Second order elastic anomalies in barium titanate from orthorhombic to rhombohedral phase transition

The anomalies in second order elastic constants have been derived for barium titanate for the phase transition from orthorhombic to rhombohedral state. The equilibrium values of order parameter, strain variables and fluctuations in order parameter have been derived using stability conditions and Landau-Khalatnikov equations respectively. Expression for shift in specific heat is obtained. All the anomalies in second order elastic constants have been derived and relations among them reported. The numerical values of anomalies in the individual constants are calculated and their variation is represented graphically. Changes in elastic constants occur over a range of temperature of the order 10⁻²K.     

Second order elastic anomalies in barium titanate from cubic to tetragonal phase transition

The anomalies of the second order elastic constants have been derived for barium titanate for the phase transition from cubic to tetragonal. The equilibrium values of the components of the order parameter and the strain variables have been obtained from the stability conditions. The fluctuations in the order parameter have been derived from the Landau-Khalatnikov equations. Expression for the shift in the zero point energy in the tetragonal phase is obtained and is shown to be proportional to (T −T _c)². The anomalies for all the second order elastic constants have been derived and relations among them reported. It is shown that the second order elastic anomalies suffer a discontinuity at the transition temperature.     

Effect of Sn substitution on the elastic anomalies and phase transition behaviors of antiferroelectric PbHfO3 single crystals studied by Brillouin scattering

The phase transition sequence of a PbHf_0.7Sn_0.3O₃ single crystal was investigated by using Brillouin spectroscopy. The longitudinal acoustic mode showed three distinct changes at ∼370 K, ∼455 K and ∼495 K which corresponded to the antiferroelectric 1 → antiferroelectric 2 → intermediate → paraelectric phase transitions upon heating. The paraelectric phase was characterized by softening acoustic mode, increasing acoustic damping and the appearance of quasielastic central peaks which were observed upon approaching the phase transition temperature. The relaxation times derived from the acoustic mode anomalies and the central peak were consistent with each other and showed a slowing-down behavior. These precursor phenomena were attributed to the polar clusters having broken inversion symmetry. The substitution of Hf with Sn induced a very soft intermediate phase between the paraelectric and the antiferroelectric phases, where the longitudinal acoustic mode exhibited the lowest mode frequency along with substantially high acoustic damping. The transverse acoustic mode, which was observed in the two antiferroelectric phases, did not appear in the intermediate phase. These results indicated that the average symmetry of the intermediate phase may be cubic consisting of fine ferroelastic domains.     

Phase structures and stability in barium titanate ferroelectric ultrathin films

Under taking into account both stress and surface effects, an extended Landau–Devonshire theory is developed to investigate the phase structures and ferroelectric stability in barium titanate ultrathin films. The phase diagrams of temperature-stress, film thickness-stress and polarization-film thickness are calculated. For the surface polarization smaller than the bulk, the paraelectric phase starts at temperature below the bulk Curie temperature under small stresses and the ferroelectric phases can be stabilized in the ultrathin films under large stresses. For the surface polarization larger than the bulk, the paraelectric phase appears at temperature above the bulk Curie temperature and the ferroelectricity can be sustained in the ultrathin films by the “superpolarized” surface layer.     

Uniaxial stress dependence of the dielectric properties of barium titanate single crystals

BaTiO₃ single crystals were grown by the melt-grown method. The effect of uniaxial pressure (0–1700 bar) on the dielectric properties of these crystals has been systematically studied. The external stress showed obvious effects on these properties. An increase in the difference between the Curie T_c and Curie–Weiss T₀ temperatures induced by the applied pressure is observed. This could be ascribed to the inducing of non-ferroelectric cubic islands in the tetragonal phase by the applied compressive stress. On the other hand, the pressure behavior of thermal hysteresis and the ??/?T vs. T plot strongly suggests that the phase transition changes to second-order type with increasing pressure. The Curie–Weiss constant obtained from a modified Curie–Weiss law strongly decreases with increasing pressure, suggesting that the mechanism of phase transition is going to order–disorder type. An increase in the difference between the Curie T_c and Burn's T_B temperatures with increasing pressure is observed. This could be ascribed to the narrowing of the temperature range on which the Curie–Weiss law is valid. In general, the obtained results are in good agreement with hydrostatic pressure data. Some kind of relaxation near T_c, which is strongly coupled with strain caused by applied compressive stress, is postulated.     

Acoustic anomalies and relaxation dynamics of relaxor ferroelectric Na1/2Bi1/2TiO3 single crystals studied by using Brillouin spectroscopy

Acoustic anomalies of relaxor ferroelectric Na_1/2Bi_1/2TiO₃ single crystals were investigated over a wide temperature range from −196 °C to 900 °C by using Brillouin spectroscopy. The longitudinal sound velocity, the acoustic absorption coefficient and the elastic constant C₁₁ were determined for the acoustic phonon mode propagating in the [100] direction. Two acoustic anomalies, weaker ones at the cubic-tetragonal phase transition temperature of ~540 °C and more pronounced ones at temperatures near 315 °C near the dielectric maximum temperature, were investigated and discussed in relation with the relevant order parameters coupled to the acoustic waves. The relaxation dynamics in the cubic phase were studied based on the flattening of the mode frequency and the half width, which was observed for the first time, and a modified Arrhenius law.     

