Anharmonic properties of TmTe

Data on elastic constants and associated properties at high temperature for TmTe crystal are presented and discussed starting from primary physical parameters viz. nearest neighbour distance and hardness parameter assuming long- and short-range potentials. When the values of the higher order elastic constants are known for a crystal, many of the anharmonic properties of the crystal can be treated within the limit of the continuum approximation in a quantitative manner. In this study, higher order elastic constants and related properties are computed upto 1000 K for TmTe. The first-order pressure derivatives of second- and third-order elastic constants, the second-order pressure derivatives of second-order elastic constants and partial contractions are also evaluated at different temperatures. The results thus obtained are compared with other available data and found in well agreement with present values.     

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.     

Third-order elastic constants of ZnS and ZnSe

The complete set of non-vanishing third-order elastic constants of the semiconductors ZnS and ZnSe is obtained theoretically. The strain energy density is estimated using finite strain elasticity theory by considering the interactions up to two nearest neighbours of each atom in the unit cell of these compounds. This energy density is compared with the strain dependent lattice energy density from the continuum model approximation. The second-order parameter of the potential function φ is obtained from the measured principal axis C_ij. The third-order potential parameter is estimated by assuming a Lennard-Jones type of interatomic potential. The interlattice displacements as well as the second-order elastic constants are evaluated along with the six third-order elastic constants of ZnS and ZnSe. Using these second- and third-order elastic constants of ZnS, the pressure derivatives of second-order elastic constants are evaluated. The second- and third-order elastic constants of ZnSe are compared with the available experimental values. The third-order elastic constants show anisotropy in different directions.     

Elastic constants of solids at high pressures

The isothermal and adiabatic nth-order (n ?? 2) elastic constants of a loaded crystal are defined. These constants fully determine the behavior of solids at an arbitrary load and are controlled by both an interatomic interaction and an applied load. Expressions that relate these constants (of the second, third, and fourth order) to Brugger elastic constants of the corresponding order, which are only determined by an inter-atomic interaction, are found for cubic symmetry crystals under hydrostatic pressure. These expressions are used to calculate the equation of state and the second- and third-order elastic constants of bcc tantalum at T = 0 K over a wide pressure range (0?C600 GPa) using an electron density functional method. The results of calculating the equation of state and the second-order elastic constants agree with available experimental data and the calculation results obtained in other works.     

Study of phase transformation and elastic properties of ThX (X = N,P, As and Sb) under high-pressure

An improved interaction potential model (IIPM) has been formulated to theoretically predict the pressure induced phase transition, elastic properties and thermophysical properties of thorium monopnictides (ThX; X = N, P, As and Sb). The phase transition pressures and volume drop obtained from this model show a better agreement with the available experimental than theoretical results. We have achieved elastic moduli, anisotropy factor, Poisson's ratio, Kleinman parameter, shear and stiffness constants on the basis of the calculated elastic constants. To know the anharmonic properties, we have also computed the third-order elastic constants, first-order pressure derivatives of second-order elastic constants and thermophysical quantities. Our results are in reasonable agreement with available measured and others reported data which supports the validity of model.     

Study of the anharmonic properties of copper halides

Summary We have investigated the anharmonic properties of cooper halides by means of a three-body interaction potential extended to include the van der Waals effects. For this purpose, we have computed the thirdorder elastic constants and the pressure derivatives of second-order elastic constants after deriving their correct expressions from the present potential following the lines of Sharma and Verma. Our results have, generally, followed a systematic trend and given a satisfactory prediction of the available experimental data on the anharmonic properties of copper halides. This potential has as scope of its application to describe the dynamical and dielectric properties of these halides. To speed up publication, the authors of this paper have agreed to not receive the proofs for correction.     

Analysis of the pressure derivatives of the shear modulii in ionic solids

Suitably modified theory based on Lundqvist potential of ionic cohesion, to explain the pressure derivatives of the solids, has been applied to evaluate the pressure derivatives of second order elastic (SOE) constants and the values of third order elastic (TOE) constants of ionic solids. The calculated values of the pressure derivatives of SOE constants are in good agreement with the experimental values.     

Vibrational and thermal properties of ScN and YN: quasi-harmonic approximation calculations and anharmonic effects

The structural, vibrational and thermal properties of rocksalt ScN and YN are investigated by using a first-principles plane-wave approach. The results are discussed in comparison with the similarly calculated results for rocksalt MgO and zincblende AlN. The thermal expansivity (α(V)) computed within the quasi-harmonic approximation shows that there are significant anharmonic effects in ScN and YN, which are comparable to those in MgO. Since no experimental results are available for α(V) of either ScN or YN, the anharmonic effects are accounted for by a variant of the very recently introduced effective semiempirical ansatz (Phys. Rev. B 2009 79 104304) for calculating anharmonic free energy, which does not require any input from experiment. The validity of this very simple approach is demonstrated first by applying it to MgO. For the considered phase of AlN, the quasi-harmonic approximation is valid up to very high temperatures, and the thus obtained α(V) is in good agreement with experiment. The values of α(V) for semiconductor transition metal nitrides that crystallize in the rocksalt phase are higher than those for the zincblende phase of group-IIIB nitrides, and a major part of these differences is due to the crystal structure.     

