Elastic,mechanical, electronic properties and hardness of Nb2AsC from first principles

The study aims at the elastic, mechanical, electronic properties and hardness of Nb₂AsC using first principles based on the density functional theory method within the generalised gradient approximation. The calculated lattice parameters of Nb₂AsC are in good agreement with the experimental data. The five independent elastic constants are firstly calculated as a function of pressure, and our results indicate that it is mechanically stable in the applied pressure. The elastic anisotropy is examined through the computation of the direction dependence of Young's modulus. The pressure dependences of the bulk modulus, shear modulus, average velocity of acoustic waves and Debye temperature of Nb₂AsC are systematically investigated. The band structure and density of states are discussed, and the results show that the strong hybridisations C p–Nb d and As p–Nb d would be beneficial to the structure stability of Nb₂AsC. Based on the Mulliken population analysis, the hardness of Nb₂AsC is predicted.     

External strain effect on the electronic and mechanical properties of the superconductor Nb2InC

We use first-principles method to investigate the effects of external strain ε on the structural, mechanical and electronic properties for the superconductor Nb₂InC. The results show that the tensile strain induces an isostructural phase transition in Nb₂InC. The elastic constants C_ij, bulk modulus B, shear modulus G, Young's moduli E, and Poisson ratio v_ij of Nb₂InC were also investigated in the range from ε=−10% to ε=10%. It indicates that Nb₂InC is mechanically stable under external strain, and its brittle–ductile transition occurs at ε=3.5%. Moreover, Nb₂InC gets a negative Poisson ratio at ε=4%. The calculated electronic structures indicate that the Nb–C bonding is stronger than Nb–In bonding in Nb₂InC. The energy band structures and densities of states of strained Nb₂InC were also calculated and discussed in detail. From these calculations, it is clear that the related properties of Nb₂InC can be easily tuned by strain. Therefore, our findings are very useful to tailor the physical properties of Nb₂InC by using strain engineering.     

Calculated structural, electronic and elastic properties of M2GeC (M=Ti, V, Cr, Zr, Nb, Mo, Hf, Ta and W)

Using ab initio calculations, we have studied the structural, electronic and elastic properties of M₂GeC, with M=Ti, V, Cr, Zr, Nb, Mo, Hf, Ta and W. Geometrical optimizations of the unit cell are in agreement with the available experimental data. The band structures show that all studied materials are electrical conductors. The analysis of the site and momentum projected densities shows that bonding is due to M d-C p and M d-Ge p hybridizations. The elastic constants are calculated using the static finite strain technique. The shear modulus C ₄₄, which is directly related to the hardness, reaches its maximum when the valence electron concentration is in the range 8.41–8.50. We derived the bulk and shear moduli, Young’s moduli and Poisson’s ratio for ideal polycrystalline M₂GeC aggregates. We estimated the Debye temperature of M₂GeC from the average sound velocity. This is the first quantitative theoretical prediction of the elastic constants of Ti₂GeC, V₂GeC, Cr₂GeC, Zr₂GeC, Nb₂GeC, Mo₂GeC, Hf₂GeC, Ta₂GeC and W₂GeC compounds, and it still awaits experimental confirmation.     

过渡金属Tc及其氮化物TcN，TcN$lt;sub$gt;2$lt;/sub$gt;，TcN$lt;sub$gt;3$lt;/sub$gt;与TcN$lt;sub$gt;4$lt;/sub$gt;低压缩性的第一性原理计算研究

采用基于密度泛函理论的第一性原理计算方法研究了Tc及其氮化物的弹性性质、电子结构、原子布局数等,并分析和计算了它的氮化物的理论硬度. 结果表明随着Tc中氮的掺入量的渐增,出现层状结构,它们的弹性模量并非单调增加,其中TcN的体弹模量最大而剪切模量最小;层状结构的TcN₃的剪切模量最大而体弹模量最小,TcN₄的理论计算硬度最大. 说明在Tc的氮化物中,其体弹模量与材料的晶体结构、平均每个原子上的电荷密度和材料的质量密度有关;化学键的共价性结构和氮元素的含量对理论计算硬度有正作用;而剪切模量的极大值则与其层状结构及体系中一定量的方向基本一致的N—N键相关. 关键词： 第一性原理 弹性性质 电子结构     

