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.     

Interlattice displacements and elastic constants of the A-15 compounds V3Si,V3Ge and Nb3Sn

General expressions for the interlattice displacements of the A-15 structure compounds are obtained in terms of the strain components making use of the deformation theory. The nature of the interlattice displacements of all the 8 atoms in the unit cell is discussed. It is found that the interlattice displacements occur in such a way that the pair of atoms along any linear chain move in opposite directions with equal magnitudes. Expression for the strain energy of these compounds is developed using deformation theory and this is compared with the strain energy expression from continuum theory to obtain the elastic constants. The theoretical values of the elastic constants fairly agree with the experimental values for V₃ Si, V₃Ge and Nb₃ Sn.     

Anomalous Grüneisen constants in V3Si

The change of the soft mode sound velocity under external tetragonal shear strain is calculated from the one-dimensional model of A 15-compounds. We find that thed-electrons give rise to Grüneisen constants which are large compared to unity and which show a characteristic temperature dependence. Modifications of the Grüneisen constants of non-transforming samples in the superconducting state are also discussed.     

Third order elastic constants of NaCl

A brief review is given of the meaning of the third order elastic constants and of the general significance of the anharmonic parameters for mechanical and thermodynamic properties. The measurements of the third order elastic constants of NaCl and KCl by Chang and of NaCl by Swartz are described. In each case the changes in ultrasonic velocities were observed as a function of applied uniaxial stress. More recently a program in beam mixing has been initiated by Dunham to study the third order constants of NaCl through the conversion efficiency of the T+T →L interaction.     

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.     

Third order elastic constants of rubidium chloride

The third order elastic constants of RbCl, determined by measurements of the static stress dependence of ultrasonic waves, are found to be (in units of 10¹²$\text{dynes}\text{cm}{}^2$)

$\text{C}{}_{111}\text{= ?6.71 ± 0.1 C}{}_{123}\text{= 0.05 ± 0.07}$

$\text{C}{}_{112}\text{=?0.18 ± 0.04 C}{}_{144}\text{= 0.11 ± 0.02}$

$\text{C}{}_{166}\text{=?0.17 ± 0.01 C}{}_{456}\text{= 0.4 ± 0.01}$

. The calculation of third order constants using a rigid ion Born model is briefly discussed, and results are compared to the measurements. The comparison qualitatively supports the model, but no quantitative evaluation of the repulsive interaction is possible.     

Third order elastic constants and thermal expansion of terbium

The third-order elastic constants and the temperature variation of the effective Grüneisen functions of terbium have been calculated on the basis of Keating's method. The pressure derivatives of the second order elastic constants of terbium have been obtained by interpolation of the experimental pressure derivatives of gadolinium and dysprosium. The ten third order elastic constants of terbium are calculated using four third order anharmonic parameters obtained from its interpolated pressure derivatives. The low and high temperature limits $\text{λ}{}_{\mathrm{L}}$ and $\text{λ}{}_{\mathrm{H}}$ of the lattice thermal expansion are evaluated. The agreement between the calculated $\text{λ}{}_{\mathrm{H}}$ and that obtained from thermal expansion and specific heat data of terbium is good.     

Third order elastic constants of V3Si and V3Ge

General expressions have been derived for the second order elastic constants and third order elastic constants of the A-15 structure compounds with the nearest neighbour central interaction. The second order elastic constants, the third order elastic constants and the pressure derivatives of the second order elastic constants of V₃Si and V₃Ge are reported and compared with the available experimental measurements.     

Self-consistent theory of second order elastic constants for nonionic anharmonic crystals

Elastic constants of strongly anharmonic nonionic dielectric crystals are studied within the pseudoharmonic approximation by means of two-time Green functions. The relation between the method of homogeneous deformation by Leibfried and Ludwig and that of long waves is investigated. These considerations lead to a generalization of the method of homogeneous deformation for the case of strongly anharmonic crystals. A comparison between the results of the two methods shows that the pseudoharmonic approximation satisfies the exact elastic sum rule. On leave from the Institute of Theoretical Physics University of Wrocław, Wrocław, Poland.     

