First principles studies on the elastic,thermodynamic properties and electronic structure of Ti15−xMoxSn compounds

The structural, elastic, thermodynamic and electronic properties of the Ti_15−xMo_xSn compounds were systematically investigated by means of first-principles calculations based on the density functional theory (DFT). The calculated results demonstrate the Ti_15−xMo_xSn compounds still remain the stable β phase structure. The calculation of cohesive energy shows that the structural stability of the Ti_15−xMo_xSn compounds increases apparently with the increase of Mo content. According to Hooke's law, the single crystal elastic constants were obtained and show that all the calculated compounds keep mechanical stability. Then the bulk modulus B, shear modulus G, Young's modulus E and Poisson's ratio ν of polycrystalline aggregates were calculated at zero pressure. The calculated results show that among these Ti_15−xMo_xSn compounds, Ti₄Mo₁₁Sn exhibits the largest stiffness while Ti₁₂Mo₃Sn shows the greatest ductility. The compounds Ti₁₂Mo₃Sn and Ti₁₁Mo₄Sn with the two lowest elastic Young's modulus of 61.01 GPa and 65.59 GPa are expected to be promising metallic biomaterials for implant applications. Besides, the Debye temperature Θ_D and the electronic density of states (DOS) are also investigated and discussed.     

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.     

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.     

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.     

First-principles study of elastic and electronic properties of layered ternary nitride SrZrN2 under pressure

The structural, elastic, and electronic properties of SrZrN₂ under pressure up to 100?GPa have been carried out with first-principles calculations based on density functional theory. The calculated lattice parameters at 0?GPa and 0?K by using the GGA-PW91-ultrasoft method are in good agreement with the available experimental data and other previous theoretical calculations. The pressure dependence of the elastic constants and the elastic-dependent properties of SrZrN₂, such as bulk modulus B, shear modulus G, Young's modulus E, Debye temperature Θ, shear and longitudinal wave velocity V_S and V_L, are also successfully obtained. It is found that all elastic constants increase monotonically with pressure. When the pressure increases up to 140?GPa, the obtained elastic constants do not satisfy the mechanical stability criteria and a phase transition might has occurred. Moreover, the anisotropy of the directional-dependent Young's modulus and the linear compressibility under different pressures are analysed for the first time. Finally, the pressure dependence of the total and partial densities of states and the bonding property of SrZrN₂ are also investigated.     

Ab initio study of ultra-incompressible ternary BeCN2 polymorph

The structural, mechanical, thermodynamic, and electronic properties calculated by projector-augmented wave method are presented for BeCN₂ in chalcopyrite and wurtzite-like structures. The calculated high bulk modulus (321 and 309 GPa) and large shear modulus (302 and 298 GPa) suggest that they are ultra-incompressible and hard materials. The ultra-incompressibility is attributed to a stacking of strongly three-dimensional covalent bonded CN₄ and BeN₄ tetrahedrons connected by corners. Thermodynamic study demonstrates that these two structures can be synthesized at ambient condition. Furthermore, the structural transformation from the wurtzite-like to the chalcopyrite phase was predicted at about 17 GPa according to the enthalpy difference calculations.     

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.     

Theoretical investigation on structural, magnetic and electronic properties of ferromagnetic GdN under pressure

The tight-binding linear muffin tin orbital (TB-LMTO) method within the local density approximation is used to calculate structural, electronic and magnetic properties of GdN under pressure. Both nonmagnetic (NM) and magnetic calculations are performed. The structural and magnetic stabilities are determined from the total energy calculations. The magnetic to ferromagnetic (FM) transition is not calculated. Magnetically, GdN is stable in the FM state, while its ambient structure is found to be stable in the NaCl-type (B₁) structure. We predict NaCl-type to CsCl-type structure phase transition in GdN at a pressure of 30.4 GPa. In a complete spin of FM GdN the electronic band picture of one spin shows metallic, while the other spin shows its semiconducting behavior, resulting in half-metallic behavior at both ambient and high pressures. We have, therefore, calculated electronic band structures, equilibrium lattice constants, cohesive energies, bulk moduli and magnetic moments for GdN in the B₁ and B₂ phases. The magnetic moment, equilibrium lattice parameter and bulk modulus is calculated to be 6.99 μ_B, 4.935 Å and 192.13 GPa, respectively, which are in good agreement with the experimental results.     

Phase stability,elastic, electronic,thermal and optical properties of Ti3Al1−xSixC2 (0≤x≤1): First principle study

The structural parameters with stability upon Si incorporation and elastic, electronic, thermodynamic and optical properties of Ti₃Al_1−xSi_xC₂ (0≤x≤1) are investigated systematically by the plane wave pseudopotential method based on the density functional theory (DFT). The increase of some elastic parameters with increasing Si-content renders the alloys to possess higher compressive and tensile strength. The Vickers hardness value obtained with the help of Mulliken population analysis increases as x is increased from 0 to 1. The solid solutions considered are all metallic with valence and conduction bands, which have a mainly Ti 3d character, crossing the Fermi level. The temperature and pressure dependences of bulk modulus, normalized volume, specific heats, thermal expansion coefficient, and Debye temperature are all obtained through the quasi-harmonic Debye model with phononic effects for T=0−1000 K and P=0−50 GPa. The obtained results are compared with other results available. Further an analysis of optical functions for two polarization vectors reveals that the reflectivity is high in the visible–ultraviolet region up to ∼10.5 eV region showing promise as a good coating material.     

