Anharmonic properties of rocksalt structure solids

An effort has been made for obtaining the anharmonic properties of rocksalt structure solids starting from primary physical parameters viz. nearest-neighbor distance and hardness parameter assuming long- and short-range potentials at elevated temperatures. The elastic energy density for a deformed crystal can be expanded as power series of strains for obtaining coefficients of quadratic, cubic and quartic terms which are known as the second-, third- and fourth-order elastic constants, respectively. When the values of the higher-order elastic constants are known for a crystal, many of the anharmonic properties of the crystal can be treated within the limit of the continuum approximation in a quantitative manner. In this study, higher-order elastic constants are computed up to their melting temperature for rocksalt structure solids, which are alkali cyanides, sodium and potassium halides. The first order pressure derivatives of second- and third-order elastic constants, the second-order pressure derivatives of second-order elastic constants and partial contractions are also evaluated at different temperatures for these substances. The results thus obtained are compared with experimental data and found in well agreement with present values.     

Study of phase transformation and elastic properties of ThX (X = N,P, As and Sb) under high-pressure

An improved interaction potential model (IIPM) has been formulated to theoretically predict the pressure induced phase transition, elastic properties and thermophysical properties of thorium monopnictides (ThX; X = N, P, As and Sb). The phase transition pressures and volume drop obtained from this model show a better agreement with the available experimental than theoretical results. We have achieved elastic moduli, anisotropy factor, Poisson's ratio, Kleinman parameter, shear and stiffness constants on the basis of the calculated elastic constants. To know the anharmonic properties, we have also computed the third-order elastic constants, first-order pressure derivatives of second-order elastic constants and thermophysical quantities. Our results are in reasonable agreement with available measured and others reported data which supports the validity of model.     

Anharmonic properties of TmTe

Data on elastic constants and associated properties at high temperature for TmTe crystal are presented and discussed starting from primary physical parameters viz. nearest neighbour distance and hardness parameter assuming long- and short-range potentials. When the values of the higher order elastic constants are known for a crystal, many of the anharmonic properties of the crystal can be treated within the limit of the continuum approximation in a quantitative manner. In this study, higher order elastic constants and related properties are computed upto 1000 K for TmTe. The first-order pressure derivatives of second- and third-order elastic constants, the second-order pressure derivatives of second-order elastic constants and partial contractions are also evaluated at different temperatures. The results thus obtained are compared with other available data and found in well agreement with present values.     

The elastic constants and their temperature and pressure derivatives of AgBr-AgCl mixed crystals

The three independent second-order elastic constants and their temperature and pressure derivatives have been measured for four AgBr-AgCl mixed crystals, with 19.5, 39.1, 56.6 and 78.7 mole % AgCl, using the ultrasonic pulse-echo technique at room temperature. The explicit temperature dependence of the elastic constants is calculated and is found to be much larger than that of other NaCl structure crystals. The violation of the Cauchy relation C₁₂ = C₄₄ is found to be significant and increases between AgBr and AgCl. The high temperature limit of the Gruneisen parameter is calculated from the elastic data. A comparison is made between the elastic properties of the silver halides and the alkali halides.     

Third order elastic constants of NaCl

A brief review is given of the meaning of the third order elastic constants and of the general significance of the anharmonic parameters for mechanical and thermodynamic properties. The measurements of the third order elastic constants of NaCl and KCl by Chang and of NaCl by Swartz are described. In each case the changes in ultrasonic velocities were observed as a function of applied uniaxial stress. More recently a program in beam mixing has been initiated by Dunham to study the third order constants of NaCl through the conversion efficiency of the T+T →L interaction.     