The second and third order elastic constants of alkali metals

The second and third order elastic constants of the alkali metals have been calculated on the long wave method using the Heine-Abarenkov lacal model potential with different exchange-correlation corrections. It is found that the use of an exchange correlation correction which satisfies the compressibility sum rule leads to a good agreement between the calculated and measured second order elastic constants of the alkali metals Na, K, Rb and Cs. The shear elastic constants however come out correct even if the compressibility sum rule is violated by the exchange-correlation correction. The third order elastic constants and the pressure derivatives of the second order elastic constants and the pressure derivatives of the second order elastic constants calculated on the HA local potential are lower than the experimental values at room temperature. The discrepancy is pronounced for the heavier alkali metals. Similar calculations using the Wallace potential for Li, Na and K and the Schneider-Stoll potential for Rb give the pressure derivative in good agreement with experiment. In view of the important role by the exchange correlation correction, Suzuki's results calculated without taking this correction into account can only be accepted with some reservation.     

Anomalies in second order elastic constants and gyrotropic constants of triglycine sulphate near phase transition

The anomalies in second order elastic constants and gyrotropic constants have been considered for the phase transition of triglycine sulphate. Expressions have been derived for the equilibrium values of order parameter and strain variables in both phases. Using Landau-Khalatnikov equation the fluctuation in order parameter is expressed in terms of fluctuations in strain variables. Substitution of these in free energy gives anomalies arising from Landau and coupling energies in second order elastic constants. The real part of the anomalies decreases steeply across the transition temperature and thereafter flatly tend to ferroelectric values. The anomalies in the components of the gyrotropic tensor have been derived and their temperature variation discussed.     

On the third order elastic constants of AgCl-AgBr mixed system

Lowdin's many body effect is accounted to explain the violation of Cauchy's relation (C₁₂=C₄₄) in silver halides. Lundqvists potential model with many body effect has been used to evaluate the third order elastic constants of AgCl and AgBr. A modified Lundqvist potential model is used to calculate the third order elastic constants for the simple AgCl- AgBr mixed system with varying concentration of AgCl and AgBr.     

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.     

Lattice dynamics,third order elastic constants and thermal expansion of gadolinium

A systematic investigation of the lattice dynamics, second and third order elastic constants and the temperature variation of the effective Grüneisen functions has been carried out in gadolinium using Keating's approach. The ten third order elastic constants are calculated using five anharmonic parameters. The present model reproduces the measured pressure derivatives of the second order elastic constants of gadolinium well. The low and high temperature limits gg_L and gg_H of the lattice thermal expansion are evaluated. The agreement between the calculated gg_H and that obtained from the thermal expansion and specific heat data of gadolinium is good.     

Lattice dynamics,third order elastic constants and thermal expansion of Cadmium

The lattice dynamics, second and third order elastic constants, pressure derivatives of the second order elastic constants and the temperature variation of the lattice thermal expansion of Cadmium have been worked out utilising Keating's approach. The ten TOE constants are calculated using four anharmonic parameters. The model used here reproduces the measured pressure derivatives of the SOE constants of Cadmium extremely well. The low temperature limit of the volume Gruneisen function γ_L is found to be nearer to the value of Andres. The high temperature limit γ_v(T) is in good agreement with the value calculated by Gschneidner Jr. from the Cv data for Cadmium. The lattice dynamics of Cadmium is found to be essentially similar to that of Zinc.     

Lattice dynamics,third order elastic constants and thermal expansion of rhenium

A systematic investigation of the lattice dynamics, second and third order elastic constants and thermal expansion has been carried out in rhenium using Keating's approach. The ten third-order elastic constants of rhenium are calculated using four anharmonic parameters. The present model reproduces the measured pressure derivatives of the second order elastic constants well. The low and high temperature limits γ̄L and γ̄H of the lattice thermal expansion are calculated. The agreement between the calculated γ̄H and that obtained by Gschneidner from the thermal expansion and specific heat data of rhenium is satisfactory.     

Anharmonic force constants of GaSb from the measured third order elastic constants at 300°K

The third-order elastic constants of single crystal GaSb are determined using ultrasonic pulse interferometer at 10 MHz. The constants at 300°K, in units of 10¹¹ N.m.⁻², are C_l11 = ™ 4 ·75 ± 0·06 C₁₄₄ = + 0·50 ± 0·25 C₁₁₃ = ™ 3 ·08 ± 0·02 C₁₆₆ = ™ 2·16 ± 0·13 C₁₂₃ = ™ 0 ·44 ± 0·29 C₄₅₆ = ™ 0·25 ± 0·15 These constants are used to evaluate the three anharmonic first and second neighbour force constants based on modified Keating’s model. The constants are (in units of 10¹¹ N.m⁻²)γ=− 2·406;δ=0·407;ε=−0·222.