Theoretical investigation on the electronic structure, elastic properties, and intrinsic hardness of Si2N2O

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.     

The elastic behavior of dense C3N4 under high pressure: First-principles calculations

We have carried a detailed theoretical study on the geometry, density of states, elastic properties, sound velocities and Debye temperature of α-, β-, c- and p-C₃N₄ compounds under a maximum of pressure up to 100 GPa by using first principles calculations. The optimized lattice constants under zero pressure and zero temperature agreed well with the previous experimental and theoretical results. The band gaps of the four types of dense C₃N₄ were widened gradually with the increase of pressure. The calculated Poisson’s ratio γ and B/G values suggest α-, c- and p-C₃N₄ are brittle materials under 0–100 GPa, whereas β-C₃N₄ will become a ductile material as external pressure reaches 57 GPa. We found that the Debye temperature of the four dense C₃N₄ gradually reduces in the order of c-C₃N₄>p-C₃N₄>α-C₃N₄>β-C₃N₄ at 0 GPa and 0 K. However, the Debye temperature of c-C₃N₄ was lower than p-C₃N₄ when external pressure exceeds 6.3 GPa. It may hint that the results could be served as a valuable prediction for further experiments.     

A new superhard carbon allotrope: Orthorhombic C20

A new superhard carbon orthorhombic allotrope oC20 is proposed, which exhibits distinct topologies including C4, C3 and two types of C6 carbon rings. The calculated elastic constants and phonon spectra reveal that oC20 is mechanically and dynamically stable at ambient pressure. The calculated electronic band structure of oC20 shows that it is an indirect band gap semiconductor with a band gap of 4.46 eV. The Vickers hardness of oC20 is 75 GPa. The calculated tensile and shear strength indicate that the weakest tensile strength is 64 GPa and the weakest shear strength is 48 GPa, which means oC20 is a potential superhard material.     

Elastic property and intrinsic hardness of novel superhard ternary nitrides (CSi2N4 and SiC2N4)

In this work, the new ternary nitrides (CSi₂N₄ and SiC₂N₄) are designed by the substitution method. The structures, elastic properties, intrinsic hardness and Debye temperature of the new ternary nitrides (CSi₂N₄ and SiC₂N₄) are studied by first-principles calculations based on the density-functional theory. The elastic constants C_ij$C_{ij}$ of these new ternary nitrides are obtained using the stress–strain method. Derived elastic constants, such as bulk modulus, shear modulus, Young's modulus, Poisson coefficient and brittle/ductile behavior are estimated using Voigt–Reuss–Hill theories. The results indicate that γ-CSi₂N₄, p-CSi₂N₄ and p-SiC₂N₄ are mechanically stable. Calculated B/G$B/G$ values and Poisson's ratio for γ-CSi₂N₄, p-CSi₂N₄ and p-SiC₂N4 indicate that these materials are brittle. The calculated anisotropy parameters indicate that γ-CSi₂N₄ shows weak anisotropy and p-SiC₂N₄ and p-CSi₂N₄ have larger anisotropy. Based on the microscopic hardness model, p-CSi₂N₄, p-SiC₂N₄ and γ-CSi₂N₄ should be viewed as superhard materials with some peculiar mechanical properties.     

o-C8碳：新的超硬碳同素异形体

通过粒子群优化算法和密度泛函计算,证明了空间群为PMMA的正交晶系的碳同素异形体o-C₈是稳定的超硬相. 声子谱计算表明,o-C₈碳相是动力学稳定的;体积压缩计算表明,它是体模量为298.6 GPa的高度不可压缩材料. o-C₈相是一种新型的密度为2.993 g/cm³、维氏硬度为67.0 GPa的低密度超硬材料.     

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.     

