Multidomain Single Crystals Research Articles

Size Asymmetry in Multidomain Single Crystals and the Development of Curved Surfaces

Size Asymmetry in Multidomain Single Crystals and the Development of Curved Surfaces

Temperature-dependent characterization of full tensor properties of [111]c poled Mn-doped 28PIN-43PMN-29PT single crystals

The temperature-dependent characterization of full tensor properties of single-domain relaxor-based single crystals (SCs) is important for understanding the influence of temperature on the properties of their multidomain SCs. However, no relevant results have been published because characterization is difficult to achieve using the traditional electric resonance method. In this Letter, the temperature-dependent elastic and piezoelectric properties of single-domain [111]c poled Mn-doped 28Pb(In1/2Nb1/2)O3-43Pb(Mg1/3Nb2/3)O3-29PbTiO3 SCs were investigated in the range of 20–80 °C by resonant ultrasound spectroscopy (RUS) using a rectangular parallelepiped sample. The temperature-dependent dielectric constants were calculated from the measured capacitances of the sample. The results are self-consistent because they were obtained from the same sample. The elastic constants obtained using the ultrasonic pulse-echo method agree closely with those obtained using RUS. Moreover, the experimental results of electric impedance spectrum agree closely with those simulated using the material constants characterized herein, indicating that the characterization is reliable.

Molecular cannibalism: Sacrificial materials as precursors for hollow and multidomain single crystals

The coexistence of single-crystallinity with a multidomain morphology is a paradoxical phenomenon occurring in biomineralization. Translating such feature to synthetic materials is a highly challenging process in crystal engineering. We demonstrate the formation of metallo-organic single-crystals with a unique appearance: six-connected half-rods forming a hexagonal-like tube. These uniform objects are formed from unstable, monodomain crystals. The monodomain crystals dissolve from the inner regions, while material is anisotropically added to their shell, resulting in hollow, single-crystals. Regardless of the different morphologies and growth mechanism, the crystallographic structures of the mono- and multidomain crystals are nearly identical. The chiral crystals are formed from achiral components, and belong to a rare space group (P622). Sonication of the solvents generating radical species is essential for forming the multidomain single-crystals. This process reduces the concentration of the active metal salt. Our approach offers opportunities to generate a new class of crystals.

Magnetism of powder samples and of single crystals

The temperature dependence of the magnetic order parameter of NiF2, MnCO3 and K2NiF4 measured on powder samples is compared with data obtained on single crystals. It is found that the dynamic dimensionality of the NiF2 and MnCO3 powder samples is one-dimensional (1D) for all temperatures T<TN. This shows that the powder grains are mono-domain particles. In the multi-domain single crystals isotropic 3D dynamic symmetry is observed. In order to explain isotropy in the bulk single crystals a dynamic averaging process over all domain orientations has to be postulated. For single crystal material of K2NiF4 a critical exponent of β=0.14±0.01 has been reported. Our neutron diffraction measurements on powder material yield to a very good approximation mean field critical behaviour indicating isotropic dynamics in the critical range. This unexpected result points to a dynamic averaging process over all differently oriented powder grains. As we have argued earlier, the observed universality in the dynamics of ordered magnets is due to a boson guiding field. Averaging over all powder grains, requests that the mean free path of the field bosons is larger than the size of the grains. Additionally, it must be assumed that the field quanta are able to tunnel across the interface between adjacent grains. In polycrystalline bulk samples of the 2D ferromagnet Rb2CrCl4 and of the 1D antiferromagnet KCuF3 also mean field critical behaviour is identified. As a consequence, a similar averaging process as in the K2NiF4 powder sample can be assumed to average over the mosaic structure of polycrystalline bulk material of Rb2CrCl4 and KCuF3. High quality single crystals of Rb2CrCl4 and of KCuF3 exhibit critical exponent of β~0.3. Dependence of the critical exponents on the mesoscopic morphology of the sample is considered as a typical indication of a boson controlled dynamics, and may partly explain the surprisingly broad distribution of critical exponent values reported in literature.