Lattice dynamics,third order elastic constants and low temperature lattice thermal expansion of zirconium

The lattice dynamics and the anharmonic properties of the hexagonal Zirconium are worked out using Keating's approach. The dispersion curves are fitted using twelve second order parameters and the six second order elastic constants are evaluated. The ten third order elastic constants are calculated using five third order parameters. The experimental measurements on the pressure derivatives of the second order elastic constants in Zirconium are in good agreement with the calculated values. The low-temperature limit of the lattice thermal expansion is calculated which agrees well with the value obtained from thermal expansion data. The variation of the generalised GPs of the elastic modes with the direction of propagation is illustrated by polar diagram.     

Lattice dynamics of quantum crystals

A theory of lattice dynamics for quantum crystals is developed. This is done by summing an infinite class of diagrams of the usual anharmonic expansion and by avoiding the harmonic approximation as starting point. The zero order of the expansion given in this paper corresponds to the harmonic approximation with an effective potential. Higher orders correspond to higher anharmonic corrections with the same potential. Since the new potential varies more slowly the expansion seems to converge more rapidly than the usual anharmonic expansion. Numerical calculations on bcc He³ show that the ground state energy is lowered by about 3–4 cal/mol by taking into account long range correlations due to phonons. The elastic constants and the Debye temperature are calculated in zero and second order. The lowering of the bulk modulus due to the second order is about 10%. Experiments agree quite well with the second order results.     

Anisotropic breathing shell model and phonons in NaCl structures

Callow, Diller and Norgett, in their investigations on the dynamics of alkali halides, have developed analytic potentials for the short range interactions between the anions and cations. These potentials consisting of Buckingham and van der Waals contributions have been determined from the elastic, dielectric constants and the equilibrium conditions of the lattice and are found to satisfactorily explain the defect properties of many halides. We employ the analytic potentials of Catlow et al. and use anisotropic breathing corrections for the computation on phonon dispersions and Debye-Waller factors of all NaCl structure alkali halides. The results of our study show that good agreement can be obtained with these more physical parameters.     

LBO晶体的光散射研究

ＬＢＯ晶体的光散射研究王越，蒋毅坚，刘玉龙（北京工业大学应用物理系北京１０００２２）（中科院物理研究所北京１０００８０）ＳｔｕｄｙｏｎｏｎＬＢＯＣｒｙｓｔａｌｂｙＬｉｇｈｔＳｃａｔｔｅｒｉｎｇ￥Ｙ．Ｗａｎｇ￣１；Ｙ．Ｊ．Ｊｉａｎｇ￣１ａｎｄＹ，Ｌ．Ｌ...     

Thermal equation of state, and melting and thermoelastic properties of bcc tantalum from molecular dynamics

We performed molecular dynamics simulations with the extended Finnis-Sinclair (EFS) potential to investigate thermal equation of state (EOS), and melting and thermoelastic properties of tantalum. The agreement of the obtained thermal EOS with experiments at ambient conditions is reasonably good. The EFS potential with the two-phase method also reproduced very satisfyingly the high-pressure melting curve, excellently consistent with both the experiments of melting temperature at ambient pressure and shock melting at high pressure. From molecular dynamics simulations, we also obtained the thermoelastic properties of Ta for temperatures up to 3000 K at ambient pressure. Fully including anharmonic effects in molecular dynamics, our calculated elastic constants are in excellent agreement with experimental data. Shear modulus G decreases quickly with increasing temperature.     

Higher order elastic constants of alkali halides

The Coulomb, van der Waals and repulsive lattice sums occurring in the higher order elastic constants up to sixth order have been calculated for the rocksalt and cesium chloride structures. Numerical values of the static elastic constants up to sixth order based on a rigid ion model with van der Waals and Born-Mayer type central force interaction between first and second nearest neighbors are calculated for several alkali halides representing both structure types. Fair agreement with the available experimental third and fourth order elastic constant data is found.     

Effect of many body forces on the photoelastic constants of the alkali halides

A simple phenomenological lattice theory based on the Lundqvist potential of ionic cohesion (many body theory of elastic dielectric), to explain photoelastic behaviour of the solids with rock-salt structure, is presented and shown to apply within reasonable errors to the known experimental constants. The predicted values of the photoelastic constants of the alkali halides are very close to the experimental values and are better than obtained by all earlier workers.     

