A Calculation Approach to Elastic Constants of Crystallines at High Pressure and Finite Temperature

Elastic constants of Na and Li metals are calculated successfully for temperatures up to 350K and pressures up to 30GPa using a scheme without involving any adjustable parameter.Elastic constants are assumed to depend only on an effective pair potential that is only determined by the average interatomic distance.Temperature has an effect on elastic constants by way of charging the equilibrium.The elastic constants can be obtained by fitting the relationship between total energy and strain tensor using the new set of lattice parameters obtained by calculating displacement of atoms at the finite temperature and at a fixed pressure.The relationship between the effective pair potential and the interatiomic distance is fitted by using a series of data of cohesive energy corresponding to lattice parameters.     

Elastic Constants of NaC1 under Pressure via First-Principles Calculations

The elastic constants of the B1 structure NaCl under pressure are obtained by using the ab initio plane-wave pseudopotential density functional theory method. The obtained zero pressure lattice constant and elastic constants are in good agreement with the available experimental data. It is found that the elastic constants C11 and C12 and the bulk modulus B increase monotonically with pressure P, however C44 increases monotonically when P_〈28 GPa and decreases when P〉28 GPa. Moreover, we discuss the B1-B2 structure phase transition of NaCl and obtain the transition pressure of 28.3 GPa.     

First-Principles Study of Structural,Elastic and Electronic Properties of OsSi

First-principles study of structural, elastic, and electronic properties of the B20 structure OsSi has been reported using the plane-wave pseudopotential density functional theory method. The calculated equilibrium lattice and elastic constants are in good agreement with the experimented data and other theoretical results. The dependence of the elastic constants, the aggregate elastic modulus, the deviation from the Cauchy relation, the elastic wave velocities in different directions and the elastic anisotropy on pressure have been obtained and discussed. This could be the first quantitative theoretical prediction of the elastic properties under high pressure of OsSi compound. Moreover, the electronic structure calculations show that OsSi is a degenerate semiconductor with the gap value of 0.68 eV, which is higher than the experimental value of 0.26 eV. The analysis of the PDOS reveals that hybridization between Os d and Sip states indicates a certain covalency of the Os-Si bonds.     

Theoretical Study of Elastic Properties of Tungsten Disilicide1

The plane-wave pseudopotential method using the generalized gradient approximation within the framework of density functional theory is applied to analyse the lattice parameters, elastic constants, bulk moduli, shear moduli and Young＇s moduli of WSi2. The quasi-harmonic Debye model, using a set of total energy versus cell volume obtained with the plane-wave pseudopotential method, is applied to the study of the elastic properties and vibrational effects. The athermal elastic constants of WSi2 are calculated as a function of pressure up to 35 GPa. The relationship between bulk modulus and temperature up to 1200 K is also obtained. Moreover, the Debye temperature is determined from the non-equilibrium Gibbs function. The calculated results are in good agreement with the experimental data.     

First-Principles Calculation of Static Equation of State and Elastic Constants for GaSe

The all-electron full potential augmented plane-wave plus local orbital （APW_Io） method with the local-density approximation （LDA） is used to calculate the static equation of state （EOS） and elastic constants of crystalline GaSe. After the full relaxation of atomic positions, the calculated band structure at ambient pressure is consistent with the experimental data to the extent expected to give the known limits of LDA one-electron energies. The equilibrium lattice parameters found here exhibit the usual LDA-induced contraction. However, constrained with the experimental cell volume, the interlayer separation exhibits an expansion due to the LDA underestimate of the weak interlayer bonding. The calculated values of elastic constants are in good agreement with acoustic measurements. The pressure derivatives of the lattice constants derived from the theoretical elastic constants are in very good agreement with x-ray spectra measurements. Two analytical EOSs have been determined at pressures up to 4.5 GPa. The pressure evolution of the structure indicates that the layer thickness decreases slightly under pressure.     

First-Principle Calculations of Elastic Properties of Wurtzite-Type Aluminum Nitride Under Pressure

The elastic properties of the wurtzite-type aluminum nitride （w-AlN） are investigated by ab initio plane-wave pseudopotential density functional theory method. The pressure dependences of the normalized primitive cell volume V/Vo, the elastic constants cij, the aggregate elastic modulus （B, G, E）, the Poisson＇s ratio （v）, and the Debye temperature θD are successfully obtained. From the elastic constants of the w-AlN under pressure, we find that the w-AlN should be unstable at higher pressure than 61.33 GPa.     

