Supreme shear modulus predicted in the monocarbide system: the Rex W1–x C alloy

The energetic, mechanical and electronic properties as a function of composition for Re_x W_1–x C alloys in the WC structure have been investigated. It has been demonstrated that the shear modulus of WC can be enhanced by alloying with a small amount of Re, to a maximum shear modulus of 311 GPa at x = 0.23. The designed alloy is energetically stable and could be expected to be a potential extremely hard transition‐metal monocarbide, which is attributed to the strong metal–metalloid interaction with modulated valence electron concentration with respect to WC. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

First-principles study on electronic structure and elastic properties of Ti2SC

We have performed first-principles study on electronic structure and elastic properties of Ti₂SC. The absence of band gap at the Fermi level and the finite value of the density of states at the Fermi energy reveal the metallic behavior of this compound. The five independent elastic constants were derived and the bulk modulus, Young's modulus, shear modulus, and Poisson's ratio were determined. The high bulk modulus and hardness was found to be originated from the strong Ti 3d-S 2p hybridization. Such strong MA bonding is unusual in the MAX phases studied so far. Ti₂SC is elastically stable and exhibits highly elastic isotropy.     

Electronic structure,chemical bonding and elastic properties of the first thorium‐containing nitride perovskite TaThN3

The full‐potential linearized augmented plane wave method with the generalized gradient approximation for the exchange and correlation potential (LAPW‐GGA) is used to understand the electronic and elastic properties of the first thorium‐containing nitride perovskite TaThN₃. Total and partial density of states, charge distributions as well as the elastic constants, bulk modulus, compressibility, shear modulus, Young modulus and Poisson ratio are obtained for the first time and analyzed in comparison with cubic ThN. The chemical bonding in TaThN₃ is a combination of ionic Th–N and of mixed covalent–ionic Ta–N bonds. The cubic TaThN₃ is semiconducting with the direct gap at about 0.65 eV. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Lattice mechanical properties of alkaline earth metals in bcc and fcc phases

A model pseudopotential depending on an effective core radius treated as a parameter is used for alkaline earth metals in bcc and fcc phases to study the Binding energy, Interatomic interactions, phonon dispersion curves, Phonon density of states, Debye-Waller factor, mean square displacement, Debye-Waller temperature parameters, dynamical elastic constants (C₁₁, C₁₂ and C₄₄), bulk modulus (B), shear modulus (C′), deviation from Cauchy relation (C₁₂−C₄₄), Poisson's ratio (σ), Young's modulus (Y), behavior of phonon frequencies in the elastic limit independent of the direction (Y₁), limiting value in the [1 1 0] direction (Y₂), degree of elastic anisotropy (A) and propagation velocities of the elastic waves. The contribution of s-like electrons is incorporated through the second-order perturbation theory due to model potential. The theoretical results are compared with the existing experimental data. A good agreement between theoretical investigations and experimental findings has confirmed the ability of our potential to yield large numbers of lattice mechanical properties of certain alkaline earth metals.     

Ab initio calculation of the electronic structure,Fermi surface,and elastic properties of the new 7.5-K superconductor Nb<Subscript>2</Subscript>InC

Ab initio calculations were performed to investigate electronic and elastic properties of the newly discovered 7.5 K superconductor: layered Nb₂InC. As a result, electronic bands, total and site-projected l—decomposed density of states at the Fermi level, shape of the Fermi surface for Nb₂InC were obtained for the first time. Besides, independent elastic constants, bulk modulus, compressibility, shear modulus, Young’s modulus, Poisson’s ratio together with the elastic anisotropy parameters and indicator of brittle/ductile behavior of Nb₂InC were evaluated and analyzed in comparison with the available data.     

Structural,elastic, electronic,optical and thermal properties of c-SiGe<Subscript>2</Subscript>N<Subscript>4</Subscript>