Effect of lanthanum substitution on the Raman spectra of barium titanate thin films

Thin films of Ba_1−xLa_xTiO₃ on platinum substrates were synthesized using the sol–gel method for x values of 0.0, 0.03, 0.05, and 0.10, and the effect of trivalent La³⁺ substitution on the structural and dielectric properties was studied. Using X‐ray diffraction, structural analysis of these compositions revealed a slight increase in the tetragonal distortion of the unit cell with increase in La content. Accordingly, an increase in the tetragonal to cubic transition temperature T_T/C was detected by temperature‐dependent Raman spectroscopy in the range of 70–500 K. Unlike the results from Raman scattering for the La‐doped BaTiO₃ films, the dielectric measurements showed broad and diffused dielectric maxima, making the estimation of the transition temperature merely qualitative. Copyright © 2006 John Wiley & Sons, Ltd.     

Effect of sintering temperature on phase formation,microstructure and dielectric properties of nanogold modified barium titanate ceramics

In this work, BaTiO₃ ceramics modified with 0.5 mol% Au nanoparticles were fabricated by using a combination of the solid-state reaction and pressureless-sintering techniques. By employing a combination of X-ray diffraction (XRD), scanning electron microscopy (SEM), energy-dispersive X-ray (EDX), Archimedes principle and dielectric measurement techniques, it was found that no phases other than tetragonal BaTiO₃ were observed in all ceramics. In contrast to the tetragonality, the relative density, grain size and maximum dielectric constant at Curie temperature of the ceramics were found to increase with sintering temperature. In addition, it has been found that, under suitable sintering temperature, dense perovskite nanogold modified BaTiO₃ ceramics with fine-grained microstructure (∼1 μm) and better dielectric properties than those of gold-free ceramics can be produced.     

Structural phase transition and elastic properties of ZnSe at high pressure

We have evolved an effective interionic interaction potential to investigate the pressure-induced phase transitions from zinc blende (B3) to rock salt (B1) structure in II-VI [ZnSe] semiconductors. The elastic constants, including the long-range Coulomb and van der Waals (vdW) interactions and the short-range repulsive interaction of up to second-neighbor ions within the Hafemeister and Flygare approach, are deduced. Keeping in mind that both of the ions are polarisable, we employed the Slater-Kirkwood variational method to estimate the vdW coefficients. The estimated value of the phase transition pressure (P _t ) is higher than in the reported data, and the magnitude of the discontinuity in volume at the transition pressure is consistent with that data. The major volume discontinuity in the pressure-volume phase diagram identifies the structural phase transition from zinc blende to rock salt structure.

The variation of second-order elastic constants with pressure resembles that observed in some binary semiconductors. It is inferred that the vdW interaction is effective in obtaining the thermodynamic parameters such as the Debye temperature, the Gruneisen parameter, the thermal expansion coefficient and the compressibility. However, the inconsistency between the thermodynamic parameters as obtained from present model calculations and their experimental values is attributed to the fact that we have derived our expressions by assuming the overlap repulsion to be significant only up to the nearest second-neighbor ions, as well as neglecting thermal effects. It is thus argued that full analysis of the many physical interactions that are essential to binary semiconductors will lead to a consistent explanation of the structural and elastic properties of II–VI semiconductors.     

Preparation and optical properties of barium titanate thin films

Barium titanate (BTO) films were prepared by sol-gel spin-coating technique. The crystal structure and optical properties of BTO films have been investigated. The results indicate that the BTO films are single perovskite phase having tetragonal symmetry. The band gap of the BTO films increases with the increasing of layer number and decreasing of solution concentration. The transmittance and band gap of the BTO films annealed at 900 °C is more than that of the BTO films annealed at 700 °C when wavelength is 200-1000 nm. When wavelength is 400-1000 nm, the absorption coefficient α obtained by experiment is higher than that obtained by calculation (close to zero).     

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.     

Importance of annealing on the order-disorder phase transition in alkali cyanides

Abstract

Contrary to monocrystals powdered KCN displays, after grinding and without annealing, an intermediate monoclinic phase between the high-temperature pseudocubic and the low-temperature orthorhombic phases. The consequence of annealing is the total disappearance of this intermediate phase. A further effect of the annealing process is the reduction of the cubic distortion at the transition. In this paper, we analyse this effect on the intermediate rhombohedral phase observed in the (KCN) _x (KBr)_1?x mixed system.     

