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.     

Contribution of the multipole polarization to the elastic constants in fluorite structure crystals

Numerical calculations are presented for the contribution of the multipole polarization to the elastic constants in fluorite structure crystals. The multipole polarizability is calculated by the self-consistent field treatment of the local density approximation and the spherical solid model. The elastic constants are significantly affected by the multipole polarization of the ions. The contributions of the multipole polarization of the ions to the elastic constant C₁₁, C₁₂, and C₄₄ are about 25%, 40% and 20% of the experimental values, respectively. The calculated values of the deviation from the Cauchy relation are in good agreement with the experimental 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.     

The fractional ionic character of alkali and silver halide crystals

The fractional ionic character of alkali and silver halide crystals is defined in terms of the deviations from the additivity rule for polarizabilities of ions. The electronic polarizabilities of ions are calculated using an empirical relationship according to which the electronic polarizability of an ion can be assumed to be directly proportional to the cube of its radius. The calculated ionicities indicate that the alkali halides are nearly or more than 90% ionic and silver halides are much less ionic which is also evident from the Phillips ionicity scale.     

Elastic properties of compressed crystalline Ne in the model of deformable atoms

An ab initio version of the model with deformable atoms has been constructed to investigate the elastic properties of compressed crystalline neon. Approximations for the calculating parameters of quadrupole deformation of atomic electron shells have been discussed. It has been shown that the pressure dependence of the deviation from the Cauchy relation δ is the result of two competitive interactions, namely, the many-body and electron-phonon interactions, which manifests itself in the deformation of atomic electron shells during the shift of nuclei. In the case of Ne, contributions of these interactions are compensated to a large degree, which provides a weakly pressure-dependent positive value for δ. The agreement of calculated elastic moduli and deviations from the Cauchy relation for Ne with the experiment is good.     

On the pressure dependence of the effective ionic charge of cesium halides

The importance of temperature effects in the use of the second Szigeti relation to calculate the volume dependence of the effective ionic charge of cesium halide crystals is studied. The effect obtained is larger than the one for alkali halide crystals of the NaCl structure. Positive values of (? ln s/? In v) are obtained using low temperature experimental data with the Grüineisen parameter γ_t(T → 0K) calculated using the generalized first Szigeti relation. Values of γ_t are also obtained with a rigid ion model and they differ little from the previous ones.     

A simple model for the surface energy of ionic crystals

The surface energy of ionic materials is empirically related to bulk properties (elastic constants, electronic dielectric constant and optical band gap) through an analysis of the cleavage force. This is evaluated at small and large separations of the two crystal halves from phonon dispersion curves and from van der Waals interactions, respectively, and these two limiting behaviours are connected by a scaling hypothesis introduced for metals by Kohn and Yaniv. The experimental data that are available for a few ionic crystals seem to satisfy the suggested relation, with an empirical universal parameter which has roughly the same value as determined for metals.     

Quadrupole deformation of electron shells in the lattice dynamics of compressed rare-gas crystals

The lattice dynamics of rare-gas crystals has been constructed taking into account the deformation of electron shells of the atoms of the dipole and quadrupole types, depending on the displacement of the nuclei. The obtained equations of lattice vibrations have been investigated in the long-wavelength approximation. The role played by the three-body interaction and the deformation of the electron shells in the violation of the Cauchy relation has been discussed. The calculated Birch elastic moduli for Xe and deviations from the Cauchy relation are in good agreement with the available experimental data over a wide range of pressures.     

The static and elastic properties of mixed diatomic crystals

An interionic potential model has been proposed to study the static and elastic properties of mixed diatomic crystals. The interaction system of this potential consists of the long-range Coulomb and three-body interaction and the short-range overlap repulsion. This potential has been used to calculate the cohesive energy, phase-transition pressure and volume, third-order elastic constants and pressure derivatives of the effective second-order elastic constants for NaCl-NaBr mixed crystals. These results agree reasonably well with the available experimental results on the host crystals and allow us to draw some meaningful conclusions for the mixed alkali halide crystals.     

Elastic constants of solid solutions of single crystals of the alkali halides

On the basis of the Leibfried-Ludwig theory of anharmonic effects in crystals, a theoretical calculation is given of the elastic constants of solid solutions of alkali halide single crystals. The results of the calculations are compared with experimental data.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, Vol. 16, No. 7, pp. 57–61, July, 1973.     

Kinetic Constants Method for the Vibrational Analysis of Thallous Halide Dimers

The kinetic constants method is applied to the case of thallous halide dimers to evaluate the molecular constants such as, potential constants, compliance constants, mean amplitudes of vibration, coriolis coupling constants and centrifugal distortion constants, using the recent vibrational frequencies¹. The values of mean amplitude of vibration obtained by this method are in good agreement with the experimental values². The thermodynamic functions of thallous flouride for eleven temperatures ranging from 100K to 1000K are calculated on the basis of rigid-rotor, harmonic-oscillator approximation and are reported.     