Theoretical study on stability,mechanical properties and thermodynamic parameters of the orthorhombic-A2N2O (A=C,Si and Ge)

The structural stability, mechanical properties and thermodynamic parameters such as Debye temperature, minimum thermal conductivities of orthorhombic-A₂N₂O (A=C, Si and Ge) are calculated by first principles calculations based on density functional theory. The calculated lattice parameters, elastic constants of Si₂N₂O and Ge₂N₂O using PBEsol function are consisted with the experimental data and other calculated values. The full set elastic constants of the orthorhombic-A₂N₂O (A=C, Si and Ge) are calculated by stress–strain method. The mechanical moduli (bulk modulus, shear modulus and Young's modulus) are evaluated by the Voigt–Reuss–Hill approach. The orthorhombic-C₂N₂O exhibits larger mechanical moduli than the other two structures. The hardness of orthorhombic-A₂N₂O (A=C, Si and Ge) is evaluated according to the intrinsic hardness calculation theory of covalent crystal relying on Mulliken overlap population. The results indicate that the orthorhombic-C₂N₂O is a super hard material. Furthermore, the mechanical anisotropy, Debye temperature and minimum thermal conductivity of the orthorhombic-A₂N₂O (A=C, Si and Ge) have been estimated by empirical methods. The orthorhombic-Ge₂N₂O shows the lowest thermal conductivity, which may have useful applications as gas turbine engines and diesel engines.     

First-principles study on electronic structure and elastic properties of Fe16N2

We have performed first-principles study on structural stability, elastic properties and electronic structure of Fe₁₆N₂ by applying LSDA+U method. The calculated values of formation energy and reaction enthalpy for decomposition reaction indicate that Fe₁₆N₂ is a thermodynamically stable phase at the ground state. The six independent elastic constants are derived and the bulk modulus, Young's modulus, shear modulus, and Poisson's ratio are determined as 180 GPa, 199 GPa, 76 GPa and 0.32, respectively. The elastic constants meet all the mechanical stability criteria. The ductility of Fe₁₆N₂ is predicted by Pugh's criterion. The strong bonding between Fe and N atoms results in high values of elastic constants C₁₁ and C₃₃, and contributes to the strengthening of the Fe₁₆N₂ structural stability. The total and partial densities of states (DOS) suggest the existence of hybridization between N-p and Fe-d bands. The position of the Fermi level in DOS curve implies that Fe₁₆N₂ is a metastable phase.     

Mechanical properties,anisotropy and hardness of group IVA ternary spinel nitrides

In this work, new ternary cubic spinel structures are designed by the substitutional method. The structures, elasticity properties, intrinsic hardness and Debye temperature of the cubic ternary spinel nitrides are studied by first principles based on the density-functional theory. The results show that γ-CSn₂N₄, γ-SiC₂N₄, γ-GeC₂N₄ and γ-SnC₂N₄ are not mechanically stable. The elastic constants C_ij of these cubic spinel structures are obtained using the stress–strain method. Derived elastic constants, such as bulk modulus, shear modulus, Young's modulus, Poisson coefficient and brittle/ductile behaviour are estimated using Voigt–Reuss–Hill theories. The B/G value, the Poisson's ratio and anisotropic factor are calculated for eight ternary stable crystals. Based on the microscopic hardness model, we further estimate the Vickers hardness of all the stable crystals. From the calculated hardness of the stable group IVA ternary spinel nitrides by Gao's and Jiang's methods, it is observed that the stable group IVA ternary spinel nitrides are not superhard materials except for γ-CSi₂N₄. Furthermore, the Debye temperature for the eight stable crystals is also estimated.     

Infrared crystal spectra of C2H4, C2D4, and as-C2H2D2 and the general harmonic force field of ethylene

Carbon-13 frequency shifts for C₂H₄, C₂D₄, and as-C₂H₂D₂ have been measured in isotopic solid solutions in crystalline films at 60 K. All but two of the shifts (for as-C₂H₂D₂) are compatible with recently determined ζ data for C₂H₄, with ¹³C frequency shifts for C₂H₄ and C₂D₄ in the gas phase and with conventional frequency data. Together, these data completely determine with precision all 18 parameters of the GHFF for ethylene, the previous ambiguity in choice between two sets of A_g species force constants being removed. The force field reproduces closely the observed centrifugal distortion constants for C₂H₄, a ζ constant observed for trans-C₂H₂D₂, and the inertia defects for C₂H₄, C₂D₄, and as-C₂H₂D₂. Vibration and rotation constants for all isotopically deuterated ethylenes are calculated.Possible explanations for the two anomalous crystal shifts in as-C₂H₂D₂ involve the effects of the crystal field, and failure of the use of Dennison's rule for making anharmonic corrections to the shifts. The former explanation is preferred as a result of thorough analysis of the anharmonicity constants for as-C₂H₂D₂ determined from many overtone and combination bands in the gas and crystal spectra.     