Hardness and elastic moduli of high pressure synthesized MoB2 and WB2 compacts

High pressure and high temperature synthesized MoB₂ and WB₂ compacts were investigated using X-ray diffraction, energy dispersive spectroscope, scanning electron microscope, Vickers indentation test and ultrasonic measurements. Experiments showed that both MoB₂ and WB₂ compacts are phase pure and with a grain size of 100–200 nm. Vickers indentation test under a large loading force of 49 N showed that the Vickers hardness of MoB₂ and WB₂ are about 21 and 22 GPa, respectively. The bulk modulus and shear modulus are about 296 GPa, and 190 GPa for MoB₂ and 349 and 200 GPa for WB₂ through ultrasonic measurements. Our results indicate that MoB₂ and WB₂ are both hard materials with a hardness similar to that of tungsten carbide, which is widely used in industry.     

Theoretical study of the structural, elastic, electronic and thermal properties of the MAX phase Nb2SiC

Structural, elastic, electronic and thermal properties of the MAX phase Nb₂SiC are studied by means of a pseudo-potential plane-wave method based on the density functional theory. The optimized zero pressure geometrical parameters are in good agreement with the available theoretical data. The effect of high pressure, up to 40 GPa, on the lattice constants shows that the contractions along the c-axis were higher than those along the a-axis. The elastic constants C_ij and elastic wave velocities are calculated for monocrystal Nb₂SiC. Numerical estimations of the bulk modulus, shear modulus, Young’s modulus, Poisson’s ratio, average sound velocity and Debye temperature for ideal polycrystalline Nb₂SiC aggregates are performed in the framework of the Voigt-Reuss-Hill approximation. The band structure shows that Nb₂SiC is an electrical conductor. The analysis of the atomic site projected densities and the charge density distribution shows that the bonding is of covalent-ionic nature with the presence of metallic character. The density of states at Fermi level is dictated by the niobium d states; Si element has a little effect. Thermal effects on some macroscopic properties of Nb₂SiC are predicted using the quasi-harmonic Debye model, in which the lattice vibrations are taken into account. The variations of the primitive cell volume, volume expansion coefficient, bulk modulus, heat capacity and Debye temperature with pressure and temperature in the ranges of 0-40 GPa and 0-2000 K are obtained successfully.     

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,Mechanical and Dynamical Stability of Hexagonal Subcarbides M<Subscript>2</Subscript>C (M = Tc,Ru, Rh,Pd, Re,Os, Ir,and Pt): Ab Initio Calculations

Ab initio calculations were used to study the properties of a series of hexagonal (Fe₂N-like) subcarbides M₂C, where M = Tc, Ru, Rh, Pd, Re, Os, Ir, and Pt, and to calculate their equilibrium structural parameters, electronic properties, phase stability, elastic constants, compression modulus, shear modulus, Young’s modulus, compressibility, Pugh’s indicator, Poisson ratio, elastic anisotropy indices, and also hardness, Debye temperature, sound velocity, and low-temperature heat capacity. It is found based on these results that all the subcarbides are mechanically stable; however, their formation energies E_form are positive with respect to a mixture of d-metal and graphite. In addition, the calculation of the phonon spectra of these subcarbides shows the existence of negative modes, which indicates their dynamical instability. Thus, a successful synthesis of these subcarbides at normal conditions is highly improbable.     

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.     