First-Principles Calculations of Elastic and Thermal Properties of Molybdenum Disilicide

The first-principles plane-wave pseudopotential method using the generalized gradient approximation within the framework of density functional theory is applied to anaylse the equilibrium lattice parameters, six independent elastic constants, bulk moduli, thermal expansions and heat capacities of MoSi2. The quasi-harmonic Debye model, using a set of total energy versus cell volume obtained with the plane-wave pseudopotential method, is applied to the study of the elastic properties, thermodynamic properties and vibrational effects. The calculated zero pressure elastic constants are in overall good agreement with the experimental data. The calculated heat capacities and the thermal expansions agree well with the observed values under ambient conditions and those calculated by others. The results show that the temperature has hardly any effect under high pressure.     

Structural Stability and Elastic Properties of Wurtzite TIN under Hydrostatic Pressure

The structural stability and elastic properties of wurtzite thallium nitride （TIN） under hydrostatic pressure are studied for the first time by first-principles calculations. The enthalpy calculations predict that TIN undergoes a phase transition from the wurtzite structure to the rocksalt structure at 19.2 GPa with a volume collapse of 13.0%. Our calculated results also show that this nitride is ductile in nature and exhibits high elastic anisotropy. Our ground-state results are in good agreement with the data of other theoretical calculations.     

Theoretical investigation on the electronic structure,elastic properties, and intrinsic hardness of Si2N20

According to the density functional theory we systematically study the electronic structure, the mechanical prop- erties and the intrinsic hardness of Si2N2O polymorphs using the first-principles method. The elastic constants of four Si2N2O structures are obtained using the stress-strain method. The mechanical moduli （bulk modulus, Young’s mod-ulus, and shear modulus） are evaluated using the Voigt-Reuss-Hill approach. It is found that the tetragonal Si2N2O exhibits a larger mechanical modulus than the other phases. Some empirical methods are used to calculate the Vickers hardnesses of the Si2N2O structures. We further estimate the Vickers hardnesses of the four Si2N2O crystal structures, suggesting all Si2N2O phases are not the superhard compounds. The results imply that the tetragonal Si2N2O is the hardest phase. The hardness of tetragonal Si2N2O is 31.52 GPa which is close to values of β-Si3N4 and γ-Si3N4.     

First-principles study of the structural,elastic, and optical properties for Sr0.5Ca0.5TiO3

A detailed theoretical study of the structural, elastic, and optical properties for Sr0.5Ca0.5TiO3 is carried out by first- principles calculations. The band structure exhibits a direct bandgap of 2.08 eV at the F point in the Brillouin zone. The bulk modulus, shear modulus, Young＇s modulus, and Poisson＇s ratio are derived based on the calculated elastic constants. The bulk modulus B = 153 GPa and shear modulus G = 81GPa are in good agreement with available experimental data. Poisson＇s ratio v = 0.275 suggests that Sr0.sCa0.sTiO3 should be classified as being a ductile material. Using the electronic band structure and density of states, we analyze the interband contribution to the optical properties. The real and imaginary parts of the dielectric function, as well as the optical properties such as the optical absorption coefficient, refractive index, extinction coefficient, and energy-loss spectrum are calculated. The static dielectric constant ε1 （0） and the refractive index n（0） are also investigated.     

Pressure-induced structural transition and thermodynamic properties of RhN2 and the effect of metallic bonding on its hardness

The elastic constant, structural phase transition, and effect of metallic bonding on the hardness of RhN2 under high pressure are investigated through the first-principles calculation by means of the pseudopotential plane-wave method. Three structures are chosen to investigate for RhN2, namely, simple hexagonal P6/mmm （denoted as SH）, orthorhombic Pnnm （marcasite）, and simple tetragonal P4/mbm （denoted as ST）. Our calculations show that the SH phase is energetically more stable than the other two phases at zero pressure. On the basis of the third-order Birch Murnaghan equation of states, we find that the phase transition pressures from an SH to a marcasite structure and from a marcasite to an ST structure are 1.09 GPa and 354.57 GPa, respectively. Elastic constants, formation enthalpies, shear modulus, Young＇s modulus, and Debye temperature of RhN2 are derived. The calculated values are, generally speaking, in good agreement with the previous theoretical results. Meanwhile, it is found that the pressure has an important influence on physical properties. Moreover, the effect of metallic bonding on the hardness of RhN2 is investigated. This is a quantitative investigation on the structural properties of RhN2, and it still awaits experimental confirmation.     

