Brillouin and ultrasonic study of the temperature dependence of the elastic constants in NaCN

The temperature dependence of the elastic constants of NaCN has been studied by propagation of ultrasonic waves at 15 MHz and by Brillouin scattering at 3 GHz over the temperature range from 287K to 355K. c₄₄ is observed to soften linearly with temperature as the order-disorder phase transition at 284K is approached from above. The other elastic constants also soften, except for c₁₂ which stiffens. Considerable dispersion is seen in the values of c₄₄ obtained ultrasonically and by Brillouin scattering. Measurements of the temperature dependence of the density are also reported.     

First-principles calculations on elasticity of under pressure

First-principles calculations of the crystal structure and the elastic properties of OsN₂ have been carried out with the plane-wave pseudopotential density functional theory method. The calculated values are in very good agreement with experimental data as well as with some of the existing model calculations. The dependence of the elastic constants c_ij, the aggregate elastic moduli (B,G,E), Poisson’s ratio, and the elastic anisotropy on pressure has been investigated. Moreover, the variation of the Debye temperature and the compressional and shear elastic wave velocities with pressure P up to 60 GPa at 0 K have been investigated for the first time.     

RUS study of the elastic constants in silver halide crystals

By using RUS method, the temperature dependence of the elastic constants in the silver halide crystals has been measured above room temperature. The elastic constants decrease linearly with increasing temperature. Numerical calculations are presented for the contribution of the multipole polarization to the elastic constants in the silver halide crystals. The calculated values of the deviation from the Cauchy relation are about a quarter of the experimental values. The multipole polarization significantly affects the elastic constants and contributes to the violation of the Cauchy relation.     

钽铌酸锂晶体的布里渊散射研究

研究了钽铌酸锂(LiTa_xNb_(1-x)O_3,x=0.0013,0.0052,0.015,0.06)晶体在室温的布里渊散射.给出了它们的弹性刚度常数和压电应力常数.测量了一种组份晶体的布里渊散射频移在50K～580K范围内的温度特性.发现某些声子散射谱中除三个正常峰外还存在一个异常峰.     

Single crystal elastic constants and magnetoelasticity of holmium from 4·2 to 300 K

The five independent elastic coefficients of holmium single crystals have been determined by means of an ultrasonic pulse technique at a frequency of 10 MHz, between 4·2 and 300 K. From the elastic constants the temperature variation of the directional adiabatic compressibilities, the limiting Debye temperature and the elastic anisotropy ratio were calculated. The elastic coefficients exhibit anomalies at the magnetic ordering transitions known to occur in holmium. Anomalous behavior in the elastic constants was also observed at about 80 K. The limiting value of the Debye temperature was found to be 191·5 K. The present measurements of the elastic constants, and the reported magnetostriction and thermal expansion data, enabled the calculation of the magnetoelastic contribution to the total Hamiltonian of holmium in the magnetically ordered states. A very small discontinuity in the temperature dependence of the magnetoelastic energy was observed at the Curie point of holmium. Below the Neel temperature, the magnetoelastic energy varies smoothly with decreasing temperature, attaining a value of ?2·13 J cm^?3 at liquid helium temperature. The temperature dependence of the magnetoelastic energy in the vicinity of the Curie point in holmium suggests that the magnetic transition from the antiferromagnetic arrangement into the ferromagnetic state is of second order.     

Ab initio investigation of the pressure influence on elastic properties of the GaS layered compound

From first principles, in the pressure range of 0–20 GPa, taking into account the structural phase transition at 3 GPa, all independent elastic constants of GaS compound have been calculated. From obtained data, the pressure dependences of the velocities of propagation of elastic waves in different symmetry directions have been determined. The values of averaged elastic moduli, Young’s modulus and Poisson’s ratio and their pressure dependence have also been calculated..     

