Order-disorder component in the phase transition mechanism of 18O enriched strontium titanate

Ti and Sr nuclear magnetic resonance spectra of 18O enriched SrTiO3 (STO-18) provide direct evidence for Ti disorder already in the cubic phase and show that the ferroelectric transition at T(C)=24 K occurs in two steps. Below 70 K rhombohedral polar clusters are formed in the tetragonal matrix. These clusters subsequently grow in concentration, freeze out, and percolate, leading to an inhomogeneous ferroelectric state below T(C). This shows that the elusive ferroelectric transition in STO-18 is indeed connected with local symmetry lowering and implies the existence of an order-disorder component in addition to the displacive soft mode one. Rhombohedral clusters, Ti disorder, and a two-component state are found in the so-called quantum paraelectric state of STO-16 as well. The concentration of the rhombohedral clusters is, however, not high enough to allow for percolation.     

A study of the structural phase transition in strontium titanate single crystal by coherent and incoherent second optical harmonic generation

The surface phase transition in a SrTiO₃ crystal was studied by second optical harmonic generation. Nonlinear optical response singularities were observed at temperature T*=145 K, which was 40 K higher than the T_c structural phase transition temperature in the crystal volume. Nonlinear critical opalescence in the crystal volume caused by the presence of point defects was studied. The second harmonic field and the intensity of critical opalescence were calculated based on the phenomenological model of nonlinear optical processes with the use of the Landau theory of phase transitions.     

Dielectric properties of betaine arsenate crystal near the phase transition

Dielectric measurements for single crystal of betaine arsenate (CH₃)₃NCH₂COO·H₃AsO₄ connected with the ferroelectric phase transition at 119 K were performed. The temperature dependence of electric permittivity was measured at dc electric fields up to 700 kV/m. The results show significant suppression of the dielectric constant by the application of dc field. Deviation from the classical behavior was observed. The electric permittivity was also measured in the paraelectric phase at constant temperature as a function of electric field intensity up to 700 kV/m. The electric permittivity might be well described by the classical relation with additional term including contribution to permittivity coming from clusters. The fit parameters indicate that the polar-clusters carries polarization P₀=0.7- with the clusters size of L=12-20 nm.     

Plasticity and an inverse brittle-to-ductile transition in strontium titanate

The use of ceramic materials is often restricted by a transition from ductile behavior to brittle fracture with decreasing temperature. For example, strontium titanate ( SrTiO3) is known to be extremely fragile and brittle below 1300 K. It is therefore surprising to find that SrTiO3 single crystals can be deformed in compression below 1050 K again. Extensive plastic deformation up to 7% strain at low yield stresses of the order of only 120 MPa is possible at room temperature. Low temperature plasticity is carried by the same [110] [110] dislocations as the high temperature deformation along the [001] axis. From this we conclude that these dislocations must exist in two different core configurations.     

Viscosity of a liquid crystal near the nematic-smectic A phase transition

We report the results of an x-ray scattering study where both the dynamic and the static properties of a liquid crystal (8OCB) near the nematic-smectic A phase transition were probed. The static, time-averaged data show the gradual formation of smectic layers in the nematic phase, and we find that the smectic order correlation length parallel to the molecular axis diverges with the critical exponent nu( parallel )=0.70(4) at the transition. The literature value is nu( perpendicular )=0.58 for the perpendicular direction. By x-ray photon correlation spectroscopy, we find that the viscosity coefficient eta(3) shows critical, diverging behavior at the phase transition with a critical exponent x=0.95(5). This contradicts previous light scattering work (x=0.50), but is in good agreement with the theoretical prediction x=3nu( parallel )-2nu( perpendicular ) by Hossain et al.     

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 T_c to about T_c + 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].     