We have investigated the structural, elastic, electronic, optical and thermal properties of c-SiGe₂N₄ by using the ultrasoft pseudopotential density functional method within the generalized gradient approximation. The calculated structural parameters, including the lattice constant, the internal free parameter, the bulk modulus and its pressure derivative are in agreement with the available data. The independent elastic constants and their pressure dependence, calculated using the static finite strain technique, satisfy the requirement of mechanical stability, indicating that c-SiGe₂N₄ compound could be stable. We derive the shear modulus, Young’s modulus, Poisson’s ratio and Lamé’s coefficients for ideal polycrystalline c-SiGe₂N₄ aggregate in the framework of the Voigt-Reuss-Hill approximation. We estimate the Debye temperature of this compound from the average sound velocity. Band structure, density of states, Mulliken charge populations and pressure coefficients of energy band gaps are investigated. Furthermore, in order to understand the optical properties of c-SiGe₂N₄, the dielectric function, refractive index, extinction coefficient, optical reflectivity and electron energy loss are calculated for radiation up to 40 eV. Thermal effects on some macroscopic properties of c-SiGe₂N₄ are predicted using the quasi-harmonic Debye model in which the lattice vibrations are taken into account. We have obtained successfully the variations of the primitive cell volume, volume expansion coefficient, heat capacities and Debye temperature with pressure and temperature in the ranges of 0–40 GPa and 0–2000 K. For the first time, the numerical estimates of the elastic constants and related parameters, and the thermal properties are performed for c-SiGe₂N₄.     

Lattice mechanical properties of noble and transition metals

A model pseudopotential depending on an effective core radius but otherwise parameter free is used to study the interatomic interactions, phonon dispersion curves (inq and r-space analysis), phonon density of states, mode Grüneisen parameters, dynamical elastic constants (C ₁₁,C ₁₂ andC ₄₄), bulk modulus (B), shear modulus (C′), deviation from Cauchy relation (C ₁₂–C ₄₄), Poisson’s ratio (σ), Young’s modulus (Y), behavior of phonon frequencies in the elastic limit independent of the direction (Y ₁), limiting value in the [110] direction (Y ₂), degree of elastic anisotropy (A), maximum frequencyω _max, mean frequency 〈ω〉, 〈ω ²〉^1/2=(〈ω〉/〈ω ⁻¹〉)^1/2, fundamental frequency 〈ω ²〉, and propagation velocities of the elastic constants in Cu, Ag, Au, Ni, Pd, and Pt. The contribution of s-like electrons is calculated in the second-order perturbation theory for the model potential while that of d-like electrons is taken into account by introducing repulsive short-range Born-Mayer like term. Very recently proposed screening function due to Sarkar et al. has been used to obtain the screened form factor. The theoretical results are compared with experimental findings wherever possible. A good agreement between theoretical investigations and experimental findings has proved the ability of our model potential for predicting a large number of physical properties of transition metals.     

Structural and elastic properties of Zr<Subscript>2</Subscript>AlX and Ti<Subscript>2</Subscript>AlX (X = C and N) under pressure effect

Using first-principles density functional calculations, the effect of high pressures, up to 20 GPa, on the structural and elastic properties of Zr₂AlX and Ti₂AlX, with X = C and N, were studied by means of the pseudo-potential plane-waves method. Calculations were performed within the local density approximation to the exchange-correlation approximation energy. The lattice constants and the internal parameters are in agreement with the available results. The elastic constants and their pressure dependence are calculated using the static finite strain technique. We derived the bulk and shear moduli, Young's moduli and Poisson's ratio for ideal polycrystalline Zr₂AlX and Ti₂AlX aggregates. We estimated the Debye temperature of Zr₂AlX and Ti₂AlX from the average sound velocity. This is the first quantitative theoretical prediction of the elastic properties of Zr₂AlC, Zr₂AlN and Ti₂AlN compounds, and it still awaits experimental confirmation.     

Ab initio study on elastic and thermodynamical properties of Ti<Subscript>1-x</Subscript>Zr<Subscript>x</Subscript>C

Elastic and Thermodynamical properties of Ti_1-xZr_xC have been investigated using LAPW + lo within the density-functional theory with the generalized gradient approximation. We have studied the stability of the alloy Ti_1-xZr_xC as a function of Zr composition in rocksalt (B1) structure by calculating the elastic constants C₁₁, C₁₂ and C₄₄ using the tetragonal and trigonal distortions. Mechanical properties such as Poisson ratio, bulk, shear and Young’s modulii of Ti_1-xZr_xC are calculated. The Debye temperature and hardness are also computed for the first time to our knowledge for Ti_1-xZr_xC in various compositions.     

Electronic and elastic properties of the superconducting nanolaminate Ti<Subscript>2</Subscript>InC

The electronic properties and elastic parameters of the superconducting nanolaminate Ti₂InC are analyzed using the ab initio full-potential linearized augmented-plane-wave (FLAPW) method with the generalized gradient approximation (GGA) of the local spin density. The equilibrium parameters of the crystal lattice, the band structure, the total and partial densities of states, and the Fermi surface are determined within a unified approach. The independent elastic constants, the bulk modulus, and the shear modulus are calculated, and the elastic parameters are numerically estimated for the first time for polycrystalline Ti₂InC.     