Theory of surface force-constant changes in body-centered cubic lattices

A calculation has been made of force-constant changes at the (100) and (110) surfaces of body-centered cubic crystals. A model consisting of first, second and third-neighbor Lennard-Jones interactions together with harmonic angle-bending interactions is employed. The parameters characterizing the interactions are chosen to fit the equilibrium lattice spacing, the elastic constants, and certain phonon frequencies at high symmetry points in the Brillouin zone. The procedure consists of first calculating the static displacements produced by the creation of the surface and then calculating the change in force constants produced by the cubic and quartic anharmonic terms in the potential energy. Specific results have been obtained for chromium, iron, tungsten, and molybdenum.     

On the third order elastic constants of AgCl-AgBr mixed system

Lowdin's many body effect is accounted to explain the violation of Cauchy's relation (C₁₂=C₄₄) in silver halides. Lundqvists potential model with many body effect has been used to evaluate the third order elastic constants of AgCl and AgBr. A modified Lundqvist potential model is used to calculate the third order elastic constants for the simple AgCl- AgBr mixed system with varying concentration of AgCl and AgBr.     

Calculation of rotationally vibrational energy of HDO molecule

The anharmonic constants and the constants of rotation-vibration interaction have been calculated for an asymmetrical non-linear three atomic molecule on the assumption that Pliva's potential function for polyatomic molecules is valid.     

Elastic properties of oxides in the NaCl-structure

The single crystal elastic constants and their first pressure derivatives have been measured by means of the ultrasonic pulse superposition technique for the NaCl-structure oxides CaO, SrO and BaO. Within the experimental precision the pressure dependence was found to be linear in the range up to 10 kbar, except for a few shear modes measured for SrO and BaO. This nonlinearity, however, was not sufficient to unambiguously determine second pressure derivatives of the elastic constants. The present values are in fundamental agreement with the results of other investigators who used both ultrasonic and static compression methods. However, the additional precision and accuracy afforded by the present technique allows a clear demonstration of the systematic behavior of the elastic properties of MgO, CaO, SrO and BaO with respect to interionic distance. As in the case of the alkali halides, it appears that the size of the cation provides the dominant effect on the elastic constants. Moreover, calculations based on a lattice theoretical model consisting of Coulomb and Born-Mayer type repulsive forces between first and second nearest neighbor ions also support the contention that cation size has the major effect on the systematic behavior of the first pressure derivatives of the bulk moduli of these oxides.     

Dispersion relations and lattice thermal expansion of dysprosium

The lattice dynamics, second and third order elastic constants and the lattice thermal expansion of dysprosium have been calculated using Keating's approach. The ten third order elastic constants are calculated using four anharmonic parameters. The present model reproduces the measured pressure derivatives of the second order elastic constants of dysprosium well. The low and high temperature limits γ?_I and γ?_H of the lattice thermal expansion are evaluated and the agreement between the calculated γ?_H and that obtained from the thermal expansion and specific heat data is satisfactory.     

On the Hulburt-Hirschfelder potential function for the Ar2 molecule

The modified Morse potential function known as the Hulburt-Hirschfelder function has been used for the Ar₂ molecule using experimental values for the spectroscopic constants. The consistency of this potential is checked by recalculating the vibrational levels using Cashion's method. The results are satisfactory. The potential may be useful for calculating the anharmonic properties of crystalline argon.     

Temperature derivatives at constant volume of the elastic constants of alkali halide crystals

A new method has been developed for calculating the temperature derivatives at constant volume of the elastic constants of the alkali halides using the concept of phonon pressure. Calculated values of temperature derivatives of elastic constants are compared with the corresponding values recently derived from ultrasonic experimental data.