First-principles calculations on crystal structure and physical properties of rhenium dicarbide

Structural stability, elastic behavior, hardness, and chemical bonding of ideal stoichiometric rhenium dicarbide (ReC₂) in the ReB₂, ReSi₂, Hex-I, Hex-II, and Tet-I structures have been systematically studied using first-principles calculations. The results suggest that all these structures are mechanically stable and ultra-incompressible characterized by large bulk moduli. Formation enthalpy calculations demonstrated that they are metastable under ambient conditions, and the relative stability of the examined candidates decreases in the following sequence: Hex-I>Hex-II>ReB₂>Tet-I>ReSi₂. The hardness calculations showed that these structures are all hard materials, among which the Hex-I exhibits the largest Vickers hardness of 32.2 GPa, exceeding the hardness of α-SiO₂ (30.6 GPa) and β-Si₃N₄ (30.3 GPa). Density of states and electronic localization function analysis revealed that the strong C–C and C–Re covalent bonds are major driving forces for their high bulk and shear moduli as well as small Poisson's ratio.     

The mechanical,thermodynamic and electronic properties of Al3Nb with DO22 structure: A first-principles study

The lattice constants, elastic properties, electronic structure and thermodynamic properties of Al₃Nb with DO₂₂ structure have been investigated by the first-principles calculation. The calculated lattice constants were consistent with the experimental values, and the structural stability was also studied from the energetic point of view. The single-crystal elastic constants (C_ij) as well as polycrystalline elastic parameters (bulk modulus B, shear modulus G, Young's modulus E, Poisson's ratio υ and anisotropy value A) were calculated, and brittleness of Al₃Nb was discussed in detail. Besides, the electronic structure of tetragonal Al₃Nb was studied, which indicates a mixture of metallic bond and covalent bond in Al₃Nb and reveals the underlying mechanism of the stability and elastic properties of Al₃Nb. Finally, the thermodynamic properties of Al₃Nb were calculated and the physical properties such as heat capacity and Debye temperature were predicted within the quasi-harmonic approximation.     

Effects of alloying element on stabilities,electronic structures,and mechanical properties of Pd-based superalloys

The thermodynamic stabilities, electronic structures, and mechanical properties of the Pd-based superalloys are studied by first principles calculations. In this work, we discuss the effect of Pd-based superalloys made from Al, Si, Sc, Ti,V, Cr, Mn, Fe, Cu, Zn, Y, Zr, Nb, Mo, Tc, Hf, Ta, W, Re, Os, Ir and Pt, and we also calculate a face centered cubic(fcc)structure 2 × 2 × 2 superalloy including 31 Pd atoms and one alloying element T M(Pd_(31)TM). The mixing energies of these Pd-Based superalloys are negative, indicating that all Pd-based superalloys are thermodynamically stable. The Pd_(31)Mn has the lowest mixing energy with a value of-0.97 eV/atom. The electronic structures of the Pd-based superalloys are also studied, the densities of states, elastic constants and moduli of the mechanical properties of the Pd-based superalloys are determined by the stress-strain method and Voigt–Reuss–Hill approximation. It is found that Pd_(31)TM is mechanically stable, and Pd_(31)Tc has the largest C_(11), with a value 279.7 GPa. The Pd_(31)Cr has the highest bulk modulus with a value of299.8 GPa. The Pd_(31)Fe has the largest shear modulus and Young's modulus with the values of 73.8 GPa and 195.2 GPa,respectively. By using the anisotropic index, the anisotropic mechanical properties of the Pd_(31)T M are discussed, and threedimensional(3 D) surface contours and the planar projections on(001) and(110) planes are also investigated by the Young modulus.     

MAX相Nb2SnC和Nb2SnN的力学和热力学性质的第一性原理计算

利用基于密度泛函理论的第一性原理,在广义梯度近似下研究了MAX相Nb₂SnC和Nb₂SnN的力学、晶格动力学、电子以及热力学性质.通过弹性常数和声子的计算,研究了Nb₂SnC和Nb₂SnN两种结构的力学稳定性和动力学稳定性;通过对Nb₂SnC和Nb₂SnN的力学性质计算,证明了它们均具有较高的体积模量和剪切性,并且说明了Nb₂SnC和Nb₂SnN是具有弹性各向异性的韧性材料.此外,通过计算电子能带结构和态密度,研究了Nb₂SnC和Nb₂SnN的电子性质和成键性质,结果表明,两个化合物均具有金属导电性和较强的共价键,而且Nb₂SnN比Nb₂SnC具有更强的金属导电性.最后利用声子色散曲线预测了热容、自由能、焓和熵等热力学性质,结果标明,计算出的熵、焓和自由能值变化符合热力学第三定律.     

