Third-order elastic constants and pressure derivatives of the second-order elastic constants of β-tin

The second- and third-order elastic constants and pressure derivatives of second-order elastic constants of tetragonal β-tin have been obtained using the deformation theory. The strain energy density derived using the deformation theory is compared with the strain dependent lattice energy obtained from the elastic continuum model approximation to get the expressions for the second- and third-order elastic constants. Higher order elastic constants are a measure of the anharmonicity of a crystal lattice. The 12 non-vanishing third-order elastic constants and the six pressure derivatives of the second-order elastic constants in tetragonal β-tin are obtained in the present work and are compared with the available experimental values. The second-order elastic constant C₃₃ obtained in the present study is in reasonable agreement with the experimental values. The third-order elastic constants are generally one order of magnitude greater than the second-order elastic constants as expected of a crystalline solid. The third-order elastic constant C₃₃₃ is higher in magnitude than all other values. This shows a greater anharmonicity of β-tin along the c-axis direction of the crystal.     

Charge ordering and elastic anomalies in NaxCoO2

We report in-plane resistivity and elastic constant C₃₃ measurements on the Na_0.8CoO₂ and Na_0.5CoO₂ systems. An ordering transition is found at T₀=280 K for Na_0.8CoO₂. The temperature dependence of the elastic constant C₃₃ propagating perpendicular to the CoO₂ layers is interpreted, in a phenomenological approach, as being due to the anharmonicity of atomic vibrations. The effective Grüneisen parameter γ_eff deduced directly from the temperature dependence of C₃₃ exhibits important changes at the charge ordering, magnetic and metal-insulator phase transitions.     

Low temperature elastic constants and Debye temperature of NbO2

The transit times of ultrasonic waves have been measured in single crystal NbO₂ from 295 K down to 1.5 K for quasilongitudinal and shear waves propagating in the [100] direction and down to 160 K for eight other waves. Values are obtained for the C₄₄ elastic constant and for an elastic constant combination which is approximately equal to C₁₁ for temperatures down to 1.5 K and for C₁₁, C₁₂, C₁₃, C₁₆, C₃₃, and C₆₆ down to 160 K. These results are used to deduce 0 K values for the elastic constants and an elastic Debye temperature of 596 ± 7 K at 1.5 K. The acoustic mode heat capacity calculated from the latter is significantly smaller than the heat capacity measured by Wenger and Keesom at low temperatures. Following Wenger and Keesom, the difference is attributed to phasons (excitations involving the phase modulation of charge density waves). An average velocity is deduced for the phasons.     

Theoretical and computer simulation study of density fluctuations in liquid binary alloys

The dynamical properties of liquid alloys are investigated by means of memory function equations and molecular-dynamics simulation. A simple model for the second-order memory function in a binary liquid, based on Mori's memory function formalism, is proposed and applied in numerical calculations of the time correlation functions and dynamic structure factor of liquid K_0.7Cs_0.3 and K_0.3Cs_0.7 alloys. Obtained results are discussed in comparison with the results of computer simulations. Received: 27 February 1998 / Revised: 24 July 1998 / Accepted: 27 July 1998     

Investigations of twist elastic constant K<Subscript>22</Subscript> of new nematic liquid crystal materials using threshold IPS method

The liquid crystal technology is one of the most popular at the present time. To the most important parameters of liquid crystals belong optical anisotropy, viscosity, and twist elastic constants. One of the most difficult and problematic to measure parameters is a twist elastic constant K₂₂. For new liquid crystalline materials, we have to characterize their physical properties, also a twist elastic constant K₂₂.     

Electrohydrodynamic instability in a nematic liquid crystal: Effect of an additional stabilizing AC electroc field on the spatial period of “chevrons”

The spatial period of bend oscillations in nematic N-(p-methoxybenzylidene)-p-n- butylaniline (MBBA) at the threshold of electrohydrodynamic instability increases under the application of an additional high frequency stabilizing field, giving a measurement of the elastic constant K₃₃ = 7.3 ± 1.5 dyne.     

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)     

Magnetic properties of the low dimensional spin system (VO)PO:ESR and susceptibility

Experimental results on magnetic resonance (ESR) and magnetic susceptibility are given for single crystalline (VO)₂P₂O₇. The crystal growth procedure is briefly discussed. The susceptibility is interpreted numerically using a model with alternating spin chains. We determine J =51 K and . Furthermore we find a spin gap of meV from our ESR measurements. Using elastic constants no indication of a phase transition forcing the dimerization is seen below 300 K. Received: 22 December 1997 / Accepted: 17 March 1998     

Four constant potential function of amorphous selenium and evaluation of its thermodynamic and acoustic properties