Pressure dependence of acoustic behaviors and refractive index of amorphous Kel F-800 copolymer studied by Brillouin spectroscopy

The pressure dependences of the longitudinal sound velocity and the refractive index of amorphous Kel F-800 copolymer were investigated for pressures up to 13 GPa using high-pressure Brillouin spectroscopy combined with a diamond-anvil-cell technique. The sound velocity increased rapidly with increasing pressure at pressures below ～2 GPa, whereas it showed a mild change at higher pressure values. This was attributed to substantial collapse of effective free volume in this amorphous material. The refractive index could be measured by comparing the Brillouin spectra measured from backward and forward, symmetric scattering geometries. The pressure–density relationship could be obtained by using Lorentz–Lorenz equation based on an assumption of constant polarizability, which was consistent with that reported by previous study.     

Superiority of sonochemical processing method for the synthesis of barium titanate nanocrystals in contrast to the mechanochemical approach

The results indicated that the ultrasonic sonochemistry which brings into play the acoustic cavitation phenomenon is more powerful and feasible in synthesizing the mixed oxides in contrast to the conventional solid-state approaches. The obtained results demonstrated that the sonochemical approach is able to obtain highly pure powder product at a much lower processing temperature of about 323 K (50 °C) in contrast to 1173 K (900 °C) which is essential for the synthesis by the mechanochemical approach. Sonochemical synthesis benefits from homogenous ordering the reactant ions (which have been dissolved in the solution mixture) into perovskite structure using ultrasonication. This indicates that the acoustic cavitation phenomenon is much more powerful and cost-effective than high energy ball milling in synthesizing nanopowders of the mixed oxide materials. Moreover, the sonochemical processing method is able to prepare the final powder products in a much shorter time by a one-step synthesis approach without the need for the successive calcination in contrast to the solid-state approach.     

A strong correlation of crystal structure and Curie point of barium titanate ceramics with Ba/Ti ratio of precursor composition

A series of barium titanate powders were synthesized from precursors BaCO₃ and TiO₂ with Ba/Ti ratio ranged from 0.96 to 1.04. For the ceramics sintered at 1300 °C for 2 h, with increasing Ba/Ti ratio from 0.96 to 1.04, the tetragonal distortion of perovskite barium titanate phase was decreased continuously and the Curie point was decreased monotonously from 122.9 to 98.0 °C. At the same time, the content of secondary phases was very low. This correlation of crystal structure and Curie point of barium titanate ceramics was explained by composition variation of the perovskite phase itself rather than by the influence from secondary phases. Due to very controversial results reported by different groups, it was proposed that BaTiO₃ has some different states with different solubilities for BaO and TiO₂. Further investigations should be conducted on the preparation and the properties of BaTiO₃ with much BaO or TiO₂ dissolved.     

Inelastic light scattering studies of diffuse phase transition in ferroelectric Sr1.9Ca0.1NaNb5O15 thin films

The dynamic behavior of highly oriented ferroelectric Sr_1.9Ca_0.1NaNb₅O₁₅ thin films has been investigated by Brillouin light scattering over a wide temperature range between 25 and 450 °C. The temperature variations of the full‐width at half‐maximum (FWHM) of the central peak (CP) are found to exhibit marked changes around the Curie temperature (T_c = 246 °C). The CP reveals a relaxational mode behavior, which is attributed to thermally activated fast relaxation of polar nanoregions (PNRs). The width of the CP decreases steadily upon cooling from ∼400 °C to T_c and shows little subsequent change within the ferroelectric state, indicating an increase of the number of PNRs and a slowing down of their dynamics. By using a modified superparaelectric model, the activation energy (H₀) of the relaxation processes and the Burns temperature (T_B) are determined to be 2939 and 385 °C, respectively. The evidence for this diffuse phase transition provided by Brillouin scattering is in agreement with results obtained from the temperature‐dependent dielectric permittivity, refractive index, and Raman spectra. Copyright © 2011 John Wiley & Sons, Ltd.     

Brillouin scattering study on elastic and piezoelectric properties of laser irradiated ZnO single crystals

Brillouin light scattering technique can be successfully used to determine the whole set of elastic and piezoelectric constants of a ZnO single crystal irradiated by different laser energy densities,into a micron range (radiation layer thickness).It is found that the scattering intensity,the linewidth and the Brillouin scattering shift of acoustic phonons are all strongly dependent on laser energy density.Based on the sound propagation equations and these results,the directional dependences of the compressional and shear moduli of the irradiated ZnO sample in the (001) plane are investigated.It is found that under an appropriate laser condition,248 nm KrF excimer laser irradiation can significantly improve the surface quality and increase the elastic properties of ZnO single crystal.This procedure has potential applications in the fabrication of ZnO-based surface acoustic wave and optic-electronic devices.     

Characterization of phase transition in liquid crystals by voltaic potential difference

Our investigations show that the determination of voltaic potential differences is a useful method to characterize the phase transition N → I and I → N for a liquid-crystal (LC) mixture and for a phase transition from one liquid-crystalline phase into another. The ΔV/T curves show reversible as well as an irreversible behaviour. Moreover, the transition from the smectic into the nematic phase is demonstrated on liquid-crystalline polymers.