Elastic and thermodynamic properties of CaB6 under pressure from first principles

The elastic and thermodynamic properties of CsCl-type structure CaB₆ under high pressure are investigated by first-principles calculations based on plane-wave pseudopotential density functional theory method within the generalized gradient approximation (GGA). The calculated lattice parameters of CaB₆ under zero pressure and zero temperature are in good agreement with the existing experimental data and other theoretical data. The pressure dependences of the elastic constants, bulk modulus B (GPa), and its pressure derivative B′, shear modulus G, Young's modulus E, elastic Debye temperature Θ_B, Zener's anisotropy parameter A, Poisson ratios σ, and Kleinmann parameter ζ are also presented. An analysis for the calculated elastic constants has been made to reveal the mechanical stability of CaB₆ up to 100 GPa. The thermodynamic properties of the CsCl-type structure CaB₆ are predicted using the quasi-harmonic Debye model. The pressure-volume-temperature (P-V-T) relationship, the variations of the heat capacity C_V, Debye temperature Θ_D, and the thermal expansion α with pressure P and temperature T, as well as the Grüneisen parameters γ are obtained systematically in the ranges of 0-100 GPa and 0-2000 K.     

Pressure effect on structural,electronic and thermodynamic investigations of europium filled skutterudite EuFe4Sb12: LDA and LSDA approximations

Numerical calculations based on the full potential muffin-tin orbitals method (FP-LMTO) within the local density approximation (LDA) and the local spin-density approximation (LSDA) to investigate the structural, electronic and thermodynamic properties of filled skutterudite EuFe₄Sb₁₂ are presented. The electronic band structure and density of states profiles prove that this material is a conductor. The present investigation is also extended to the elastic constants, such as the bulk modulus B, anisotropy factor A, shear modulus G, young's modulus E, Poisson's ratio ν, and the B/G ratio with pressure in the range of 0–40 GPa. The sound velocities and Debye temperatures are also predicted from the above constants. The variations of the primitive cell volume, expansion coefficient α, bulk modulus B, heat capacity (C_p and C_v), Debye temperature θ_D, Helmholtz free energy A, Gibbs free energy G, entropy S, and internal energy U with pressure and temperature in the range 0–3000 K are calculated successfully.     

Elastic and thermodynamic properties of AVO3 (A=Sr, Pb) perovskites

We have investigated the elastic and thermodynamic properties for the perovskite type metavanadate SrVO₃ and the multiferroic PbVO₃, probably for the first time by the means of a Modified Rigid Ion Model (MRIM). We present the elastic constants (C_11,C_12,C₄₄) and other elastic properties like Bulk modulus (B), Young′s modulus (E), shear modulus (G), Poisson′s ratio (σ) and wave velocity (υ_l, υ_s, υ_m). Besides we have reported the thermodynamic properties molecular force constant (f), Reststrahlen frequency (ν), cohesive energy (?), Debye temperature (θ_D) and Gruneisen parameter (γ). We have also computed the variation of heat capacity (C_P) and there by volume thermal expansion coefficient (α) in a wide temperature range. We found that the computed properties reproduce well with the available data in literature. To our knowledge some of the properties are reported for the first time.     

Structural, high pressure and elastic properties of transition metal monocarbides: A FP-LAPW study

The structural, elastic and thermal properties of four transition metal monocarbides ScC, YC (group III), VC and NbC (group V) have been investigated using full potential linearized augmented plane wave (FP-LAPW) method within generalized gradient approximation (GGA) both at ambient and high pressure. We predict a B₁ to B₂ structural phase transition at 127.8 and 80.4 GPa for ScC and YC along with the volume collapse percentage of 7.6 and 8.4%, respectively. No phase transition is observed in case of VC and NbC up to pressure 400 and 360 GPa, respectively. The ground state properties such as equilibrium lattice constant (a₀), bulk modulus (B) and its pressure derivative (B′) are determined and compared with available data. We have computed the elastic moduli and Debye temperature and report their variation as a function of pressure.     

Structural and elastic properties of LaTiO3 under pressure

We investigate the structural and elastic properties of LaTiO₃ by the plane-wave pseudopotential density functional theory method. The lattice constants, bulk modulus and its pressure derivative are obtained. These properties in the equilibrium phase are well consistent with the available experimental data. The pressure dependence of the elastic constants, ductility, mechanical stabilities, sound velocity and Debye temperatures are investigated for the first time. From the ratio G/B, we conclude that LaTiO₃ is ductile at 0 GPa and becomes more ductile at high pressure. In addition, the anisotropy factors for every symmetry plane and axis as well as linear bulk modulus at diverse pressures have been obtained.     