Strain incompatibility and residual strains in ferroelectric single crystals

Residual strains in ferroelectrics are known to adversely affect the material properties by aggravating crack growth and fatigue degradation. The primary cause for residual strains is strain incompatibility between different microstructural entities. For example, it was shown in polycrystalline ferroelectrics that residual strains are caused due to incompatibility between the electric-field-induced strains in grains with different crystallographic orientations. However, similar characterization of cause-effect in multidomain ferroelectric single crystals is lacking. In this article, we report on the development of plastic residual strains in [111]-oriented domain engineered BaTiO3 single crystals. These internal strains are created due to strain incompatibility across 90° domain walls between the differently oriented domains. The average residual strains over a large crystal volume measured by in situ neutron diffraction is comparable to previous X-ray measurements of localized strains near domain boundaries, but are an order of magnitude lower than electric-field-induced residual strains in polycrystalline ferroelectrics.

Near-field terahertz imaging of ferroelectric domains in barium titanate

We report on results of a near-field imaging experiment with broadband terahertz pulses applied to a BaTiO3 multidomain single crystal. Data with a spatial resolution below 15 µm were collected by our scanning time-domain terahertz imaging setup. We performed the scanning by an asymmetric skewed sapphire probe metallised from two sides ended with a 60 µm × 140 µm facet. The imaging scans were performed with various angles of the polarisation of the probing field with respect to the direction of the domain walls in order to identify the orientations with optimal sensitivity. The raw experimental data were prewhitened and processed by the singular value decomposition. In this way, independent components belonging to experimental features (polarisation, noise and external perturbations) were found. The spatial resolution of the sensing probe was found significantly higher than that allowed by the outer dimensions of the probe end facet. This result was also confirmed by electromagnetic-field simulations.

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.

Piezoelectric coefficients of PMN-0.29PT single crystals in the temperature range of phase transitions

The temperature dependencies of piezoelectric coefficients d 33 and d 31 for Pb(Mg1/3Nb2/3)O3-0.29PbTiO3 multi-domain single crystals, poled in [001]-direction, were investigated. The two samples had x- and y-axes identical with crystallographic [100] and [010] directions respectively, and the second two samples with [−110] and [110] directions. The laser interferometry method was used for the piezoelectrically induced displacement measurement. Piezoelectric coefficients were similar for all samples at room temperature and were roughly d 31 = −550 pC/N and d 33 = 1,100 pC/N. Very high increase of coefficients to values about d 31 = −2,100 pC/N and d 33 = 3,900 pC/N was observed below temperature of the first phase transition 101 °C. The coefficients exhibited only negligible frequency dependence at room temperature. But coefficient increases of about 10–30% as were observed at temperatures about 98 °C for 1 Hz applied field frequency in comparison to values received at 1 kHz. The second phase transition to cubic phase was observed at the temperature 124 °C. The temperature dependencies of dielectric and piezoelectric coefficients were compared too.

Three-dimensional finite element simulations of ferroelectric polycrystals under electrical and mechanical loading

Complex, non-linear, irreversible, hysteretic behavior of polycrystalline ferroelectric materials under a combined electro-mechanical loading is a result of domain wall motion, causing simultaneous expansion and contraction of unlike domains, grain sub-divisions that have distinct spontaneous polarization and strain. In this paper, a 3-dimensional finite element method is used to simulate such a polycrystalline ferroelectric under electrical and mechanical loading. A constitutive law due to Huber et al. [1999. A constitutive model for ferroelectric polycrystals. J. Mech. Phys. Solids 47, 1663–1697] for switching by domain wall motion in multidomain ferroelectric single crystals is employed in our model to represent each grain, and the finite element method is used to solve the governing conditions of mechanical equilibrium and Gauss's law. The results provide the average behavior for the polycrystalline ceramic. We compare the outcomes predicted by this model with the available experimental data for various electromechanical loading conditions. The qualitative features of ferroelectric switching are predicted well, including hysteresis and butterfly loops, the effect on them of mechanical compression, and the response of the polycrystal to non-proportional electrical loading.