Litov and Anderson after various considerations suggested a four constant potential function for a-Se as well as a-As₂S₃. Hence we also used a four constant potential function with the sole purpose of applying this potential function to obtain several acoustic, thermodynamic and other properties. We calculated several acoustic properties of a-Se like second order elastic constants (SOECs), their pressure derivatives, the longitudinal and transverse Grüneisen constant by two different methods, phonon frequencies, absorption band position through the use of Nath-Smith-Delaunay’s equation, and the thermodynamic properties like heat capacity, bulk modulus, thermal Grüneisen constant, the pressure derivative of the bulk modulus (dK _T/dP=C ₁), the pressure derivative ofC ₁ which is related to Anderson-Grüneisen parameter, pressure derivative of Grüneisen constant namelyγ′ _g which is related to second Grüneisen constant, characteristics of phonon frequencies, potential energy function through the use of fitted parameters and third order elastic constants. Finally we calculatedK _T at the reduced density ofρ/ρ ₀=1.1.K _T is obtained from the potential function with the fitted parameters. In all the above cases the calculated values are found to be in good agreement with experiment wherever available. In this connection it is important to point out that we eliminated ‘C’ a constant in the potential function using the equilibrium condition as was done by Litovet al in a-Se and Gerlichet al in the case of a-As₂S₃ as all amorphous substances are isotropic as mentioned by several authors. We contemplate to calculate several other properties for a-Se and a-As₂S₃ and present them at a later stage.     

Material tensor parameters of LiNbO3 relevant for electro- and elasto-optics

The complete set of self-consistent parameters of nominally undoped LiNbO₃ crystals of congruent composition that describe the electro-optic, piezoelectric, elasto-optic, elastic, and dielectric response has been determined by numerically evaluating available measurements. The parameters were determined at room temperature and consist of the low-frequency clamped dielectric constants ε^S _ij, elastic stiffness constants at constant electric field C^E _ijkl, piezoelectric stress coefficients e_ijk, elasto-optic constants at constant electric field p^E _ijkl, and clamped electro-optic coefficients r^S _ijk. It is shown that the complete set is required for calculating the effective electro-optic coefficients and dielectric constants in photorefractive applications of LiNbO₃. Received: 4 January 2002 / Revised version: 1 February 2002 / Published online: 14 March 2002     

Non-interferometric transient quantitative phase microscopy for ultrafast engineering

Lead-free piezoelectric ceramics Bi_0.5(Na_1-x-yK_xAg_y)_0.5TiO₃ [BNKAT(x/y)] have been synthesized by the mixed oxide method. The effects of the amount of K⁺ and Ag⁺ on the electrical properties were examined. X-ray diffraction patterns indicate that K⁺ and Ag⁺ ions partially substitute for the Na⁺ ions in Bi_0.5Na_0.5TiO₃ and form a solid solution during sintering. At room temperature, the ceramics exhibit good performances with piezoelectric constant d₃₃=189 pC/N, electromechanical coupling factor k_p=35.0%, remanent polarization P_r=39.5 μC/cm², and coercive field E_c=3.3 kV/mm, respectively. The curves of the dielectric constant ε_r and loss tangent tan δ versus temperature show that the transition temperature from ferroelectric to anti-ferroelectric phase decreases with increasing the K⁺ content for the compositions researched. The dependencies of k_p and polarization versus electric (P–E) hysteresis loops on temperature reveal that the depolarization temperature T_d of BNKAT(0.15/0.015) ceramics, which have good piezoelectric properties (d₃₃=134 pC/N, k_p=32.5%) and strong ferroelectricity (P_r=39.5 μC/cm², E_c=4.1 kV/mm) at room temperature, is above 160 °C. PACS 77.22.-d; 77.65.Bn; 77.80.Bh; 77.80.Dj; 77.84.Dy     

The K * Kπ and ρππ couplings in QCD

The light cone QCD sum rules are derived for the K ^* Kπ coupling g _K ^* Kπ and the ρππ coupling g _ρππ. The contribution from the excited states and the continuum is subtracted cleanly through the double Borel transform with respect to the two external momenta, p ₁ ², p ₂ ²= (p−q)². Our result g _K ^* Kπ= (8.7 ± 0.5) and g _ρππ= (11.5 ± 0.8) is in good agreement with the experimental value. Received: 31 July 1998 / Revised version: 20 November 1998     

Different temperature dependences of photorefractive parameters of Ce-doped and Rh-doped BaTiO3

eff and the electro-optic coefficient r₃₃ in Ce-doped and Rh-doped BaTiO₃ were determined by two-beam coupling measurements. It was found that the effective trap density N_eff of BaTiO₃:Ce increases whereas that of BaTiO₃:Rh decreases with increasing temperature. The electro-optic coefficient r₃₃ of both crystals increases with temperature. The photorefractive response times were also measured and found to decrease with different rates as temperature increases in the two crystals. The results were discussed by using the two-centre model for BaTiO₃:Ce and three-charge-state model for BaTiO₃:Rh. We found that the different temperature dependence of N_eff in the two crystals was due to the fact that the deep- and shallow-trap levels in BaTiO₃:Ce are caused by different impurity centres whereas those in BaTiO₃:Rh are caused by different charge states of the same impurity centre. Received: 16 July 1998/Revised version: 26 October 1998     

Interaction between disinclinations in nematic liquid crystals

The forces of interaction between disinclinations in nematic liquid crystals as well as between a disinclination and a wall are calculated on the basis of the elastic theory of Oseen and Frank under the assumption K₁₁ = K₃₃.     