Elastic and electronic properties of YNi2B2C under pressure from first principles

The elastic and electronic structure properties of YNi₂B₂C under pressure are investigated by performing the generalized gradient approximation (GGA) and local density approximation (LDA) correction scheme in the frame of density functional theory (DFT). The pressure dependences of the normalized lattice parameters a/a₀ and c/c₀, the ratio c/a, and the normalized primitive volume V/V₀ of YNi₂B₂C are also obtained. The lattice constants and bulk modulus obtained are in agreement with the available experimental and other theoretical data. We have also studied the pressure dependences of elastic properties. It is found that, as pressure increases, the elastic constants C₁₁, C₃₃, C₆₆, C₁₂, and C₁₃ increase, the variation of elastic constant C₄₄ is not obvious. Moreover, our compressional and shear wave velocities V_L=6.99 km/s and V_S=3.67 km/s as well as the Debye temperature Θ=549.7 K at 0 GPa compare favorably with the available experimental data. The pressure dependences of band structures, energy gap and density of states are also investigated.     

First-principles calculations of structural stability and mechanical properties of tungsten carbide under high pressure

The structural stability and mechanical properties of WC in WC-, MoC- and NaCl-type structures under high pressure are investigated systematically by first-principles calculations. The calculated equilibrium lattice constants at zero pressure agree well with available experimental and theoretical results. The formation enthalpy indicates that the most stable WC is in WC-type, then MoC-type finally NaCl-type. By the elastic stability criteria, it is predicted that the three structures are all mechanically stable. The elastic constants C_ij, bulk modulus B, shear modulus G, Young?s modulus E and Poisson?s ratio ν of the three structures are studied in the pressure range from 0 to 100 GPa. Furthermore, by analyzing the B/G ratio, the brittle/ductile behavior under high pressure is assessed. Moreover, the elastic anisotropy of the three structures up to 100 GPa is also discussed in detail.     

Investigations of phase transition, elastic and thermodynamic properties of GaP by using the density functional theory

The phase transition of gallium phosphide (GaP) from zinc-blende (ZB) to a rocksalt (RS) structure is investigated by the plane-wave pseudopotential density functional theory (DFT). Lattice constant a₀, elastic constants c_ij, bulk modulus B₀ and the pressure derivative of bulk modulus B₀' are calculated. The results are in good agreement with numerous experimental and theoretical data. From the usual condition of equal enthalpies, the phase transition from the ZB to the RS structure occurs at 21.9 GPa, which is close to the experimental value of 22.0 GPa. The elastic properties of GaP with the ZB structure in a pressure range from 0 GPa to 21.9 GPa and those of the RS structure in a pressure range of pressures from 21.9 GPa to 40 GPa are obtained. According to the quasi-harmonic Debye model, in which the phononic effects are considered, the normalized volume V/V₀, the Debye temperature θ, the heat capacity C_v and the thermal expansion coefficient α are also discussed in a pressure range from 0 GPa to 40 GPa and a temperature range from 0 K to 1500 K.     

First-principles investigations on elastic, phonon and thermodynamic properties of SrB6 under pressure

The elastic, phonon and thermodynamic properties of the divalent alkaline-earth hexaboride SrB₆ are investigated by using plane-wave pseudopotential density functional theory method. The calculated structure parameters and bulk modulus are well consistent with the available experiment and theoretical data. The pressure dependences of elastic constants C_ij, bulk modulus B₀, shear modulus G, Young's modulus E and Poisson's ratio σ are also presented. With these elastic parameters, we investigate the mechanical stability and compressibility of SrB₆. For the thermodynamic properties, both phonon and quasi-harmonic Debye model methods are adopted. Through the comparison with experimental and other theoretical results, we found the method of quasi-harmonic Debye model is a little better. Moreover, the phonon dispersion relations are also obtained. It is found that there are two LO/TO splitting around 5 THz and 26 THz, respectively.     

