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.     

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.     

Temperature dependence of third order elastic constants of ammonium halides

The third order elastic constants of ammonium halides have been evaluated for the first time using Lundqvist three body potential incorporating the effect of thermal contributions. Theoretical investigations have been carried out above λ-temperature where both NH₄Cl and NH₄Br have cubic CsCl structure. Analysis has been extended to mixed NH₄Cl_1−x Br _x . The repulsive potential which is assumed significant up to first neighbours is taken of the Born-Mayer type. Results have been compared with the recently measured values wherever available.     

Temperature and volume dependence of the elastic constants of palladium

A separation between lattice and electronic contributions to the elastic constants of Pd is obtained. The temperature dependence at constant volume is measured by applying hydrostatic pressure. The apparatus and results for Pd are presented.     

Evaluation of the second order strain derivatives of the electronic dielectric constant of alkali halides

We have evaluated the second order strain derivatives of the electronic dielectric constant of alkali halides employing two different theories viz. the Clausius—Mossotti theory of polarizability and the Penn model of energy gap. The results obtained from the two theories are in fair agreement with each other. It has been emphasised that the present calculations can be used to separate the electronic and ionic contributions to the second order strain derivative of the static dielectric constant.     

Analysis of first and second order strain derivatives of the dielectric constants of alkali halides

Expressions for evaluating the first and second order strain derivatives of the electronic and static dielectric constants of alkali halides are derived. The strain derivatives of the electronic dielectric constant are calculated by taking account of the effect of the crystalline potential on the variation of electronic polarizabilities with volume. The strain derivatives of the static dielectric constant are evaluated adopting the exponential and the inverse power forms for the short range repulsive potential. Two sets of the Born repulsive parameters derived from ultrasonic data and dielectric data are used to evaluate the lattice contribution to the volume dependence of static dielectric constant of alkali halides.     

Temperature and pressure derivatives of the elastic constants of cubic rubidium cyanide

The temperature and pressure derivatives of all elastic constants of rubidium cyanide have been measured from 133 to 380 K respectively from 0 to 1500 × 10⁵ Nm^-2 by ultrasonic methods. The thermoelastic behaviour resembles that of KCN and NaCN. A strong softening of the shear resistance c₄₄ approaching the transition temperature from higher temperatures is observed. The pressure derivatives are also quite similar to those of KCN and NaCN, but fully different from those of normal alkali halides of rocksalt-type. This behaviour confirms a rule already observed in other isotypic crystal groups: the quasi-invariant pressure derivatives are shifted in a characteristic way for a certain structure type, if rare-gas-like ions are replaced by asymmetric ions. The nonlinear elastic behaviour is qualitatively interpreted by interactions of volume-conserving type as existing in fluids.     

Melting and elastic shear instability of alkali halides

Ultrasonic data for the elastic moduli c_ij as functions of pressure and temperature are used to calculate critical temperatures T_cr(P = 0) and their initial pressure derivatives (?T_cr/?P)_P=0 for the elastic stability of the alkali halides with the rocksalt and CsCl structures. The stability criteria used for the two structures are c′ = ½(c₁₁ ? c₁₂) = 0 and c₄₄ = 0, respectively. The critical parameters T_cr(P = 0) and (?T_cr/?P)_P=0 exhibit remarkable correlations with the melting temperatures T_m(P = 0) and their initial pressure derivatives (?T_m/?P)_P=0, offering strong support to the existence of a connexion between shear instability and melting, as postulated by previous investigators. Critical parameters for the rocksalt oxides MgO, CaO, and SrO compare favourably with the critical and melting parameters for their fluoride analogues LiF, NaF and KF respectively.     

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.     

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.     

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.     

Condensed state physics elastic constants of alkali metal alloys

The second-and third-order Brøgger elastic constants of the disordered Cs-K, Cs-Rb, and Rb-K alloys with different concentrations of the second component are calculated for the pseudopotential model with the use of the Krasko-Gurskii model potential. Results of calculations are in good qualitative agreement with the available experimental data on the elastic constants of alloys.     

Temperature dependence of the elastic constants of aluminium

Published results for the temperature variation of the elastic constants of single crystal aluminium are discussed with special reference to the possibility that error propagation in the conversion of compliances to stiffness may contribute to the discrepancies between the different sets of data for the stiffnesses.     

Temperature dependence of the elastic constants of aluminum

The single crystal elastic constants of aluminum have been measured using a piezoelectric composite oscillator from room temperature to just 20 K below the melting point. The elastic moduli differ markedly from previous high temperature results, but match in well with previous cryogenic results. Over the temperature range investigated the isothermal bulk modulus and the two shear moduli have a simple exponential dependence on isobaric volume, and the cryogenic data indicate this dependence may be preserved down to absolute zero. As has been found previously for a wide range of materials, the isothermal bulk modulus and the shear modulus $\text{(c}{}_{11}\text{– c}{}_{12}\text{)}\text{2}$ appear to be continuous functions of volume through the melting expansion, and melting seems to find its origin in the mechanical instability associated with this shear modulus vanishing at the volume of the melt at the freezing point. Grüneisen's parameter divided by the molar volume is very nearly independent of isobaric volume.     

Temperature dependence of Szigeti effective charge of alkali halides

The second Szigeti relation was used to obtain the temperature dependence of the Szigeti effective charge, e_s. The results are discussed in the framework of the deformation dipole model. Recent experimental data are used to show that the volume derivatives of e_s of most ionic solids are positive, thus providing evidence that the deformation dipole model is qualitatively valid.