High-pressure radial X-ray diffraction study of osmium to 58 GPa

Nonhydrostatic compression behavior of osmium (Os) was investigated up to 58.2 GPa using radial X-ray diffraction (RXRD) together with lattice strain theory in a diamond-anvil cell. The apparent bulk modulus of Os derived from RXRD data varies from 262 GPa to 413 GPa, depending on Ψ, the orientation of the diffraction planes with respect to the loading axis. Fitting to the third-order Birch-Murnaghan equation of state, the RXRD data obtained at Ψ = 54.7° yields a bulk modulus K₀ = 390 ± 6 GPa with pressure derivative K^′ ₀ fixed at 4. The ratio of differential stress to shear modulus t/G ranges from 0.024 to 0.029 at the pressures of 15.7–58.2 GPa. The yield strength was observed to increase with compression and reach the value of 11.7 GPa at the highest pressure. This confirms that Os is the strongest known pure metallic material compared with the reported stiff elemental metals such as W, Mo and Re. It was found that the apparent c/a ratio changed with the nonhydrostatic compression, as well as the orientation Ψ in our experiments. Moreover, the aggregate moduli of Os at high pressure were determined from the RXRD measurements.     

Pressure-dependent mechanical and thermodynamic properties of newly discovered cubic Na2He

Recently for the first time, a stable compound of He and Na (Na₂He) is predicted at high pressure. We explore the pressure-dependent elastic, mechanical and thermodynamic properties of this newly discovered Na₂He by using ab initio technique. The calculation presents good accordance between the theoretical and experimental lattice parameters. Though the most stable structure of Na₂He is found at 300?GPa, present study ensures the mechanical stability of this compound up to 500?GPa. The study of Cauchy pressure, Pugh's ratio, and Poisson's ratio implies the ductile manner of Na₂He up to 500?GPa. According to the value of Poisson's ratio the bonding force exists in Na₂He is central. The study of Zener anisotropy factor indicates that Na₂He is an anisotropic material but near at 300?GPa approximately isotropic nature of Na₂He is revealed. The study of the bulk modulus, shear modulus, Young's modulus and Vickers hardness implies that the hardness of Na₂He can be improved by applying external pressure. However, the Debye temperature, melting temperature and minimum thermal conductivity of Na₂He are also calculated and discussed at different pressures.     

Elastic stability and electronic structure of tantalum boride investigated via first-principles density functional calculations

The elastic properties, electronic structure and thermodynamic behavior of the TaB have been investigated for the first time in this work. Using first-principles plane-wave ultrasoft-pseudopotential density functional theory (DFT), the ground state properties and equation of state of TaB have been obtained. The average zero-pressure bulk modulus of TaB is 302 GPa. By analyzing the elastically anisotropic behavior and the relative structure parameters of TaB, we found that the crystal cell along the b-axis was more compressible than along the a and c axes. The calculated ratio of bulk modulus and shear modulus (B/G) for TaB is 1.58, demonstrating that TaB is rather brittle. From the elastic stiffness constants, we found that TaB in the Cmcm phase is mechanically stable. The calculated hardness of TaB is 28.6 GPa which is close to the previous data. Moreover, using the Gibbs 2 model, the thermodynamic properties such as the thermal expansion and Debye temperature of TaB have been obtained firstly. At the ambient temperature, the Debye temperatures of TaB are 792 K and 845 K from GGA calculation and LDA calculation, respectively.     