Application of R-matrix method to electron-H<Subscript>2</Subscript>S collisions in the low energy range

Electron-H₂S collision process is studied using the R-matrix method. Nine low-lying states of H₂S molecule are considered in the R-matrix formalism to obtain elastic integral, differential, momentum transfer and excitation cross sections for this scattering system. We have represented our target states using configuration interaction (CI) wavefunctions. We obtained adequate representation of vertical spectrum of the target states included in the scattering calculations. The cross sections are compared with the experiment and other theoretical results. We have obtained good agreement for elastic and momentum transfer cross sections with experiment for entire energy range considered. The differential cross sections are in excellent agreement with experiment in the range 3–15 eV. A prominent feature of this calculation is the detection of a shape resonance in ²B₂ symmetry which decays via dissociative electron attachment (DEA). Born correction is applied for the elastic and dipole allowed transition to account for higher partial waves excluded in the R-matrix calculation. The electron energy range is 0.025–15 eV.     

Magneto-elastic properties of Tb<Subscript>3</Subscript>Ga<Subscript>5</Subscript>O<Subscript>12</Subscript> (TGG)

The temperature dependence of the elastic constants in Tb₃Ga₅O₁₂ was measured and analysed with a simple crystal field model. The magneto-elastic coupling constants have been deduced from this experiment. The coupling constant g_Γ5, related to the c₄₄ mode, is anomalously large. These coupling constants are important for the interpretation of the phonon Hall effect.     

Calculated elastic properties of M2AlC (M=Ti, V, Cr, Nb and Ta)

M₂AlC phases, where M is a transition metal, are layered ternary compounds that possess unusual properties. In this paper, we have calculated the elastic properties of M₂AlC, with M=Ti, V, Cr, Nb and Ta, by means of ab initio total energy calculations using the projector augmented-wave method. We have derived the bulk and shear moduli, Young's moduli and Poisson's ratio for ideal polycrystalline M₂AlC aggregates. We have estimated the elastic modulus of Cr₂AlC with 357.7 GPa while the values of all other phases are in the range 309±10 GPa. We suggest that this can be understood based on the calculated bond energies for the M-C bonds. Furthermore, our results indicate a profound elastic anisotropy of M₂AlC even compared to materials with a well-established anisotropic character such as α-alumina. Finally, we have estimated the Debye temperatures of M₂AlC from the average sound velocity.     

First-principles study of the structural,elastic, mechanical,electronic, and optical properties of cubic Mg<Subscript>2</Subscript>TiO<Subscript>4</Subscript>

We have performed ab-initio total energy calculations using the plane-wave ultrasoft pseudopotential technique based on the first-principles density-functional theory (DFT) to study structural, elastic, mechanical, electronic, and optical properties of cubic Mg₂TiO₄. The calculated lattice parameter a is in good agreement with the experimental values. The independent elastic constants are calculated. The mechanical properties including bulk, shear and Young’s modulus, Poisson’s coefficient, compressibility and Lamé’s constants are obtained using the Voigt-Reuss-Hill method. Debye temperature is estimated using the Debye-Grüneisen model. Band structure, density of states and charge densities are shown and analyzed. In order to clarify the mechanism of optical transitions of cubic Mg₂TiO₄, the complex dielectric function, refractive index, extinction coefficient, reflectivity, absorption coefficient, loss function and complex conductivity function are calculated.     

High pressure structural phase transition and elastic properties of Ga<Subscript>1-x</Subscript>In<Subscript>x</Subscript>As semiconducting compounds

The present paper addresses the high-pressure phase transformation and mechanical properties of Ga_1-xIn_xAs (x = 0.25, 0.5 and 0.75) by formulating an effective interionic interaction potential. This potential consists of the long-range Coulomb and charge transfer caused by the deformation of the electron shells of the overlapping ions and the Hafemeister and Flygare type short-range overlap repulsion extended upto the second neighbor ions and the van der Waals (vdW) interaction. The estimated values of phase transition pressure and the vast volume discontinuity in pressure-volume (PV) phase diagram indicate the structural phase transition from zinc blende (B3) to rock salt (B1). The equation of state curves plotted between V (P)/ V (0) and pressure are for both the zincblende (B3) and rocksalt (B1) structures. Further, the variations of the second and third order elastic constants with pressure have followed a systematic trend, which are almost identical to those exhibited by the observed data measured for other compounds of this family.     