Elastic moduli of nc-TiN/a-Si3N4 nanocomposites: Compressible, yet superhard

Earlier measurements of elastic moduli of nc-TiN/a-Si₃N₄ nanocomposites of different composition and hardness by means of vibrating reed and surface Brillouing scattering, that yield Young’s and shear modulus, as well as the Poisson’s ratio, have been confirmed by high-pressure X-ray diffraction measurements, that yield bulk modulus. It is found that elastic moduli of all measured samples are essentially the same within relatively small error of measurements, and only slightly lower than that of pure TiN. The nanocomposites are superhard thanks to their unique nanostructure with strengthened SiN_x interface.     

Ab initio study of phase stability,thermodynamic and elastic properties of C3N2 derived from cubic C20

In this work, we report a quite different conclusion from Tian et al. [Phys. Rev. B 78 (2008) 235431]. It is proved that β-C₃N₂ is the only phase under high pressure, and α-C₃N₂ does not exist. β-C₃N₂ is a covalent crystal composed of strong CC and CN covalent bonds. Band gap of β-C₃N₂ increases with pressure. The width of antibonding state, shown in partial density of states (PDOS), keeps about 5 eV with rising pressures, which brings stable CN or CC covalent bonds. At sufficiently low temperatures, heat capacity (C_v) is proportional to T³; and at intermediate temperatures, C_v is governed by the details of vibrations of the atoms; finally, C_v reaches to β-C₃N₂'s Dulong–Pettit limit (about 120 J/mol K). Though thermal expansion coefficient (α) increases with temperature, α is less than 1×10⁻⁵ K⁻¹. Elastic constants rise with pressure, but shear moduli is quite steady which increases just a little with pressures.     

Structural,mechanical, and electronic properties of P21/m-Carbon✰

The structural, mechanical, and electronic properties of P2₁/m-carbon were comprehensively investigated by using first principles calculations. Our calculated structure parameters are in good agreement with the previous theoretical values. P2₁/m-carbon consists of 10 atoms in a unit cell and is made of an exclusively sp³ hybridized bonding network. The calculated phonon spectra and elastic constant verify that P2₁/m-carbon is dynamically and mechanically stable at ambient pressure. The analysis of the electronic band structure reveals that P2₁/m-carbon is an insulator with a band gap of 5.47 eV. It has a large bulk moduli of 398 GPa and a high shear moduli of 457 GPa. Further mechanical properties demonstrate that P2₁/m-carbon is prone to be ductile and possesses a high Vickers hardness value of 82.3 GPa. These values show that P2₁/m-carbon simultaneously possesses ultra-incompressible and the superhard property. Furthermore, the X-ray diffraction spectra is also theoretically simulated to provide more structure information for future experimental observations.     

Mechanical properties and electronic structure of TiC,Ti0.75W0.25C,Ti0.75W0.25C0.75N0.25, TiC0.75N0.25 and TiN

The first-principles calculations are performed to investigate the mechanical properties and electronic structure of TiC, Ti_0.75W_0.25C, Ti_0.75W_0.25C_0.75N_0.25, TiC_0.75N_0.25 and TiN. Density functional theory and ultrasoft pseudopotentials are used in this study. From the formation energy, it is found that nitrogen can increase the stability of TiC. The calculated elastic constants and elastic moduli of TiC compare favorably with other theoretical and experimental values. Tungsten and nitrogen are observed to significantly increase the bulk, shear and Young's modulus of TiC. Through the analysis of B/G and Cauchy pressure, tungsten can significantly improve the ductility of TiC. The electronic structure of TiC, TiN, Ti_0.75W_0.25C, Ti_0.75W_0.25C_0.75N_0.25, and TiC_0.75N_0.25 are used to describe nonmetal–metal and metal–metal bonds. Based on the Mulliken overlap population analysis, the hardness values of TiC, Ti_0.75W_0.25C, Ti_0.75W_0.25C_0.75N_0.25, TiC_0.75N_0.25 and TiN are estimated.     

