Contributions from the indirect ionic interactions to the elastic constants in the rock-salt structure crystals

Under the harmonic approximation, the contributions from the indirect ionic interactions to the elastic constants are calculated for the alkali halide and silver halide crystals with the rock-salt structure. The coupling constants of the indirect ionic interactions are calculated by the self-consistent field treatment of the local density approximation and the spherical solid model. The calculated values of the coupling constants are large for the silver ion. The indirect ionic interaction significantly affects the elastic constants. It quantitatively explains the deviation from the Cauchy relation in alkali halide crystals. Moreover, it provides a clear account for the large values of the deviation from the Cauchy relation in AgCl and AgBr.     

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.     

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.     

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.     

The second-order elastic constants of an AgBr-(56.6%) AgCl mixed crystal from 20°C to 400°C

Abstract

Initial measurements of the second-order elastic constants of an AgBr-(56.6%) AgCl mixed crystal have been made from 20—400°C. Over this temperature range, C'₁₁ decreased by 44%, C' by 71%, C₄₄ by 22%, C₁₁ by 53%, C₁₂ by 40%, and B _s by 46%. The decreases in the elastic constants are linear until approximately 280°C, whereupon all but C' begin to decrease more rapidly than linearly with variations from linearity of 4—20% at 400°C and C' remains linear at all temperatures. This anomalous behavior is similar to other silver halide physical properties and may be attributed to the unusually high defect concentration at high temperatures. Similar elastic constant changes are seen in superionic conductors near the superionic transition, indicating that the silver halides may be starting the transition to a superionic state when the halide sublattice melts and the transition is frustrated.     

Anomales elastisches Verhalten von Eis bei tiefen Temperaturen

The temperature dependence of the longitudinal elastic constants of ice single crystals has been measured by an ultrasonic pulse-echo method. With heating, resp. cooling rates less than a critical value, deviations to lower values of the elastic constants have been observed. The time dependence of the anomaly has been studied at fixed temperatures. Limiting values of the elastic constants have been reached after sufficiently long time; the maximum of these values was observed at about 105°K. The findings are interpreted as representing a phase transition within the protonic structure.     

Elastic properties of layered crystals

The characteristic features of the elastic properties of layered crystals and their dependence on temperature and pressure are analyzed. The relations between the elastic constants of hexagonal layered crystals are given. It is shown that the anomalous behavior of the elastic constants in the temperature region of a phase transition affects both the magnitude and sign of the thermal expansion coefficients of layered crystals. From analyzing the pressure and temperature dependences of the elastic constants, it is found that the anharmonicity of the bonding forces between the layers is much greater than the anharmonicity of the intralayer forces. The contribution from thermal expansion to the variations of the elastic constants with temperature is estimated.     

Elastic constants of iron-silicon alloy single crystals

The adiabatic elastic constants of single crystals of Fe-Si alloys in the composition range from 6.3 at.% Si to 25 at.% Si have been determined by the ultrasonic pulse echo method at room temperature. The values of the elastic constants depend significantly on the silicon content, and their composition dependences are influenced by ordering.     

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.     

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.     

One- and two-dimensional deformations in nematic liquid crystals: Influence of the flexoelectric polarization

Summary The elastic deformations in nematic liquid crystals are analysed in one and two dimensions. The influence of the flexoelectric polarization on the elastic properties of the medium is studied. It is shown that for one-dimensional deformations, the presence of the flexoelectric polarization introduces a renormalization of the elastic constants. On the contrary in the bidimensional case, the effect of the flexoelectricity is not a simple renormalization of the elastic constants. The profiles of the electric potential and of the tilt angle are evaluated for the cases in which the substrate is an insulating or conducting material. The validity of the calculations is discussed by considering the value of Debye's screening length of the nematic liquid crystal.     

Higher order elastic constants and non-linear stress-strain relation for V3Si

Relations for the third and fourth order elastic constants are derived from a Landau-Devonshire type free energy function for crystals with the A15 structure which undergo the structural transformation at low temperature. Application to transforming V₃Si at 21° K gives in connection with experimental data for the pressure derivatives of the elastic constants unusually large numerical values for c₁₁₁, c₁₁₂, c₁₂₃ and c₁₁₁₁. The stress-' strain relation calculated from these data is in semiquantitative agreement with the directly measured, strongly non-linear behavior.     

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.     

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.     

Flexoelectric effect modelling

A statistical theory of dipole flexoelectric (FE) polarization in liquid crystals is used to calculate temperature dependence of order parameters, elastic constants and FE coefficients. Two systems with polar wedge-shaped and banana-shaped molecules are investigated. In both cases, the FE coefficients are proportional to the dipole moment component parallel to the molecule symmetry axis. It results from the symmetries of interactions and of the Mayer function. The origin of the FE effect and microscopic pictures of the distorted phases are discussed.     

Many body forces and elastic constants of rare gas crystals

The effect of many body Van der Waals forces on the elastic constants of solid rare gases is calculated. These results are combined with contributions from the two body potential and zero point energy. The violation of the Cauchy relation is studied.     

First-principles calculations on temperature-dependent elastic constants of rare-earth intermetallic compounds: YAg and YCu

We present the temperature-dependent elastic constants of two ductile rare-earth intermetallic compounds YAg and YCu with CsCl-type B2 structure by using a first-principles approach. The elastic moduli as a function of temperature are predicted from the combination of static volume-dependent elastic constants obtained by the first-principles total-energy method with density-functional theory and the thermal expansion obtained by the first-principles phonon calculations with density-functional perturbation theory. The comparison between our calculated results and the available experimental data for Ag and Cu provides good agreements. In the calculated temperature 0-1000 K, the elastic constants of YAg and YCu follow a normal behavior with temperature that those decrease with increasing temperature, and satisfy the stability conditions for B2 structures. The Cauchy pressure for YAg and YCu as a function of temperature is also discussed, and our results mean that YAg and YCu become more ductile while increasing temperature.     

Debye temperature of alkali halide crystals

The Debye temperature _D is calculated from the elastic constants for 18 alkali halide crystals. Comparison of the results with calorimetric data _D reveals an agreement within the experimental error. The temperature dependence of _D is determined for NaCl, NaBr, KCl, and KBr crystals from the elastic constants, and this dependence is compared with the calorimetric data.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 3, pp. 89–94, March, 1971.     

Flexoelectric polarization and second order elasticity for nematic liquid crystals

The flexoelectric properties of nematic liquid crystals are analysed. It is shown that in the frame of the usual elasticity two coefficients characterize completely the flexoelectric properties of the liquid crystal. These coefficients, in the limit of small scalar order parameter, i.e. near the clearing point, are approximately equal. More precisely they have the same linear term in the scalar order parameter, and differ for terms quadratic in this parameter. Their difference behaves, hence, as the usual nematic liquid crystal elastic constants, whereas their sum depends on the temperature, like the mixed splay-bend elastic constant. It is shown furthermore that in the frame of a second order elastic theory in the flexoelectric polarization there are no terms from the second order spatial derivatives of the nematic director, or the nematic tensor order parameter. Consequently also in the frame of the second order elasticity the flexoelectric polarization is given by the usual expression. This conclusion is important in connection with the surface polarization recently discovered in pretilted nematic liquid crystal samples.