Elastic properties of alkaline earth oxides under high pressure

In this article, we have investigated the high-pressure structural phase transition of alkaline earth oxides using the three-body potential (TBP) model. Phase transition pressures are associated with elastic constants. An effective inter-ionic interaction potential (TBP) with long-range Coulomb interactions and the Hafemeister–Flygare type short-range overlap repulsion and the vdWl interaction is developed. The present calculations have revealed reasonably good agreement with the available experimental data on structural transition (B1–B2 structure). The phase transition pressures Pt of MgO, CaO, SrO, and BaO occur at 220, 45, 40, and 100?GPa, respectively. Further, the variations of the second-order elastic constants with pressure have followed a systematic trend, which are almost identical to those exhibited by the observed data measured for other semiconducting compounds with rocksalt (B1)-type crystal structure. It is found that TBP promises that we would be able to predict phase transition pressure and elastic constants for other chalcogenides as well. The results may be useful for geophysical study.     

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.     

High pressure phase transition and elastic behaviour of lanthanum monochalcogenides

The Phase transition and elastic properties of La-monochalcogenides have been investigated under pressure by means of a modified charge-transfer potential model which incorporates the Coulomb interaction modified by Coulomb screening due to the delocalization of electron of rare-earth atom leading to many-body interactions, covalency effect and overlap repulsion extended up to second-nearest neighbours. Under high pressure the coordination increases and they transform from rock-salt to CsCl structure. The calculated values of cohesive energy, lattice constant, phase transition pressure, relative volume collapse, harmonic and anharmonic elastic moduli and their first- and second-order pressure derivatives agree well with the available measured data and better than those computed by earlier workers. Present model is capable of explaining the Cauchy’s discrepancy correctly.     

Third-order elastic constants of the alloy Fe72Pt28

The complete sets of second- and third-order elastic constants of the cubic Fe₇₂Pt₂₈ have been obtained using the strain energy density derived from interactions up to three nearest neighbours of each atom in the unit cell. The finite strain elasticity theory has been used to get the strain energy density of Fe₇₂Pt₂₈. The strain energy density is compared with the strain-dependent lattice energy density obtained from the continuum model approximation and the expressions for the second- and third-order elastic constants of Fe₇₂Pt₂₈ are given. The second-order potential parameter is deduced from the measured second-order elastic constants of Fe₇₂Pt₂₈ and the third-order potential parameter is estimated from the Lennard-Jones inter-atomic potential for Fe₇₂Pt₂₈. The inter-lattice displacements; the three independent second-order elastic constants and the six independent third-order elastic constants of Fe₇₂Pt₂₈ are also determined. The second-order elastic constants are compared with the experimental elastic constants of Fe₇₂Pt₂₈. We also study the effect of pressure on the second-order elastic constants of Fe₇₂Pt₂₈.     

Characterisation of the high-pressure structural transition and elastic properties in boron arsenic

This paper carries out the First principles calculation of the crystal structures (zinc blende (B3) and rocksalt (B1)) and phase transition of boron arsenic (BAs) based on the density-functional theory. Using the relation between enthalpy and pressure, it finds that the transition phase from the B3 structural to the B1 structural occurs at the pressure of 113.42GPa. Then the elastic constants C₁₁, C₁₂, C₄₄, bulk modulus, shear modulus, Young modulus, anisotropy factor, Kleinman parameter and Poisson ratio are discussed in detail for two polymorphs of BAs. The results of the structural parameters and elastic properties in B3 structure are in good agreement with the available theoretical and experimental values.     

Pressure dependence of elastic properties of wurtzite ZnO crystal

We present the pressure dependence of elastic properties of the wurtzite phase of ZnO undergoing wurtzite to the rocksalt phase transition. A simple Landau theory is developed to describe the structural phase transition between wurtzite to rocksalt phases observed in ZnO. We have defined the necessary order parameter of the wurtzite to the rocksalt phase transition. We present a detailed analysis of the pressure dependence of the elastic and shear constants of the wurtzite phase of ZnO. The theoretical predictions are in the line with experimental results.     