Relations between single-domain and multidomain piezoelastic properties in single crystals

This paper presents a new method to compute the piezoelastic properties of multidomain single crystals from the single-domain constants. Based on a quasi static assumption, a PMN-chiPT multidomain is defined as a periodic medium with a lattice composed of layers of two domains in a twin structure. Such a structure is assumed to have charged domain walls that imply specific lattice media and boundary conditions. A numerical computation has been performed for a PMN-33PT single crystal in the rhombohedral phase. The effective elastic, piezoelectric, and dielectric constants of the macroscopic structure have been calculated, as well as the wave velocities in different configurations of domain patterns.

Finite element simulation of a polycrystalline ferroelectric based on a multidomain single crystal switching model

In this paper, we compute the constitutive behavior of a ferroelectric ceramic by a plane strain finite element model, where each element represents a single grain in the polycrystal. The properties of a grain are described by the microscopic model for switching in multidomain single crystals of ferroelectric materials presented by Huber et al. [J. Mech. Phys. Solids 47 (1999) 1663]. The poling behavior of the polycrystal is obtained by employing the finite element formulation for electromechanical boundary value problems developed by Landis [Int. J. Numer. Meth. Eng. 55 (2002) 613]. In particular, we address the influence of the single grain properties and the interaction between grains, respectively.

Ferroelectric Domain Controlled Pb[(Zn 1/3 Nb 2/3 ) 0.91 Ti 0.09 ]O 3 Single Crystal with Giant Electromechanical Coupling Factor of k 31 Mode and Piezoelectric d 31 Constant

Temperature and poling field dependences of the properties of large high-quality piezoelectric single crystals of Pb[(Zn 1/3 Nb 2/3 ) 0.91 Ti 0.09 ]O 3 (PZNT91/09) grown by the Bridgman method were measured. The single crystals poled along [001] of the original cubic direction possess giant electromechanical coupling factor k 31 over 80% and piezoelectric d 31 constant nearly m 1700 pC/N. These giant k 31 and d 31 constants results from the control of ferroelectric domain configuration. PZNT91/09 multi-domain single crystal became single-domain in the directions parallel and perpendicular to the poling field resulting in the appearance of giant k 31 and d 31 .

Which Engineered Domain Structures Can be Produced by External Fields?

We outline derivation of possible domain configurations and macroscopic symmetries of domain structures that can be formed by applying external electric field and/or mechanical stress to a multidomain single crystal. The procedure is demonstrated on domain structure of ferroelectric rhombohedral crystals with a cubic prototypic phase.

Dielectric Dispersion of Triglycine Sulfate at Ferroelectric Phase

The complex dielectric constant of triglycine sulfate has been examined. Three different dispersions appear in multi-domain single crystals. Since all these dispersions disappear in the single-domain crystals, it is clear that some kind of oscillation of the domain wall is responsible for these dispersions. According to the theoretical or experimental results reported so far, the three dispersions are considered to be originated by the oscillating domain wall trapped by defects, the swinging domain wall and the moving domain wall, respectively.

Dielectric Dispersion of Triglycine Sulfate at Ferroelectric Phase

The complex dielectric constant of triglycine sulfate has been examined. Three different dispersions appear in multi-domain single crystals. Since all these dispersions disappear in the single-domain crystals, it is clear that some kind of oscillation of the domain wall is responsible for these dispersions. According to the theoretical or experimental results reported so far, the three dispersions are considered to be originated by the oscillating domain wall trapped by defects, the swinging domain wall and the moving domain wall, respectively.

Far-Infrared Reflectance and Transmittance Studies of YBa2Cu3O7-x Single-Crystal Thin Films

A new method of estimating the optical constants of thin films has been developed and applied to YBa2Cu3O7-x epitaxial single-crystal thin films (Tc=90 K) grown on MgO substrates to determine the far-infrared optical conductivity σab(ω), which is the response when an unpolarized excitation is applied parallel to the ab-plane in multidomain (twinned) single crystals of YBa2Cu3O7-x. In this method, both the transmittance spectra T(ω) and reflectance spectra R(ω) are measured as a function of the wave number ω, and the results are substituted into a set of coupled equations which exactly describe R(ω) and T(ω) of thin films on substrates, where the complex refractive index N=n+ik of the thin films is an unknown parameter. The coupled equations are numerically solved using the Newton method, and the values of n and k are determined as a function of ω. We have determined σab(ω) of YBa2Cu3O7-x thin films for ω=50–250 cm-1 at T=34–97 K. Analysis of the temperature dependence of σab(ω) based on the two-fluid model suggests that the symmetry of the superconducting pairing state of the specimen is d-wave.

