The elastic constants for single-crystal lead and indium from room temperature to the melting point

The adiabatic elastic stiffness constants of indium and lead were measured from room temperature to their respective melting points using the ultrasonic pulse-echo method. The average temperature derivatives at constant pressure, $\text{dC}{}_{\mathrm{ij}}\text{dT}\text{= C'}{}_{\mathrm{ij}}$, for the indium constants are:

$\text{C'}{}_{11}\text{= ?0.032 C'}{}_{12}\text{= ?0.0055 C'}{}_{13}\text{= ?0.011 C'}{}_{33}\text{= ?0.032 C'}{}_{44}\text{= ?0.0059 C'}{}_{66}\text{= ?0.022}$

in units of 10¹⁰dyne cm^?2deg^?1, and are referred to axes coincident with those of the face-centered tetragonal unit cell. The average temperature derivatives at constant pressure for the lead elastic constants are, in the same units,

$\text{C'}{}_{11}\text{= ?0.0264 C'}{}_{12}\text{= ?0.0156 C'}{}_{44}\text{= ?0.0155.}$

The elastic anisotropies of both lead and indium increase markedly with increasing temperature.     

Elastic constants of nionium up to the melting point

The elastic constants of a pure niobium single crystal have been measured between 1300 and 2600 K by means of an ultrasonic method and a suitable geometry. We find that the shear constant C₄₄ behaves anomalously up to the melting point and that $\text{1}\text{2}$(C₁₁–C₁₂) decreases monotonically. The anomalous behaviour of C₄₄ associated with the trigonal distortion is explained as an electronic contribution with a (local) degeneracy temperature which is considerably higher than the melting point.     

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.     

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.     

On the size dependence of surface tension in the temperature range from melting point to critical point

The problem of size dependence of surface tension was investigated in view of a more general problem of the applicability of Gibbs’ thermodynamics to nanosized objects. For the first time, the effective surface tension (coinciding with the specific excess free energy for an equimolecular dividing surface) was calculated within a wide temperature range, from the melting temperature to the critical point, using the thermodynamic perturbation theory. Calculations were carried out for Lennard-Jones and metallic nanosized droplets. It was found that the effective surface tension decreases both, with temperature and particle size.     

The kink point method and bismuth based high temperature superconductors

In this report we present the results of dc magnetization measurements on powder Bi₄Ca₃Sr₃Cu₄O_16+x samples. It is found that the temperature dependence of H_c1 can be measured using the “kink” point method. The temperature dependence of H_c1 and the initial susceptibility are close to that of a conventional superconductor.     

The effect of temperature on elastic constants and bulk modulus

A model pseudopotential depending on an effective core radius is proposed to study the elastic constants C ₁₁, C ₁₂, C ₄₄ and bulk modulus B of Cu, Ag, Au, Ni, Pt and Rh at various temperatures (300–1500 K). The contribution of d-like electron is taken into account by introducing repulsive short-range Born-Mayer term. An excellent agreement between theoretical investigation and experimental findings has confirmed our formalism.     

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.     

Elastic constants of bismuth polycrystal containing tin,lead, antimony and tellurium impurities

Investigations of ultrasonic velocity and internal friction are carried out in bismuth polycrystals containing Sn, Pb, Sb and Te impurities in the concentration range of 0–1 atomic percent using the composite oscillator technique, and elastic constants are estimated from velocity and density data. The variations of elastic constants are interpreted in terms of changes of lattice parameter, valency of the impurity, the electron-atom ratio, atomic size and Fermi energy. It is observed that the elastic constants are less affected in Bi-Te alloys compared with Bi-Sb, Bi-Pb and Bi-Sn alloys in the above concentration range.     

The elastic constants of sodium from 20 to 95°C

We report ultrasonic pulse echo measurements of the elastic constants of sodium in the high temperature region. At room temperature the results agree with those of earlier work. No pronounced effects of anharmonicity are found contrary to theoretical predictions. The behaviour of the elastic constants is further analysed in terms of compressibilities, of Grüneisen parameters and of effects caused by lattice defects. The quantity[?lnω_i(q)/?T]_v is calculated from the temperature and pressure variation of the elastic constants.     

The second-order elastic constants of AgBr from 77 to 300 K

The three independent second-order elastic constants of AgBr have been measured from room temperature down to liquid nitrogen temperature A single crystal with a (110) axis was used for the measurements The measured longitudinal elastic constant C'₁₁ = (C₁₁ + C₁₂ + 2C₄₄)/2 increases by 16% over this temperature range The elastic shear constant C₄₄) increases by almost 11%, while the elastic shear constant C' = (C₁₁ ? C₁₂)/2 increases by 50% over this range The measured bulk modulus B = (C₁₁) + 2C₁₂)/3 increases by almost 15% as the lattice becomes stiffer The initial temperature derivatives of the elastic constants are similar to those previously measured The changes in the elastic constants are basically linear down to approximately 150 K, where the temperature derivatives begin to decrease in magnitude These results are similar to those previously obtained for AgCl     

Surface resistance of single-crystal copper in the millimeter-wave region at room temperature

Measurements of the surface resistance of plane surfaces of single-crystal copper were carried out at 35 GHz. The results indicate an anomaly of the skin effect at room temperature. The investigated surfaces were prepared in stress-free processes, annealed, and manipulated in purified hydrogen and argon.     

The influence of a minor sodium addition on the contact melting of cadmium with bismuth,indium, and tin

The contact melting (CM) of Cd + 0.046 at % Na solid solution with indium, bismuth, and tin is studied. The dependence of the contact layer lengths on the duration of Cd + 0.046 at % Na CM with indium with electric current through is obtained. Addition of sodium is found to drastically affect the temperature of contact melting onset in (Cd + 0.046 at % Na)-Me (Me: In, Sn, Bi) systems. An attempt to interpret the results obtained is made.