Elastic constants and anisotropy of RuB2 under pressure

The structural, elastic constants and anisotropy of RuB2 under pressure are investigated by first-principles calcula-tions based on the plane wave pseudopotential density functional theory method within the local density approximation (LDA) as well as the generalized gradient approximation (GGA) for exchange and correlation. The results accord well with the available experimental and other theoretical data. The elastic constants, elastic anisotropy, and Debye temperature Θ as a function of pressure are presented. It is concluded that RuB2 is brittle in nature at low pressure, whereas it becomes ductile at higher pressures. An analysis for the calculated elastic constant has been made to reveal the mechanical stability of RuB2 up to 100 GPa.     

Elastic Properties of Rutile TiO2 at High Temperature

Dependence of elastic properties on temperature for rutile TiO2 is investigated by the Cambridge Serial Total Energy Package （CASTEP） program in the frame of density function theory （DFT） and the quasi-harmonic Debye model The six independent elastlc constants of rutile TiO2 at high temperature are theoretically obtained for the first time. It is found that with increasing temperature, the elastic constants will decrease monotonically. Moreover, we successfully obtain the polycrystalline moduli BH and GH, as well as the Debye temperature ⊙D.     

First-principles investigation on the elastic stability and thermodynamic properties of Ti2SC

Using Vanderbilt-type plane-wave ultrasoft pseudopotentials within the generalized gradient approximation（GGA） in the frame of density functional theory（DFT）,we have investigated the crystal structures,elastic,and thermodynamic properties for Ti2SC under high temperature and high pressure.The calculated pressure dependence of the lattice volume is in excellent agreement with the experimental results.The calculated structural parameter of the Ti atom experienced a subtle increase with applied pressures and the increase suspended under higher pressures.The elastic constants calculations demonstrated that the crystal lattice is still stable up to 200 GPa.Investigations on the elastic properties show that the c axis is stiffer than the a axis,which is consistent with the larger longitudinal elastic constants（C 33,C 11） relative to transverse ones（C 44,C 12,C 13）.Study on Poisson＇s ratio confirmed that the higher ionic or weaker covalent contribution in intra-atomic bonding for Ti2SC should be assumed and the nature of ionic increased with pressure.The ratio（B/G） of bulk（B） and shear（G） moduli as well as B/C 44 demonstrated the brittleness of Ti2SC at ambient conditions and the brittleness decreased with pressure.Moreover,the isothermal and adiabatic bulk moduli displayed opposite temperature dependence under different pressures.Again,we observed that the Debye temperature and Gru篓neisen parameter show weak temperature dependence relative to the thermal expansion coefficient,entropy,and heat capacity,from which the pressure effects are clearly seen.     

First-Principles Calculations for Elastic Properties of ZnS under Pressure

The pressure dependence of elastic properties of ZnS in zinc-blende （ZB） and wurtzite （WZ） structures are investigated by the generalized gradient approximation （GGA） within the plane-wave pseudopotential density functional theory （DFT）. Our results are in good agreement with the available experimental data and other theoretical results. From the high-pressure elastic constants obtained, we find that the ZB and WZ structures of ZnS are unstable when the applied pressures are larger than 15.8 GPa and 21.3 GPa, respectively. The sound velocities along different directions for the two structures are also obtained. It is shown that as pressure increases, the sound velocities of the shear wave decrease, and those of all the longitudinal waves increase. An analysis has been made to reveal the anisotropy and highly noneentral forces in ZnS.     

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.     

