the crystal does not cycle fully between the in-plane and out-of-plane polarized states due to large compressive stress, and consequently, a considerable reduction in actuation strain is apparent. The hysteresis evolution of the crystal under combined electromechanical loading reveals incomplete switching characteristics and a considerable disproportion of slope gradients at zero electric field for the measured polarization and strain hysteresis curves. A likely cause for the disproportion of slope gradients is the cooperative operation of multiple 90° switching systems by which “polarization-free” strain changes are induced. An in situ domain observation study reveals the formation of bubble-like micro-domains prior to the macroscopic 90° switching of the crystal bulk. The presence of these bubble-like “switching weak points” indicates that regions within the BaTiO 3 single crystal do not necessarily switch 90° at the same time, and hence, in a way, supports the existence of multiple 90° switching systems. Results obtained in the present study are expected to assist the development of reliable constitutive models for single crystal ferroelectrics.

Thermodynamic driving force in ferroelectric crystals with a rank-2 laminated domain pattern, and a study of enhanced electrostriction

The thermodynamic driving force for domain growth in a rank-2 laminated ferroelectric crystal is derived in this article, and we used it, together with a homogenization theory, to study the issue of enhanced electrostrictive actuation recently reported by Burcsu et al. [2004. Large electrostrictive actuation of barium titanate single crystals. J. Mech. Phys. Solids 52, 823–846]. We derived this force from the reduction of Gibbs free energy with respect to the increase of domain concentration. It is shown that both the free energy and the thermodynamic force consist of three parts: the first arises from the difference in M 0 and M 1, the linear electromechanical compliances of the parent and product domains, respectively, at a given level of applied stress and electric field, the second stems from the electromechanical work associated with the change of spontaneous strain and spontaneous polarization during domain switch, and the third from the internal energy due to the distribution of polarizations strain and electric polarization inside the crystal. We prove that the first term is substantially lower than the second one, and the third one is identically zero with compatible domain pattern. The second one is, however, not exactly equal to the commonly written sum of the products of stress with strain, and electric field with polarization during switch, unless both domains have identical moduli in the common global axes. We also show that, with compatible domain patterns and when M 1= M 0, this driving force is identical to Eshelby's driving force acting on a flat interface due to the jump of energy-momentum tensor. Applications of the theory to a BaTiO 3 crystal subjected to a fixed axial compression and decreasing electric field from the [0 0 1] state reveal that the crystal undergoes a three-stage switching process: (i) the 0→90° switch to form a rank-1 laminate, (ii) the 0→180° switch inside the 0° domain to form a laminate I with a concurrent 90°→−90° switch inside the 90° domain to form laminate II, creating a rank-2-laminated domain pattern, and (iii) finally the 90→180° switch. It is the exchange of stability between the 0, 90°, and 180° domains under compression and electric field that is the origin of the enhanced actuation. We illustrate these intrinsic features by showing the evolution of these domains, and demonstrate how the reported large actuation strain can be attained with a rank-2 laminate.

Domain switching contribution to piezoelectric response in BaTiO3 single crystals

Piezoelectric responses of barium titanate single crystals are investigated along the [720] and [111] directions, respectively, in order to verify the ultrahigh piezoelectric constant (2000pC∕N) reported in a previous study [Appl. Phys. Lett. 86, 012905 (2005)]. The results suggest that electric-field-induced strain can be largely enhanced by the domain switching in barium titanate single crystal along the [720] direction; however, the piezoelectric response under small field measurement has not been enhanced as much as expected because domain switching is a nonlinear and irreversible process.