Elastic properties of heavy rare-gas crystals under pressure in the model of deformable atoms

The quantum-mechanical model of deformable and polarizable atoms has been developed for the purpose of investigating the elastic properties of crystals of rare gases Kr and Xe over a wide range of pressures. The inclusion of the deformable electron shells in the analysis is particularly important for the shear moduli of heavy rare-gas crystals. It has been shown that the observed deviation from the Cauchy relation δ(p) for Kr and Xe cannot be adequately reproduced when considering only the many-body interaction. The individual dependence δ(p) for each of the rare-gas crystals is the result of two competitive interactions, namely, the many-body and electron-phonon interactions, which manifests itself in a quadrupole deformation of the electron shells of the atoms due to displacements of the nuclei. The contributions of these interactions in Kr and Xe are compensated with good accuracy, which provides a weakly pressure-dependent value for the parameter δ. The ab initio calculated dependences δ(p) for the entire series Ne-Xe are in good agreement with the experiment.     

Interionic potentials and force constant models for rocksalt structure crystals

It is suggested that the observed departure from the Cauchy relation in alkali halide structure crystals is due to ionic deformations. Interionic forces may then be taken to be central and a comparison between lattice dynamical models and interionic potential models becomes possible. In this paper attention is restricted to MgO, NaCl, LiF and KI for all of which (i) an isotropic (breathing) deformation can account for the difference C₄₄–C₁₂ and (ii) only the negative ion need be considered deformable. The interionic potential is assumed to consist of Coulombic and van der Waals terms, which are taken as known, and short range repulsive terms with an exponential dependence on separation. The constants in these repulsive terms are determined from the force constants of the lattice dynamical models. Satisfactory agreement with measured cohesive energies can be achieved only if the charge on the ions is very close to the electronic charge (2e in the case of MgO). This leads to a sacrifice in accuracy of the lattice dynamical models but this is shown to be small so that reasonable compatibility between the two sets of models is thus demonstrated. The interionic potentials are compared with those of other workers.     

Phonon dispersion in mixed alkali halide crystal Na0.5K0.5Cl

In the present paper we have calculated the phonon dispersion curves of the mixed alkali halide Na_0.5K_0.5Cl using the modified three body force shell model, in all the three symmetry directions (q, o, o), (q, q, o) and (q, q, q). The model consists of long range three body interactions and the short range overlap repulsion. The repulsive parameters are calculated from the expressions for elastic constants derived for NaCl structure. The results will stimulate the experimentalist.     

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.     

Photoelasticity in polycrystalline aggregates

A theory for the photoelastic behaviour of transparent polycrystalline aggregates consisting of randomly oriented anisotropic crystallites has been developed. Such an aggregate is isotropic but it becomes birefringent under the influence of a uniaxial load. The photoelastic constants of the aggregate are given by the components of the spatial average of the photoelastic tensor of the single crystal, and are worked out by assuming either the strain to be continuous (Voigt approximation) or the stress to be continuous (Reuss approximation). The components of the average photoelastic tensor are very different for these two limits. The elastic and the photoelastic constants of alkali halide aggregates have been evaluated for both the stress continuity and the strain continuity conditions. The maximum variation of the elastic constants in going from the Voigt to the Reuss condition is 50 per cent while the photoelastic birefringence can vary by as much as 300 per cent in alkali halides. In the case of KI and rubidium halides even the sign of the photoelastic birefringence is different for the two limits.     

Investigation of mechanical properties of alkaline-earth oxides. I. Cohesive energy function

An analysis of several calculations of the physical properties of ionic crystals and of the experimental data on the elastic moduli of alkaline-earth oxides is used to propose a semiempirical cohesive energy function, which includes not only the pair interactions of ions described by the Born-Mayer potential, but also three-body interactions. The parameters of the cohesive energy function are determined for these crystals by fitting to the experimental values of the binding energies, lattice constants, and second-order elastic moduli.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, 63–66, September, 1980.     

Noncentral forces in crystals of charged colloids

The elastic properties of fcc crystals consisting of charge stabilized colloidal particles are determined from real space imaging experiments using confocal microscopy. The normal modes and the force constants of the crystal are obtained from the fluctuations of the particles around their lattice sites using the equipartition theorem. We show that the Cauchy relation is not fulfilled and that only noncentral many-body forces can account for the elastic properties.     

Cs2XF6 (X=Si,Ge) compounds: Common and different features as uncovered by the first-principles calculations

Results of ab initio calculations of the electronic, optical and elastic constants for Cs₂GeF₆ and Cs₂SiF₆ are reported for the first time. Both compounds are the direct band gap dielectrics, with the calculated band gaps 6.926 eV (Cs₂SiF₆) and 6.417 eV (Cs₂GeF₆). Analysis of the calculated elastic constants and Cauchy condition shows both crystals as slightly covalent compounds. However, with increased pressure chemical bonds in Cs₂GeF₆ turn to be more ionic, whereas in Cs₂SiF₆ the covalent character of chemical bonds is enhanced. Pressure dependence of the chemical bond lengths and lattice constants was determined and represented as the second power functions of external pressure. Different trends in the values of the Mulliken charges for both compounds were found. The obtained results are applicable to the analysis of the luminescence properties of impurity ions at varying pressure or to the microscopic studies of crystal field effects in these crystals.     

2H-PbI2晶体的电子结构和力学性质

采用基于密度泛函平面波赝势方法(PWP)方法,计算了六角晶系2H-PbI2晶体的电子结构、力学性质和硬度。采用局域密度近似(LDA)方法计算的晶格常数、带隙、弹性常数与实验值和理论值符合较好。计算表明,2H-PbI2是一种直接带隙的半导体,带隙大约为2。38eV。运用复杂晶体硬度计算公式计算了六角晶系2H-PbI2晶体的硬度,硬度值大约为2. 54 GPa。还发现2H-PbI2晶体的各向异性非常明显。