EuS高压相变及其弹性和热力学性质

采用平面波赝势密度泛函理论,利用第一性原理的方法研究了EuS的晶体结构、高压相变以及弹性性质．计算结果和实验值以及前人利用不同计算模型得到的理论值相吻合．研究了EuS的弹性常数、弹性模量和弹性的各向异性等力学性质随压力变化的趋势．同时研究了泊松比、德拜温度及纵波和横波的弹性波速随压力的变化趋势．基于德拜模型,进而研究了EuS在0～800 K和0～60 GPa下相变前后的热膨胀系数、热熔、Grüneisen参数等热力学性质．     

Ultrasonic studies of aluminium-substituted Bi(Pb)-2223 superconductors

The compositional dependence of elastic properties of Al³⁺-substituted Bi(Pb)-2223 superconducting system with the general formula Bi_1.7−x Al_xPb_0.3Sr₂Ca₂Cu₃ O_y (x = 0.0, 0.1, 0.2 and 0.3) have been studied by means of ultrasonic pulse transmission (UPT) technique at 1 MHz (300 K). The elastic moduli of the specimens are computed and corrected to zero porosity. The observed variation of elastic constants with aluminium substitution has been explained on the basis of the strength of interatomic bonding. The applicability of heterogeneous metal mixture rule for estimating elastic constants and transition temperature has been tested.     

Pressure dependence of single crystal elastic constants and anharmonic properties of wurtzite

The single crystal, elastic constants of wurtzite (ZnS) have been measured by means of the ultrasonic pulse superposition technique at 25°C as a function of pressure, and at 1 bar as a function of temperature between 25 and 100°C. Within experimental accuracy the pressure dependence in the range up to 10 kbar was found to be linear for the longitudinal modes and quadratic for the shear modes. The elastic constants and their first pressure derivatives agree approximately with theoretical values for the hcp structure with first nearest neighbor central force interaction. The experimental data are used for the discussion of the Born stability limit in relation to the high pressure transformations of wurtzite into the sphalerite and rock salt structures, for the calculation of the Grüneisen parameter in the anisotropic elastic continuum approximation, and for the calculation of the isothermal equation of state at high pressure. The elastic properties of sphalerite (ZnS) are calculated from the data for wurtzite in the ‘equivalent sphalerite approximation’ of Sullivan and used for discussing the dependence on ionic radii of the pressure coefficients of the elastic constants in sphalerite-type II–VI compounds. The Born stability limit, the Grüneisen parameter and the isothermal equation of state of sphalerite are also calculated and compared with the corresponding quantities for wurtzite.     

Temperature dependent ultrasonic properties of aluminium nitride

Hexagonal wurtzite structured aluminium nitride has been characterized by the theoretical calculation of ultrasonic attenuation, ultrasonic velocity, higher order elastic constants, thermal relaxation time, acoustic coupling constants and other related parameters in temperature range 200-800 K for wave propagation along the unique axis of the crystal. Higher order elastic constants of AlN at different temperatures are calculated using Lennard-Jones potential for the determination of ultrasonic attenuation. A decrease in ultrasonic velocity with temperature has been predicted, which is caused by reduction in higher order elastic constants with temperature. The temperature dependent ultrasonic properties have been discussed in correlation with higher order elastic constants, thermal relaxation time, thermal conductivity, acoustic coupling constants and thermal energy density. Anomalous behaviour of the attenuation is found at 400 K. On the basis of attenuation, the ductility and performance of AlN have been studied.     

Constantes élastiques des phases cristallographiques ordonnées et désordonnées de PtCo

The elastic constants of the PtCo (1:1) alloy in the ordered and disordered states have been measured between 298 and 4.2 K by the superposition method. The Debye temperatures have been deduced. The influence of the magnetic domains on the absolute values of the elastic constants has been also studied. The room temperature values of the magnetoelastic constants of the disordered phase have been determined from the elastic constants and the magnetostriction coefficients.     

Pressure Dependences of Elastic Constants of AMg6 Aluminum–Magnesium Alloy and n-AMg6/С60 Nanocomposite Alloy

The ultrasonic study results for dependence of the elastic wave velocities and second-order elasticity coefficients of the polycrystalline aluminum alloy AMg6 and its nanocomposite n-AMg6/C₆₀ on hydrostatic pressure up to 1.6 GPa have been described. The ultrasonic research has been carried out using a highpressure ultrasonic piezometer based on the piston-cylinder device. The pressure derivatives of the secondorder elastic constants of these materials established in the present study have been compared with the results of the third-order elastic constants measurements of the test alloys using the Thurston–Brugger method. Involving available literature data, we determined the relationships between the pressure derivatives of the second-order elastic constants of the AMg6 alloy and the Mg-content and nanostructuring.