Ultrasonic properties of strontium titanate at the 105°K transition

The temperature dependence of the sound velocity and the ultrasonic attenuation has been measured by the pulse-echo method in single crystals of strontium titanate in the vicinity of the 105°K structural transformation. Special attention is paid to the anisotropy of these measured quantities. The behaviour of the attenuation in the cubic phase can nearly quantitatively be interpreted as interaction with critical fluctuations belonging to the R-corner phonon mode. A numerical estimate leads to the conclusion that also in the tetragonal phase this fluctuation scattering contributes most to the attenuation, in comparison to resonant interaction (of the Landau-Khalatnikov type) and domain effects, which under the present experimental conditions dominate the sound velocity behaviour.     

Structural phase transitions in nanosized ferroelectric barium strontium titanate films

The lattice parameters of epitaxial barium strontium titanate films with various thicknesses (from 6 to 960 nm) were measured as a function of temperature in the normal and tangential directions with respect to the film plane using x-ray diffraction. The films were grown through the layer-by-layer mechanism by rf cathode sputtering under elevated oxygen pressure. A critical film thickness (～ 50 nm) was found to exist, below and above which the films are subjected to compressive and tensile stresses, respectively. As the temperature varies from 780 to 100 K, the films undergo two diffuse structural phase transitions of the second order over the entire thickness range. The transitions in the films under tensile stresses are likely to be transformations from the paraelectric tetragonal to aa phase and then to r phase, whereas the transitions under compressive stresses are transformations from the tetragonal paraelectric to ferroelectric c phase and then, with further decreasing temperature, to r phase.     

EPR study of charge compensation of chromium centers in the strontium titanate crystal

Chromium centers and their charge compensation in two single strontium titanate crystals, i.e., SrTiO₃: Cr (0.05 at %) and Sr_0.9995TiO₃: Cr_0.0005 grown with strontium deficiency, have been studied by the electron paramagnetic resonance method. The crystals have been investigated both immediately after growth and after oxidation and reduction procedures. Oxidation and reduction are performed by crystal annealing in a corresponding gas atmosphere at high temperature. Chromium centers associated with oxygen vacancy (Cr³⁺-V _O) are detected in the reduced crystals. It is shown that strontium vacancies are formed in the crystal grown with strontium deficiency, which leads to a lowering of the tetragonal symmetry of (Cr³⁺-V _O) and Cr⁵⁺ centers to the orthorhombic symmetry. Possible compensation mechanisms for charges of various chromium centers are considered.     

光折变晶体钛酸钡锶电荷传输参数的测量

报道用两波耦合技术测量光折变晶体钛酸钡锶(Ba_(1-x)Sr_xTiO-3,BST)的电荷传输参数φμτ在激光波长λ=515nm和光功率密度I—1W/cm~2下测得光折变响应时间为0.5sec.考虑到BST晶体吸收系数的光强相关性,修改了光栅形成率的函数变量,得到BST晶体的暗电导σ_a和电荷传输参数φμτ的拟合值分别为1.0×10~(-11)(Ωcm)~(-1)和2.8×10~(-10)cm~2/V.     

Elastic anomalies in strontium titanate

The anomalies of the second and third-order elastic constants have been considered for the phase transition of strontium titanate within the framework of Landau’s theory. All the anomalies of the second-order elastic constants have been obtained in a single formula using Kronecker delta functions and relations among them have been established. The real parts ofC*₁₁ andC*₄₄ decrease steeply across the transition temperature and thereafter flatly tend to their asymptotic values in the low temperature phase agreeing qualitatively with experimental observations. We have also derived expressions for the third-order elastic anomalies and discussed the temperature variation of the real part ofC*₁₁₁. We have derived expressions for the attenuation of the longitudinal and transverse waves along certain simple symmetry directions and have shown that there is nearly good agreement with experimental observations.     