Ab initio calculations of B<Subscript>2</Subscript> type RHg (R = Ce,Pr, Eu and Gd) intermetallic compounds

Spin polarized ab initio calculations have been carried out to study the structural, electronic, elastic and thermal properties of RHg (R = Ce, Pr, Eu and Gd) intermetallic compounds in B₂ structure. The calculations have been performed by using both generalized gradient approximation (GGA) and local spin density approximation (LSDA). The calculated value of lattice constant (a ₀) for these compounds with GGA is in better agreement with the experimental data than those with LSDA. Bulk modulus (B), first-order pressure derivative of bulk modulus and magnetic moment (μ _B ) are also presented. The energy band structure and electron density of states show the occupancy of 4f states for light as well as heavy rare earth atom. The elastic constants are predicted from which all the related mechanical properties like Poisson’s ratio (σ), Young’s modulus (E), shear modulus (G _H ) and anisotropy factor (A) are calculated. The ductility or brittleness of these compounds is predicted from Pugh’s rule (B/G _H ) and Cauchy pressure (C ₁₂ ? C ₄₄). The Debye temperature (θ _D ) is estimated from the average sound velocity, which have not been calculated and measured yet.     

Pressure dependent mechanical and thermodynamical properties of Hg<Subscript>0.91</Subscript>Mn<Subscript>0.09</Subscript>Te semiconductor

The mechanical, thermodynamical and elastic properties of Hg_0.91Mn_0.09Te compound are calculated by formulating an effective interionic interaction potential. This potential consists of the long-range Coulomb, three body force parameter, the Hafemeister and Flygare type short-range overlap repulsion extended upto the second neighbor ions and the van der Waals (vdW) interaction. The estimated values of phase transition pressure have revealed reasonably good agreement with the available experimental data on the phase transition pressure P _t = 11.5 GPa and the vast volume discontinuity in pressure-volume (PV) phase diagram indicate the structural phase transition from zincblende (B3) to rock salt (B1) structure. Later on, the Poisson’s ratio ν, the ratio R _S/B of S (Voigt averaged shear modulus) over B (bulk modulus), elastic anisotropy parameter, elastic wave velocity, average wave velocity and Debye temperature as functions of pressure is calculated. From Poisson’s ratio and the ratio R _S/B it is inferred that Hg_0.91Mn_0.09Te is brittle in nature in both B3 phase and B1 phase. To our knowledge this is the first quantitative theoretical prediction of the pressure dependence of ductile (brittle) nature of Hg_0.91Mn_0.09Te compounds and still awaits experimental confirmations.     

Electronic Structure and Elastic Properties of Ti3AlC from First-Principles Calculations

We perform a first-principles study on the electronic structure and elastic properties of TiaA1C with an antiperovskite structure. The absence of band gap at the Fermi level and the finite value of the density of states at the Fermi energy reveal the metallic behavior of this compound. The elastic constants of Ti3AlC are derived yielding c11 = 356 GPa, c12 = 55 GPa, c44 = 157 GPa. The bulk modulus B, shear modulus G and Young＇s modulus E are determined to be 156, 151 and 342 GPa, respectively. These properties are compared with those of Ti3AlC2 and Ti2AlC with a layered structure in the Ti-Al-C system and FeaAlC with the same antiperovskite structure.     

Structural, electronic and elastic properties of M2SC (M = Ti, Zr, Hf) compounds

Using ab initio calculations, we have studied the structural, electronic and elastic properties of M₂SC, with M = Ti, Zr and Hf. Geometrical optimization of the unit cell are in good agreement with the available experimental data. The band structures show that all three materials are conducting. The analysis of the site and momentum projected densities shows that the bonding is achieved through a hybridization of M-atom d states with S and C-atom p states. The Md-Sp bonds are lower in energy and are stiffer than Md-Cp bonds. The elastic constants are calculated using the static finite strain technique. We derived the bulk and shear moduli, Young's moduli and Poisson's ratio for ideal polycrystalline M₂SC aggregates. We estimated the Debye temperature of M₂SC from the average sound velocity. This is a quantitative theoretical prediction of the elastic properties of Ti₂SC, Zr₂SC, and Hf₂SC compounds, and it still awaits experimental confirmation.     

Elastic and electronic properties of BeB2 in comparison to superconducting MgB2 and NbB2

A study of the structural, elastic and electronic properties of BeB₂, a promising diboride in view of the lighter mass of Be, has been made using self-consistent Density Functional Theory (DFT). The five independent elastic constants of BeB₂ are predicted for the first time. The elastic behaviour of the compound is compared with those of the superconducting MgB₂ and NbB₂. We also evaluate the electronic structure of BeB₂ in order to obtain further insight into its surprising difference from the superconducting MgB₂.