Phase transition,structural, mechanical and thermal properties of erbium pnictides under pressure

In this article, we have investigated the high-pressure structural phase transition of erbium pnictides (ErX; X?=?N, P and As). An extended interaction potential model has been developed (including the zero-point energy effect in three-body interaction potential model). Phase transition pressures are associated with a sudden collapse in volume. The phase transition pressures and associated volume collapses have been predicted successfully. The elastic constants, their combinations and pressure derivatives are also reported. The pressure behaviour of elastic constants, bulk modulus and shear modulus have been presented and discussed. Moreover, the thermophysical properties such as molecular force constant (f), infrared absorption frequency (υ ₀), Debye temperature (θ _D) and Grunneisen parameter (γ) have also been predicted.     

Elasticity and thermodynamic properties of RuB2 under pressure

First-principles calculations of the crystal structure and the elastic properties of RuB₂ have been carried out with the plane-wave pseudopotential density functional theory method. The calculated values are in very good agreement with experimental data as well as with some of the existing model calculations. The elastic constants c_ij, the aggregate elastic moduli (B, G, E), Poisson's ratio, and the elastic anisotropy with pressure have been investigated. Through the quasi-harmonic Debye model considering the phonon effects, the isothermal bulk modulus, the thermal expansions, Grüneisen parameters, and Debye temperatures depending on the temperature and pressure are obtained in the whole pressure range from 0 to 60 GPa and temperature range from 0 to 1100 K as well as compared to available data.     

Single-crystal elastic constants of magnesium difluoride (MgF2) to 7.4 GPa

The six independent elastic constants (C₁₁, C₁₂, C₁₃, C₃₃, C₄₄, and C₆₆) of single-crystal MgF₂ in the rutile structure have been measured by Brillouin spectroscopy at room temperature from ambient conditions to 7.4 GPa. Measurements were performed on two monocrystals with perpendicular faces, (001) and (100). A quasi-linear fit from finite strain theory was applied to the experimental data revealing the pressure dependence of the six elastic constants of MgF₂. The shear modulus C_S=1/2(C₁₁−C₁₂), and the aggregate shear (Voigt–Reuss–Hill) modulus G show a softening with increasing pressure, indicating the approach of the rutile-to-CaCl₂-type structural phase transition at P~9 GPa. The adiabatic bulk modulus (Reuss average) and its pressure derivative have been determined: K_0S=105.1±0.3 GPa, (∂K_0S/∂P)_T=4.14±0.05. The pressure–volume equation of state of MgF₂ was computed self-consistently from the Brillouin data. Our results are in good agreement with X-ray diffraction data. As the phase transition is approached, MgF₂ becomes strongly anisotropic and develops partially auxetic behavior (a negative Poisson's ratio in certain directions).     

Ab initio calculations of elastic constants and thermodynamic properties of Li2O for high temperatures and pressures

The elastic constants and thermodynamic properties of Li₂O for high temperatures and pressures are calculated by the ab initio unrestricted Hartree-Fock (HF) linear combination of atomic orbital (LCAO) periodic approach. The lattice constant, elastic constants, Debye temperature, and thermal expansion coefficient obtained are in good agreement with the available experimental data and other theoretical results. It is found that at zero pressure the elastic constants C₁₁, C₁₂ and C₄₄, bulk modulus B and Debye temperature Θ_D decrease monotonically over the wide range of temperatures from 0 to 1100 K. When the temperature , C₁₂ approaches zero, consistently with the transition temperature 1200 K. However, with increasing pressure, they all increase monotonically and the anisotropy will weaken.     

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.     

Elastic and thermal properties of Sr1−xYxCoO3

The elastic and thermal properties of Sr_1?xY_xCoO₃ (0 ≤ x ≤ 0.5) have been investigated, probably for the first time, by using modified rigid ion model. We present the elastic constants (C_11, C_12, C₄₄) and other elastic properties like bulk modulus (B), Young's modulus (Y), shear modulus (G), Poisson's ratio (σ), Lame's parameter (μ, λ), transverse, longitudinal and average wave velocity (υ_t, υ_l and υ_m) and anisotropy parameter (A). Besides, we have reported the thermodynamic properties molecular force constant (f), Reststrahlen frequency (υ), cohesive energy (φ), Debye temperature (θ_D) and Gruneisen parameter (γ). We have also computed the variation of specific heat (C) and volume thermal expansion coefficient (α). The computed results on the elastic and thermodynamic properties are the first report on them. This model is capable of explaining the Cauchy's discrepancy, elastic and thermal properties successfully.     