Engineering multidomain ferroic samples

The existence of domains is essential in many practical applications of ferroics. Here we discuss devices in which a fixed spatial distribution of domains plays the significant role. Depending on the prevailing attributes of multidomain single crystals, three different possibilities can be distinguished. In domain-geometry-engineered samples the spatial distribution of domains is tuned to correspond to the K-vectors of fields propagating through the material. In domain-average-engineered samples the crystal is subdivided into a very large number of domains, representing a limited number of domain states. In domain-wall-engineered samples the characteristics of static walls can play an essential role in the averaged macroscopic properties. Examples illustrating these approaches are given.

Elastic, piezoelectric, and dielectric properties of 0.955Pb(Zn/sub 1/3/Nb/sub 2/3/)O/sub 3/-0.45PbTiO/sub 3/ single crystal with designed multidomains

The elastic, piezoelectric, and dielectric properties of a 0.955Pb(Zn(1/3)Nb(2/3))O(3)-0.045PbTiO(3 ) (PZN-4.5%PT) multi-domain single crystal, poled along [001] of the original cubic direction, have been determined experimentally using combined resonance and ultrasonic methods. At room temperature, the PZN-4.5%PT single crystal has rhombohedral symmetry. After being poled along [001], four degenerate states still remain. Statistically, such a domain-engineered crystal may be treated as having an average tetragonal symmetry, and its material constants were determined based on 4 mm symmetry. It was confirmed that the electromechanical coupling coefficient k(33) for the domain-engineered samples is >90%, and the piezoelectric constant d(33) is >2000 pC/N. A soft shear mode with a velocity of 700 m/s was found in the [110] direction. From the measured experimental data, the orientational dependence of phase velocities and electromechanical coupling coefficients was calculated. The results showed that the transverse and longitudinal coupling coefficients, k(31) and k(33), reach their maximum along [110] and [001], respectively.

Macroscopic anisotropy in plastic neopentane by Raman light scattering

Polarized (VV) and depolarized (VH) Raman scattering have been performed on the 922 cm−1 internal line of neopentane both in the liquid phase and a multidomain single crystal of the plastic phase between 250 and 210 K. Small but systematic differences between the VV and VH spectra of the plastic phase, which are absent in the liquid phase, show anisotropy effects unrevealed up to now in this phase. The origin of the effect is discussed.

High-temperature hysteresis and other magnetic properties of synthetic monodomain titanomagnetites

A suite of synthetic titanomagnetites of composition Fe 2.4−δAl δTi 0.6O 4 and Fe 2.6−δAl δTi 0.4O 4 (δ = 0, 0.1 and 0.2 in both cases) have been prepared by a method of partial self-buffering and pulverized in a ball mill to particle size of about 200–500 Å. Magnetic hysteresis parameters-saturation and remanent magnetizations and coercive force were measured between room temperature and the Curie temperatures and other parameters-X-ray cell edge, initial susceptibility and coercive force of remanence were determined at room temperature. The intrinsic magnetic “hardness” increases with increasing content of Al 3+ and Ti 4+, both probably corresponding to an increase in the concentration of Fe 2+ ions on the tetrahedral sites of the spinel structure. The room-temperature hysteresis properties were compared with those resulting from monodomain models for the work done to magnetically saturate an assemblage of grains and the approach to saturation, and the separate contributions from coexisting anisotropies of cubic and uniaxial symmetries (assumed present) inferred. The cubic anisotropy energy constants so derived are larger than those determined from multidomain single crystals. The derived cubic constants are also larger than the derived uniaxial anisotropy constants. The latter, however, dominate the behaviour (e.g., coercive force) because of the lower symmetry. The materials appear to be entirely in the stable monodomain state at room temperature.