Anharmonic effects and the lattice dynamics of insulators

Anharmonic effects manifest themselves in everyday properties of solids. Two of the more obvious examples are thermal expansion and heat conductivity. More sophisticated examples anharmonicity are provided by the direct measurement of the lifetimes and of the pressure and temperature dependence of modes of vibration solids by infrared, Raman, Brillouin, or neutron spectroscopy. The present article reviews current status of the theory of anharmonic effects in insulators. We will draw our examples almost exclusively from the simplest insulators, namely the fcc rare gas solids (RGS) and alkali-halides (AH) mostly of the rocksalt structure. Much what we have to say is applicable to other kinds solids also, but we shall not dwell on this aspect. We shall arbitrarily exclude perhaps the two most interesting classes of anharmonic solids, that ferroelectrics and quantum solids. These subjects are sufficiently developed as to warrant reviews their own and it would be impossible to do them justice in the space avdable here. No mention will be made of the vast subject of impurity modes which especially in the case of alkali-halides has developed into an autonomous branch of solidstate physics. For similar reasons we have chosen to exclude thermal conductivity attenuation sound and second sound. We are then left with what we feel to be a more manageable task reviewing the basic anharmonic properties of the simplest classes of perfect insulators. Our selection of material reflects our own biased and peculiar interests. Examples wdl be illustrative rather than exhaustive. Previous reviews and basic articles dealing with anharmonic effects are listed separately in the references at the end of this article.     

Elastic phase transitions in metals at high pressures

The elastic phase transitions of cubic metals at high pressures are investigated within the framework of Landau theory. It is shown that at pressures comparable with the magnitude of the bulk modulus the phase transition is connected with the loss of stability relative to uniform deformation of the crystalline lattice. Discontinuity of the order parameter at the transition point and its equilibrium value are expressed through the second-?to fourth-order elastic constants. The second-,third-?and fourth-order elastic constants and phonon dispersion curves of vanadium under hydrostatic pressure are obtained by first-principles calculations. Structural transformation in vanadium under pressure is studied using the obtained results. It is shown that the experimentally observed at P?≈?69?GPa phase transition in vanadium is the first-order phase transition close to a second-order phase transition.     

Pressure dependence of single crystal elastic constants and anharmonic properties of wurtzite

The single crystal, elastic constants of wurtzite (ZnS) have been measured by means of the ultrasonic pulse superposition technique at 25°C as a function of pressure, and at 1 bar as a function of temperature between 25 and 100°C. Within experimental accuracy the pressure dependence in the range up to 10 kbar was found to be linear for the longitudinal modes and quadratic for the shear modes. The elastic constants and their first pressure derivatives agree approximately with theoretical values for the hcp structure with first nearest neighbor central force interaction. The experimental data are used for the discussion of the Born stability limit in relation to the high pressure transformations of wurtzite into the sphalerite and rock salt structures, for the calculation of the Grüneisen parameter in the anisotropic elastic continuum approximation, and for the calculation of the isothermal equation of state at high pressure. The elastic properties of sphalerite (ZnS) are calculated from the data for wurtzite in the ‘equivalent sphalerite approximation’ of Sullivan and used for discussing the dependence on ionic radii of the pressure coefficients of the elastic constants in sphalerite-type II–VI compounds. The Born stability limit, the Grüneisen parameter and the isothermal equation of state of sphalerite are also calculated and compared with the corresponding quantities for wurtzite.     

Mode grüneisen parameters for long-wave phonons under pressure of Si and Ge

The elastic stiffness constants under pressure of Si and Ge are studied theoretically using the higher-order perturbational formalism and the local Heine-Abarenkov model pseudopotential, and the mode Grüneisen parameters for long-wave phonons are estimated as a function of the compressed volume. The results obtained for atmospheric pressure are in good agreement with the experimental data. The long-wave LA mode Grüneisen parameters decrease slightly as the volume is reduced by compression. The TA mode Grüneisen parameters show a large decrease as function of the volume strain, and become negative near the covalent-metallic phase transition. The volume-dependences of the long-wave mode Grüneisen parameters are useful in the study of the anharmonic properties of Si and Ge.     

Electronic properties and elastic constants of wurtzite, zinc-blende and rocksalt AlN

Electronic properties and elastic constants of AlN in the wurtzite, zinc-blende and rocksalt structures are investigated using an ab initio pseudopotential method based on the density-functional theory with both the local-density approximation and the generalized gradient approximation for the exchange-correlation functional. The numerically calculated results compare well with the existing experimental data. For elastic constants of rocksalt AlN our results are predictions.     

Elastic properties of oxides in the NaCl-structure

The single crystal elastic constants and their first pressure derivatives have been measured by means of the ultrasonic pulse superposition technique for the NaCl-structure oxides CaO, SrO and BaO. Within the experimental precision the pressure dependence was found to be linear in the range up to 10 kbar, except for a few shear modes measured for SrO and BaO. This nonlinearity, however, was not sufficient to unambiguously determine second pressure derivatives of the elastic constants. The present values are in fundamental agreement with the results of other investigators who used both ultrasonic and static compression methods. However, the additional precision and accuracy afforded by the present technique allows a clear demonstration of the systematic behavior of the elastic properties of MgO, CaO, SrO and BaO with respect to interionic distance. As in the case of the alkali halides, it appears that the size of the cation provides the dominant effect on the elastic constants. Moreover, calculations based on a lattice theoretical model consisting of Coulomb and Born-Mayer type repulsive forces between first and second nearest neighbor ions also support the contention that cation size has the major effect on the systematic behavior of the first pressure derivatives of the bulk moduli of these oxides.