Elastic properties of Nb-based alloys by using the density functional theory

A first-principles density functional approach is used to study the electronic and the elastic properties of Nb₁₅X(X = Ti, Zr, Hf, V, Ta, Cr, Mo, and W) alloys. The elastic constants c₁₁ and c₁₂, the shear modulus C', and the elastic modulus E_〈100〉 are found to exhibit similar tendencies, each as a function of valence electron number per atom (EPA), while c₄₄ seems unclear. Both c₁₁ and c₁₂ of Nb₁₅X alloys increase monotonically with the increase of EPA. The C' and E_〈100〉 also show similar tendencies. The elastic constants (except c₄₄) increase slightly when alloying with neighbours of a higher d-transition series. Our results are supported by the bonding density distribution. When solute atoms change from Ti(Zr, Hf) to V(Ta) then to Cr(Mo, W), the bonding electron density between the central solute atom and its first neighbouring Nb atoms is increased and becomes more anisotropic, which indicates the strong interaction and thus enhances the elastic properties of Nb-Cr(Mo, W) alloys. Under uniaxial 〈100〉 tensile loading, alloyed elements with less (more) valence electrons decrease (increase) the ideal tensile strength.     

Structures and elastic properties of paraelectric and ferroelectric KTa0.5Nb0.5O3 from first-principles calculation

The structures, elastic properties and intrinsic hardness of B-O bonds of KTa_0.5Nb_0.5O₃ crystal in paraelectric and ferroelectric phase structures have been investigated by means of the density functional theory. Both structures are found to be elastically stable and in good agreement with available results. The elastic properties including the bulk modulus, shear modulus and Young’s modulus change largely during phase transition. The paraelectric KTa_0.5Nb_0.5O₃ crystal is more incompressible and harder than ferroelectric phase. The hardness of KTa_0.5Nb_0.5O₃ crystal is mostly determined by Nb-O bonds and the modifications of the bond strength affect the hardness of the crystal. Charge density contours indicate that the electronic distributions between B-O bonds play an important role in the formation of elastic properties.     

Electronic structure, phase stability, and hardness of the osmium borides, carbides, nitrides, and oxides: First-principles calculations

The chemical bonding, elastic behavior, phase stability, and hardness of OsB, OsB₂, OsC, OsO₂, OsN, and OsN₂ have been systematically studied using first-principles calculations. The calculation suggests that the chemical bonding in these compounds is a mixture of covalent and ionic components. The structural stability of OsB, OsC, and OsN can be understood in terms of the band filling of the bonding states, and the results indicate that the hexagonal tungsten carbide structure is more stable. The hardness of these osmium compounds is calculated using both ab initio and semiempirical model calculations. Analysis of the ab initio hardness suggested that the large occupations and high strength of the covalent bonds are crucial for a superhard material, and there is no clear connection between bulk modulus and hardness in these osmium compounds.     

Elastic,electronic and thermodynamic properties of fluoro-perovskite KZnF3 via first-principles calculations

The elastic, electronic and thermodynamic properties of fluoro-perovskite KZnF₃ have been calculated using the full-potential linearized augmented plane wave (FP-LAPW) method. The exchange-correlation potential is treated with the generalized gradient approximation of Perdew-Burke-Ernzerhof (GGA-PBE). Also, we have used the Engel and Vosko GGA formalism (GGA-EV) to improve the electronic band structure calculations. The calculated structural properties are in good agreement with available experimental and theoretical data. The elastic constants C _ij are calculated using the total energy variation with strain technique. The shear modulus, Young’s modulus, Poisson’s ratio and the Lamé coefficients for polycrystalline KZnF₃ aggregates are estimated in the framework of the Voigt-Reuss-Hill approximations. The ductility behavior of this compound is interpreted via the calculated elastic constants C _ij . Electronic and bonding properties are discussed from the calculations of band structure, density of states and electron charge density. The thermodynamic properties are predicted through the quasi-harmonic Debye model, in which the lattice vibrations are taken into account. The variation of bulk modulus, lattice constant, heat capacities and the Debye temperature with pressure and temperature are successfully obtained.