On the possibility of f 0 observation in low energy pp collisions

Within the meson-exchange model we calculate f ₀-meson production cross section in πN and NN reactions and investigate the possibility for f ₀ observation via the KˉK decay mode in pp collisions. Our studies indicate that an extraction of the f ₀ signal is unlikely due to the large background from other reaction channels. Received: 14 October 1998 / Revised version: 17 November 1998     

Phases hexagonales colonnaires thermotrope et lyotrope : défauts observés par cryofracture et caractère anomal du thermotrope

Electron microscopy observations of replicas of freeze-fractured samples of two columnar hexagonal phases of different nature (a lyotropic one, the inverse AOT in water; a thermotropic one, ) yield very different results: most defects at microscopic scales are screw dislocations in the lyotropic phase, longitudinal edge dislocations in the thermotropic phase. A possible way to interpret these differences is as follows: in the lyotropic the Lamé coefficients and μ and the bend modulus K₃ would not display any anomaly compared to expected values; in the thermotropic the shear modulus μ would be ten times smaller than the compressibility modulus , while K₃ would still be comparable to (but larger than) the bend modulus of a small molecules liquid crystal. We present an elementary theoretical model of the latter case which could explain the anomalous measurements of K₃ and of the longitudinal compressibility (Ref. [#!ref10!#]) without contradicting more recent measurements of (Refs. [#!ref17!#,#!ref22!#]). Essentially, the hexagonal phase would be a phase with defects (longitudinal dislocations) akin to an hexatic phase but with some differences. Re?u : 26 mai 1997 / Révisé : 20 Janvier 1998 / Accepté : 27 avril 1998     

Spatial characteristics of Kα radiation from weakly relativistic laser plasmas

The spatial dependence of K _α emission generated from laser-produced hot electrons is investigated experimentally and theoretically. In addition, the conversion efficiency of K _α production as a function of laser intensity is measured and compared with modeling results. We use the terawatt Ti:sapphire laser at MPQ and vary the peak intensity from 10¹⁵ to 10¹⁸ W/cm² with a pulse duration of 200 fs. A solid Cu target is placed at various positions in the laser focus, which allows one to vary the intensity but keep the total energy on the target constant. When the target is near best focus, the FWHM of the K _α emission, measured using a knife-edge, is considerably larger than the FWHM of the laser intensity. In measuring the efficiency of K _α production using the fundamental wavelength of the laser, a clear maximum of K _α emission is observed at a position away from best focus, where the peak intensity is down by more than an order of magnitude from the value at best focus. When the second harmonic of the laser is used, the K _α emission is peaked near best focus. The K _α emission from layer targets is used to obtain an estimate of the temperature of the hot electrons. Modeling of K _α production, using a Monte Carlo electron/photon transport code, shows the relationship between incident electron energy and the emitted K _α emission. Efficient K _α generation from the low-intensity wings of the laser pulse contributes to the large spot size of the K _α emission. The lower electron temperatures that are expected for the second harmonic explain the differences in the location of maximum K _α emission for the two wavelengths. We discuss the use of K _α emission in photoionizing inner-shell electrons with the goal of achieving X-ray lasing at short wavelengths. Received: 6 April 1999 / Revised version: 31 May 1999 / Published online: 11 August 1999     

Growth-induced anisotropy in Ba0.6K0.4BiO3 superconducting single crystal

0.6 K_0.4BiO₃ single crystal have been performed to study the nature of the growth-induced anisotropy revealed using chemical etching technique. It was found that this anisotropy is responsible for differences in low-field susceptibility and in hysteresis loops observed for different magnetic field orientations. Received: 9 December 1997/Accepted: 28 May 1998     

Optical measurement of KB/KS divergence in nematics

A direct optical analysis of the divergence of the elastic constant ratio K_B/K_S in a nematic material near the T_AN transition temperature is presented. The results are in excellent agreement with what obtained from more complicated techniques. The method used exhibits a large number of advantage with respect to the conventional ones.     

Effective magnetic anisotropy of nanocrystalline Nd-Fe-Ti-N hard magnetic alloys

The intermetallic compound Nd-Fe-Ti-N has been successfully synthesized by a mechanical alloying process. The structure and magnetic properties of the sample have been studied using X-ray diffraction and magnetic measurements. It is found that alloy exhibits a nanocrystalline ThMn₁₂-type tetragonal structure with lattice parameters of a=0.8723 nm and c=0.4896 nm. The saturation magnetization M_S and effective magnetic anisotropy K_eff of the compound have been determined by investigating magnetization processes. The calculated results based on the law of approach to magnetic saturation have been successfully used to determine the constant K_eff. The difference between observed and calculated values in magnetization is lower than 3%. Of all terms in the law of approach to saturation, it is the 1/H ² term, which is attributed more to non-compensated anisotropy energy, that has the prevailing effect for the compound. The absorption of nitrogen is found to increase unit cell volume, M_S and K_eff. Received: 28 October 1996 / Revised: 14 March 1997 and 4 August 1997 / Accepted: 8 August 1997