DFT Investigation of Structural,Electronic,Elastic and Optical Properties of SrMO_4(M=Mo and W)

A planes waves pseudo-potential calculations are performed for the SrMO_4(M=Mo and W) compound in order to investigate the structural, electronic, elastic and optical properties. The calculated lattice constants are in good agreement with experiment ones. The electronic structures show that SrMO_4 has a direct band gap situated at Γpoint. The calculated elastic constants indicate that both structures are mechanically stable. The bulk modulus, shear modulus, Young's modulus and Poisson ratio are investigated from the elastic constants, in the same time the anisotropy of the elastic properties is discussed. The imaginary part of the dielectric functions is calculated and the contributions of various transitions peaks are analyzed. Furthermore, the other optical properties such as absorption coefficient I(ω),optical reflectivity R(ω), energy-loss spectrum L(ω), and the refractive index n(ω) have been investigated.     

Elastic and thermodynamic properties of vanadium nitride under pressure and the effect of metallic bonding on its hardness

By the particle-swarm optimization method, it is predicted that tetragonal P42mc, 141md, and orthorhombic Amm2 phases of vanadium nitride （VN） are energetically more stable than NaCl-type structure at 0 K. The enthalpies of the predicted three new VN phases, along with WC, NaC1, AsNi, CsCl type structures, are calculated each as a function of pressure. It is found that VN exhibits the WC-to-CsCl type phase transition at 256 GPa. For the considered seven crystal- lographic VN phases, the structures, elastic constants, bulk moduli, shear moduli, and Debye temperatures are investigated. Our calculated equilibrium structural parameters are in very good agreement with the available experimental results and the previous theoretical results for the NaC1 phase. The Debye temperatures of VN predicted three novel phases, which are all higher than those of the remaining structures. The elastic constants, thermodynamic properties, and elastic anisotropies of VN under pressure are obtained and the mechanical stabilities are analyzed in detail based on the mechanical stability criteria. Moreover, the effect of metallic bonding on the hardness of VN is also investigated, which shows that VNs in P42mc, 141md, and Amm2 phases are potential superhard phases. Further investigation on the experimental level is highly recommended to confirm our calculations presented in this paper.     

Mechanical and thermodynamic properties of cubic YH_2 under high pressure:Prediction from first-principles study

First-principles calculations are used to investigate the mechanical and thermodynamic properties of cubic YH2 at different pressures and temperatures. The generalized gradient approximation （GGA） with Perdew-Burke-Ernzerhof （PBE） method is used to describe the exchange-correlation energy in the present work. The calculated equilibrium lattice constant a and bulk modulus B are in good accordance with the available experimental values. According to the Born-Huang criteria for mechanical stability, elastic constants are calculated from the strain-induced stress method in a pressure range from 0 to 67.1 GPa. Isotropic wave velocities and sound velocities are discussed in detail. It is found that the Debye temperature decreases monotonically with the increase of pressure and that YH2 has low anisotropy in both longitudinal and shear-wave velocities. The calculated elastic anisotropic factors indicate that YH2 has low anisotropy at zero pressure and that its elastic anisotropy increases as pressure increases. Through the quasi-harmonic Debye model, in which phononic effects are considered, the thermodynamic properties of YH2, such as the relations of （V-Vo）/Vo to the temperature and the pressure, the dependences of heat capacity Cv and thermal expansion coefficient a on temperature and pressure ranging from 0 to 2400 K and from 0 to 65 GPa, respectively, are also discussed.     

New ordered MAX phase Mo_2 TiAlC_2: Elastic and electronic properties from first-principles

First-principles computation on the basis of density functional theory(DFT) is executed with the CASTEP code to explore the structural, elastic, and electronic properties along with Debye temperature and theoretical Vickers' hardness of newly discovered ordered MAX phase carbide Mo_2TiAlC_2. The computed structural parameters are very reasonable compared with the experimental results. The mechanical stability is verified by using the computed elastic constants. The brittleness of the compound is indicated by both the Poisson's and Pugh's ratios. The new MAX phase is capable of resisting the pressure and tension and also has the clear directional bonding between atoms. The compound shows significant elastic anisotropy. The Debye temperature estimated from elastic moduli(B, G) is found to be 413.6 K. The electronic structure indicates that the bonding nature of Mo_2TiAlC_2 is a mixture of covalent and metallic with few ionic characters. The electron charge density map shows a strong directional Mo–C–Mo covalent bonding associated with a relatively weak Ti–C bond.The calculated Fermi surface is due to the low-dispersive Mo 4d-like bands, which makes the compound a conductive one.The hardness of the compound is also evaluated and a high value of 9.01 GPa is an indication of its strong covalent bonding.