The temperature dependence of the elastic constants of MnO

We have measured the temperature dependence of the elastic constants of a monodomain single crystal of MnO, obtained by applying a unixial stress, from 4.2 to 300 K. Measurements were made by standard ultrasonic techniques and the acoustic waves were generated and detected by CdS transducers. Problems associated with the coupling between transducer and sample encountered by previous workers were therefore overcome. For propagation down the [111] direction, only the slow shear mode [$\text{1}\text{2}$(c₁₁?c₁₂)] was observable below the Néel temperature (T_N. The fast shear and longitudinal modes were heavily attenuated. Complex behaviour in the region of T_N and a further anomaly at 42 K were observed.     

Anomalous temperature dependence of elastic constants in NbMo alloys

An unusual positive temperature coefficient ofc₄₄ was observed in the Nb-rich Mo alloys, which appears to be connected with previously reported anomalies in neutron-diffraction and specific-heat data.     

The temperature dependence of the elastic constants for highly oriented pyrolytic graphite determined by ultrasonic techniques

Sound velocities along the c-axis of highly oriented pyrolytic graphite between 4 and 325 K were measured with an ultrasonic pulse-echo phase-comparison method. The echo delay times were determined with an accuracy of 0.05 and 0.15%, respectively, for the longitudinal and transverse modes. The temperature dependence of the c-axis elastic constants C₃₃ and C₄₄ was deduced with the correction of thermal expansion. C₃₃ was found to decrease by 5.8% from 4 to 300 K and can be interpreted by a model based on the simple Lennard-Jones interlayer interaction. C₄₄ and its temperature variation are found to be strongly sample dependent.     

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.     

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 elastic constants for ionic solids

In this paper the thermal variation of volume for NaCl, KCl, MgO and CaO has been investigated on the basis of Anderson model. We have evaluated the values of elastic constants C₁₁, C₄₄ and K_T at different temperature on the basis of Murnaghan and Tallon models. Tallon's model with second approximation presents slightly better agreement with experimental results which shows that the Anderson–Grüneisen parameter is directly proportional to the volume ratio. Tallon's model can be used to evaluate the values of elastic constants for solids at different temperatures.     

Temperature dependence of the second-order elastic constants of cubic crystals

A simplified phenomenological theory of the temperature dependence of the second-order elastic constants of crystals is considered. The temperature dependences of the second-order elastic constants are calculated for a series of cubic crystals with various types of predominant chemical bonding. Satisfactory agreement between the calculation results and experimental data is obtained. Fiz. Tverd. Tela (St. Petersburg) 41, 235–240 (February 1999)     

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.     

Higher order elastic constants and generalized Gruneisen parameters of elastic waves and low temperature thermal expansion of gadolinium

Expressions for the higher order elastic constants are derived using the sublattice displacements to the second degree in strains. These expressions are used to obtain the higher order elastic constants and their pressure derivatives in gadolinium. The higher order elastic constants are used to find out the generalized Gruneisen parameters of the elastic waves propagating in different directions in gadolinium. The Brugger gammas are evaluated and the low temperature limit of the Gruneisen gamma is obtained. The results are compared with the available reported values.     

Temperature dependence of the elastic constants of single-crystal KI-KBr solid solutions

Elastic constants C₁₁, C₁₂, and C₄₄ were measured for solid KI-KBr solutions over the temperature range 20–280 °C. When plotted as functions of the composition, elastic constants C₁₁ and C₄₄ display a significant deviation toward a negative nonadditivity. The Debye temperature calculated from the elastic constants at 0 °K is 8 ° lower than the additive value at compositions containing 66 M% KI.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 58–62, April, 1971.In conclusion the authors thank A. A. Botaki for the opportunity to measure the elastic constants.     

Temperature dependence of the elastic constants of a KCl-NaCl solid solution

Measurements are made of the temperature variations of the elastic constants, the factor of elastic anisotropy, the degree of deviation from the Cauchy relation and the coefficients of thermal linear expansion of a KCl-NaCl solid solution of different concentrations in the 300–640°K temperature range. An analysis is given for the dependences obtained.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 122–125, October, 1973.In conclusion the authors thank V. N. Suslovaya for carrying out the x-ray monitoring of the concentrations of the solid solutions being investigated.     

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.     

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.     

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.     

Pressure dependence of elastic constants of trigonal Se and Te

The pressure dependence of the symmetric elastic constants of Se and Te are analyzed. The weaker interchain forces are shown to increase rapidly with decreasing interchain distances, whereas covalent intrachain forces decrease. The results are consistent with a picture of the bonding having a partially metallic contribution which increases as the crystals approach the actual phase transition to metallic structures, stable at higher pressures.