     

Anomalous elasticity and anelasticity of GdCu at low temperatures

The temperature dependence of the single crystal and polycrystalline elastic constants of GdCu compound have been determined between the ambient and 77 K, the interval in which the structural instability occurs. From the shear constants, C' and C₄₄ the magnitude of the elastic anisotropy was calculated, and found to be close to unity over the whole temperature range. This is in contrast with the expected behavior of the elastic anisotropy in the vicinity of martensitic transformations, where the anisotropy attains appreciable values. The large changes of the shear elastic constants, relative to the compressional constant suggests that the structural instability in GdCu is induced by a mechanism of isotropic shear. The peak in the ultrasonic attenuation is symmetric, typical of a relaxational process. The behavior of the elastic properties and ultrasonic attenuation in the temperature interval of the structural instability of GdCu is discussed.     

Elastic properties study of single crystal NH3 up to 26 GPa

Single crystal Brillouin and Raman scattering measurements on NH₃ in a diamond anvil cell have been performed under pressures up to 26 GPa at room temperature. The pressure dependencies of acoustic velocity, adiabatic elastic constants, and bulk moduli of ammonia from liquid to solid III and solid IV phase have been determined. All the nine elastic constants in orthorhombic structure phase IV were presented for the first time, each elastic constant grows monotonously with pressure and a crossover of the off‐diagonal moduli C₁₂ and C₁₃ was observed at around 12 GPa because of their different pressure derivative values. We also performed ab initio simulations to calculate the bulk elastic moduli for orthorhombic ammonia, the calculated bulk moduli agree well with experimental results. In Raman spectra the very weak bending modes ν₂ and ν₄ for orthorhombic ammonia are both observed at room temperature, a transition point near 12 GPa is also found from the pressure evolution of the Raman bands. Copyright © 2011 John Wiley & Sons, Ltd.     

Mechanical and dynamical stability of TiAsTe compound from ab initio calculations

The first-principles calculations are employed to provide a fundamental understanding of the structural features and relative thermodynamical, mechanical and phonon stability of TiAsTe compound. The calculated lattice parameters are in good agreement with available experimental results. We have computed elastic constants, its derived moduli and ratios that characterize mechanical properties for the first time. The calculated elastic constants indicate that these materials are mechanically stable at ambient condition. The minimum thermal conductivities of TiAsTe are calculated using both Clarke’s model and Cahill’s model. Furthermore, the elastic anisotropy has been visualized in detail by plotting the directional dependence of compressibility, Young’s modulus and shear modulus. Our results suggest strong elastic anisotropy for this compound. Additionally, the phonon spectra and phonon density of states are also obtained and discussed. The full phonon dispersion calculations confirm the dynamic stability of TiAsTe.     

The sublattice displacements and the elastic constants of A-15 compounds

The nature of the sublattice displacements in A-15 compounds has been discussed. Expressions have been derived for the elastic constants in terms of the force constants for these compounds. The numerical values of the force constants for Nb₃Sn have been evaluated.     

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.     

Structural and elastic properties of LaTiO3 under pressure

We investigate the structural and elastic properties of LaTiO₃ by the plane-wave pseudopotential density functional theory method. The lattice constants, bulk modulus and its pressure derivative are obtained. These properties in the equilibrium phase are well consistent with the available experimental data. The pressure dependence of the elastic constants, ductility, mechanical stabilities, sound velocity and Debye temperatures are investigated for the first time. From the ratio G/B, we conclude that LaTiO₃ is ductile at 0 GPa and becomes more ductile at high pressure. In addition, the anisotropy factors for every symmetry plane and axis as well as linear bulk modulus at diverse pressures have been obtained.     

First-principles study of elastic and electronic properties of layered ternary nitride SrZrN2 under pressure

The structural, elastic, and electronic properties of SrZrN₂ under pressure up to 100?GPa have been carried out with first-principles calculations based on density functional theory. The calculated lattice parameters at 0?GPa and 0?K by using the GGA-PW91-ultrasoft method are in good agreement with the available experimental data and other previous theoretical calculations. The pressure dependence of the elastic constants and the elastic-dependent properties of SrZrN₂, such as bulk modulus B, shear modulus G, Young's modulus E, Debye temperature Θ, shear and longitudinal wave velocity V_S and V_L, are also successfully obtained. It is found that all elastic constants increase monotonically with pressure. When the pressure increases up to 140?GPa, the obtained elastic constants do not satisfy the mechanical stability criteria and a phase transition might has occurred. Moreover, the anisotropy of the directional-dependent Young's modulus and the linear compressibility under different pressures are analysed for the first time. Finally, the pressure dependence of the total and partial densities of states and the bonding property of SrZrN₂ are also investigated.     

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.