Elastic constants and Debye temperature of wz-AlN and wz-GaN semiconductors under high pressure from first-principles

First-principles calculations were performed to study the elastic stiffness constants (C _ij ) and Debye temperature (?? _D) of wurzite (wz) AlN and GaN binary semiconductors at high pressure. The lattice constants were calculated from the optimized structure of these materials. The band gaps were calculated at Γ point using local density approximation (LDA) approach. The unit cell volume, lattice parameters, c/a, internal parameter (u), elastic constant (C _ij ), Debye temperature (?? _D), Hubbard parameter (U) and band gap (E _g) were studied under different pressures. The bulk modulus (B ₀), reduced bulk modulus ( \(B_{0}^{\prime })\) and Poisson ratio (υ) were also calculated. The calculated values of these parameters are in fair agreement with the available experimental and reported values.     

Theoretical study of the structural phase transition and elastic properties of HfN under high pressures

The effect of hydrostatic pressure on the structures of HfN at 0 K was investigated by using the projector augmented wave (PAW) within the Perdew–Burke–Ernzerhof (PBE) form of the generalized gradient approximation (GGA). The transition pressure between NaCl (B1) and CsCl (B2) structures is predicted to be 277.3 GPa. This value is consistent with that reported by Kroll, while in contrast to the results obtained by Ojha et al. and Meenaatci et al. Moreover, the elastic properties of B1-HfN and B2-HfN under high pressures are successfully obtained. It is found that the elastic constants, bulk modulus B, shear modulus G, compressional and shear wave velocities increase monotonically with increasing pressure. The Debye temperature Θ calculated from the elastic constants of HfN is in good agreement with the experimental values. The anisotropies of B1-HfN and B2-HfN at zero pressure have also been discussed.     

Structural, electronic, elastic and thermal properties of Mg2Si

First-principles calculations of the lattice parameter, electron density maps, density of states and elastic constants of Mg₂Si are reported. The lattice parameter is found to differ by less than 0.8% from the experimental data. Calculations of density of states and electron density maps are also performed to describe the orbital mixing and the nature of chemical bonding. Our results indicate that the bonding interactions in the Mg₂Si crystal are more covalent than ionic. The quasi-harmonic Debye model, by means of total energy versus volume calculations obtained with the plane-wave pseudopotential method, is applied to study the elastic, thermal and vibrational effects. The variations of bulk modulus, Grüneisen parameter, Debye temperature, heat capacity C_v, C_p and entropy with pressure P up to 7 GPa in the temperature interval 0-1300 K have been systemically investigated. Significant differences in properties are observed at high pressure and high temperature. When T<1300 K, the calculated entropy and heat capacity agree reasonably with available experimental data. Therefore, the present results indicate that the combination of first-principles and quasi-harmonic Debye model is an efficient approach to simulate the behavior of Mg₂Si.     

Electronic structure,elastic and thermodynamic properties of α-phase Na3N under pressure from first principles

The structural, electronic, elastic and thermodynamic properties of α-phase Na₃N under pressure are investigated by performing first principles calculations within generalized gradient approximation. The elastic constants, bulk modulus, shear modulus, Young's modulus, and Poisson's ratio dependencies on pressure are also calculated. The thermodynamic properties of the α-phase Na₃N are calculated using the quasi-harmonic Debye model. The dependencies of the heat capacity and the thermal expansion coefficient, as well as the Grüneisen parameter on pressure and temperature are investigated systematically in the ranges of 0–1 GPa and 0–100 K.     

Elastic properties and phonon dispersions of rhenium in hexagonal-close-packed structure under pressure from first principles

The elastic properties of the hexagonal-close-packed (hcp) structure rhenium (Re) and their behavior under pressure are investigated using the local density approximation (LDA) and the generalized gradient approximation (GGA). The obtained high pressure elastic constants are well consistent with previous theoretical date, while large discrepancies are found between theory and the high pressure experiments. The calculated isothermal bulk modulus B₀ (376 GPa for GGA and 389 GPa for LDA) and its initial pressure derivative (4.52 for LDA and 4.58 for GGA) compare favorably with the experimental values. Moreover, it is found that the value of c/a, B/G, Poisson's ratio, and B_c/B_a are virtually independent of pressure. We also performed calculation for phonon dispersions at high pressure. GGA in our calculation exhibits a same trend as the high pressure experimental curve.