Mechanical properties of superhard diamondlike BC5

Using first-principles calculations, we systematically studied the mechanical properties and electronic structure of the recently synthesized diamondlike BC₅. Our calculated bulk modulus B, shear modulus G, elastic constant c₄₄, and theoretical hardness H confirm that BC₅ is an ultraincompressible and superhard material. Also, it exhibits mechanical stability and metallic features. Electronic structures show that a strong covalent bond network through sp³ hybridization is the origin of the excellent mechanical properties of BC₅. Our results show that BC₅ has good prospects in electronic application as a superhard material.     

InBO3 and ScBO3 at high pressures: An ab initio study of elastic and thermodynamic properties

We have theoretically investigated the elastic properties of calcite-type orthoborates ABO₃ (A=Sc and In) at high pressure by means of ab initio total-energy calculations. From the elastic stiffness coefficients, we have obtained the elastic moduli (B, G and E), Poisson's ratio (ν), B/G ratio, universal elastic anisotropy index (A_U), Vickers hardness, and sound wave velocities for both orthoborates. Our simulations show that both borates are more resistive to volume compression than to shear deformation (B>G). Both compounds are ductile and become more ductile, with an increasing elastic anisotropy, as pressure increases. We have also calculated some thermodynamic properties, like Debye temperature and minimum thermal conductivity. Finally, we have evaluated the theoretical mechanical stability of both borates at high hydrostatic pressures. It has been found that the calcite-type structure of InBO₃ and ScBO₃ becomes mechanically unstable at pressures beyond 56.2 and 57.7 GPa, respectively.     

Structural, elastic and electronic properties of a new ternary-layered Ti2SiN

The structural, elastic and electronic properties of Ti₂SiN were studied by first-principle calculations. The calculated bond lengths of Ti-Si and Ti-C are 2.65 and 2.09 Å, respectively. The results show Ti₂SiN is mechanically stable, and its bulk modulus B, shear modulus G, Young's modulus E, Poisson's ratio μ and anisotropy factor A are determined to be 182 GPa, 118 GPa, 291 GPa, 0.233 and 1.57, respectively. The calculated electronic structure indicates that Ti₂SiN is anisotropic and conductive.     

Investigation of tetragonal ReN2 and WN2 with high shear moduli from first-principles calculations

Two new transition metal dinitrides, ReN₂ and WN₂, with the P4/mmm structure are investigated by the first-principles calculations. The computed shear moduli of 327 GPa for ReN₂ and 334 GPa for WN₂ exceed those of all transition metal dinitrides previously reported. The estimated theoretical hardness are 46.3 GPa for ReN₂ and 47.9 GPa for WN₂, respectively. The calculated high shear moduli and hardness indicate that they are potential ultrahard materials. It is important to note that the computed hardness of the weakest bond are 34.7 GPa (W-N) for WN₂ and 33.1 GPa (Re-N) for ReN₂, much higher than that of 21.1 GPa (Re-B) for ReB₂, which suggests that tetragonal ReN₂ and WN₂ are probably harder than ReB₂. The total and partial electron density of states and the electron localization function for ReN₂ and WN₂ are analyzed. We attribute the high bulk modulus, shear modulus, and hardness to a three-dimensional covalently bonded framework in tetragonal ReN₂ and WN₂. Our calculations show that tetragonal ReN₂ is expected to be synthesized above 62.7 GPa and tetragonal WN₂ may be hard to be synthesized.     

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.     

First-principles investigation on vibrational,anisotropic elastic and thermodynamic properties for L12 structure of Al3Er and Al3Yb under high pressure

To better clarify the physical properties for Al₃RE precipitates, first-principles calculations are performed to investigate the vibrational, anisotropic elastic and thermodynamic properties of Al₃Er and Al₃Yb. The calculated results agree well with available experimental and theoretical ones. The vibrational properties indicate that Al₃Er and Al₃Yb will keep their dynamical stabilities with L1₂ structure up to 100 GPa. The elastic constants are satisfied with mechanical stability criteria up to the external pressure of 100 GPa. The mechanical anisotropy is predicted by anisotropic constants A^G, A^U, A^Z and 3D curved surface of Young’s modulus. The calculated results show that both Al₃Er and Al₃Yb are isotropic at zero pressure and obviously anisotropic under high pressure. Further, we systematically investigate the thermodynamic properties and provide the relationships between thermal parameters and pressure. Finally, the pressure-dependent behaviours of density of states, Mulliken charge and bond length are discussed.