Diffuse X-ray scattering from a calomel crystal near the temperature of the structural phase transition

X-ray scattering from a calomel crystal near the temperature of a structural phase transition is analyzed theoretically. It is shown that the diffuse lines of the x-ray diffraction, which correspond to both the X points and Z point of the Brillouin zone, are formed in the high-temperature phase. The latter lines result from the scattering by the beats of fluctuations of two components of the order parameter. Such lines were previously observed experimentally, but the nature of the lines corresponding to the Z point remained unclear. It is shown that the Z line at the point (5, 0, 0) should be an order of magnitude stronger than the observed Z line at the point (4, 3, 0).     

Director dynamics near the nematic-smectic-A phase transition

The Landau-de Gennes model for the free energy of a nematic liquid crystal near the phase transition to the smectic A-phase is used to determine the frequency dependence of the fluctuation corrections to the Frank elastic constants. It is shown that the interaction of the fluctuations of the smectic order parameter and the director results in corrections to all the Frank elastic constants. In the low-frequency limit (ω→0), the corrections to the Frank elastic constants K ₂₂ and K ₃₃ are the largest, and decrease to zero in the infinite-frequency limit. The correction to K ₁₁ is negative, and vanishes in both limits. The absolute value of the correction to K ₁₁ is the largest at frequencies in the megahertz range. It is shown that in oriented nematics the interaction of the smectic fluctuations and the director limits deviations of the director from the direction of preferred orientation, as a result of which relaxation of both inhomogeneous and homogeneous distortions of the director field can be observed. It is also shown that this gives rise to a frequency interval in the megahertz range in which shear waves begin to propagate in the nematic. The propagation speed of these waves is roughly a hundred times smaller than that of sound and strongly depends on the direction of propagation. Zh. éksp. Teor. Fiz. 114, 2022–2033 (December 1998)     

Transport coefficients near chiral phase transition

We analyze the transport properties of relativistic fluid composed of constituent quarks at finite temperature and density. We focus on the shear and bulk viscosities and study their behavior near chiral phase transition. We model the constituent quark interactions through the Nambu–Jona-Lasinio Lagrangian. The transport coefficients are calculated within kinetic theory under relaxation time approximation including in-medium modification of quasi-particles dispersion relations. We quantify the influence of the order of chiral phase transition and the critical end point on dissipative phenomena in such a medium.     

Excess space charge in strontium titanate

An analysis is made of mechanisms of the formation and redistribution of space charge which influence the dielectric hysteresis in SrTiO₃. The excess space charge density in SrTiO₃ at 4.2 K is estimated by comparing calculated and experimental dependences of the initial capacitance and the dielectric hysteresis parameter ΔC/C ₀ as a function of the crystal thickness. Fiz. Tverd. Tela (St. Petersburg) 40, 245–247 (February 1998)     

Anomalous hypersonic attenuation in strontium titanate

Hypersonic attenuation in SrTiO₃ above 100°K is here reported. A temperature independent attenuation is observed for transverse waves but for longitudinal waves it is monotonically increasing with decreasing temperature. A sharply increasing attenuation is found near the 102.5°K phase transition.     

Crystal shape near the faceting phase transition point

The critical behavior of an equilibrium shape of a crystal with the size much larger than the capillary length is studied near the faceting phase transition point.     

Kurtosis and compressibility near the chiral phase transition

The properties of net quark number fluctuations in the vicinity of the QCD chiral phase transition are discussed in terms of an effective chiral model in the mean-field approximation. We focus on the ratio of the fourth- to second-order cumulants (kurtosis) and the compressibility of the system and discuss their dependence on the pion mass. It is shown that near the chiral phase transition, both observables are sensitive to the value of mπ$m_{\pi }$. For physical mπ$m_{\pi }$, the kurtosis exhibits a peak whereas the inverse compressibility shows a dip at the pseudocritical temperature. These structures disappear for large mπ$m_{\pi }$. Our results, obtained in an effective model with two flavors, are qualitatively consistent with recent results of 2+1$2+1$ flavor lattice gauge theory. We also discuss the high- and low-temperature properties of these observables and the role of the coupling of the quark degrees of freedom to the Polyakov loop.