Structural,mechanical and thermal properties of some Holmium Pnictides under pressure: A theoretical approach

The high pressure structural, elastic and thermal properties of holmium pnictides HoX (X=N, P, As and Bi) were investigated theoretically by using an inter-ionic potential theory with modified ionic charge parameter. We have predicted a structural phase transition from NaCl (B₁) to CsCl (B₂)-type structure at pressure of 139 GPa for HoN, 52 GPa for HoP, 44 GPa for HoAs and 26 GPa for HoBi. Other properties, such as lattice constant, bulk modulus, cohesive energy, second and third-order elastic constants were calculated and compared with the available experimental and theoretical data. In order to gain further information the brittle behaviour of these compounds was observed. Some other properties like Shear modulus (G), Young's modulus (E), Poisson's ratio (ν), anisotropy factor (A), sound velocities, Debye temperature (θ_D) were calculated. The variation of elastic constants (C₁₁ and C₄₄) and Debye temperature (θ_D) with pressure was also presented.     

Structural,elastic and mechanical properties of orthorhombic SrHfO3 under pressure from first-principles calculations

Structural, elastic and mechanical properties of orthorhombic SrHfO₃ under pressure have been investigated using the plane-wave ultrasoft pseudopotential technique based on the first-principles density functional theory. The calculated equilibrium lattice parameters and elastic constants of orthorhombic SrHfO₃ at zero pressure are in good agreement with the available experimental and calculational values. The lattice parameters, total enthalpy, elastic constants and mechanical stability of orthorhombic SrHfO₃ as a function of pressure were studied. With the increasing pressure, the lattice parameters and volume of orthorhombic SrHfO₃ decrease whereas the total enthalpy increases. Orthorhombic SrHfO₃ is mechanically stable with low pressure (<52.9 GPa) whereas that is mechanically instable with high pressure (>52.9 GPa). The bulk modulus, shear modulus, Young's modulus and mechanical anisotropy of orthorhombic SrHfO₃ as a function of pressure were analyzed. It is found that orthorhombic SrHfO₃ under pressure has larger bulk modulus, better ductility and less mechanical anisotropy than orthorhombic SrHfO₃ at 0 GPa.     

Crystal structure and compressibility of a high-pressure Ti-rich oxide, (Ti0.50Zr0.26Mg0.14Cr0.10)O1.81, isomorphous with cubic zirconia

A Ti-rich oxide, (Ti_0.50Zr_0.26Mg_0.14Cr_0.10)_∑=1.0O_1.81, was synthesized at 8.8 GPa and 1600 °C using a multi-anvil apparatus. Its crystal structure at ambient conditions and compressibility up to 10.58 GPa were determined with single-crystal X-ray diffraction. This high-pressure phase is isomorphous with cubic zirconia (fluorite-type) with space group Fm3¯m and unit-cell parameters a=4.8830(5) Å and V=116.43(4) Å³. Like stabilized cubic zirconia, the structure of (Ti_0.50Zr_0.26Mg_0.14Cr_0.10)O_1.81 is also relaxed, with all O atoms displaced from the (, , ) position along 〈1 0 0〉 by 0.319 Å and all cations from the (0, 0, 0) position along 〈1 1 1〉 by 0.203 Å. No phase transformation was detected within the experimental pressure range. Fitting the high-pressure data (V vs. P) to a third-order Birch-Murnaghan EOS yields K₀=164(4) GPa, K′=4.3(7), and V₀=116.38(3) Å³. The bulk modulus of (Ti_0.50Zr_0.26Mg_0.14Cr_0.10)O_1.81 is significantly lower than that (202 GPa) determined experimentally for cubic TiO₂ or that (~210 GPa) estimated for cubic ZrO₂. This study demonstrates that cubic TiO₂ may also be obtained by introducing various dopants, similar to the way cubic zirconia is stabilized below 2370 °C. Furthermore, (Ti_0.50Zr_0.26Mg_0.14Cr_0.10)O_1.81 has the greatest ratio of Ti⁴⁺ content vs. vacant O²⁻ sites of all doped cubic zirconia samples reported thus far, making it a more promising candidate for the development of electrolytes in solid oxide fuel cells.     

Structural, electronic and thermodynamic properties of cubic Zn3N2 under high pressure from first-principles calculations

The structural, electronic and thermodynamic properties of cubic Zn₃N₂ under hydrostatic pressure up to 80 GPa are investigated using the local density approximation method with pseudopotentials of the ab initio norm-conserving full separable Troullier-Martin scheme in the frame of density functional theory. The structural parameters obtained at ambient pressure are in agreement with experimental data and other theoretical results. The change of bond lengths of two different types of Zn-N bond with pressure suggests that the tetrahedral Zn-N bond is slightly less compressible than the octahedral bond. By fitting the calculated band gap, the first and second order pressure coefficients for the direct band gap ofthe Zn₃N₂ were determined to be 1.18×10⁻² eV/GPa and −2.4×10⁻⁴ eV/(GPa)², respectively. Based on the Mulliken population analysis, Zn₃N₂ was found to have a higher covalent character with increasing pressure. As temperature increases, heat capacity, enthalpy, product of temperature and entropy increase, whereas the Debye temperature and free energy decrease. The present study leads to a better understanding of how Zn₃N₂ materials respond to compression.     

Investigations on structural,elastic, thermodynamic and electronic properties of TiN,Ti2N and Ti3N2 under high pressure by first-principles

The lattice parameters, cell volume, elastic constants, bulk modulus, shear modulus, Young's modulus and Poisson's ratio are calculated at zero pressure, and their values are in excellent agreement with the available data, for TiN, Ti₂N and Ti₃N₂. By using the elastic stability criteria, it is shown that the three structures are all stable. The brittle/ductile behaviors are assessed in the pressures from 0 GPa to 50 GPa. Our calculations present that the performances for TiN, Ti₂N and Ti₃N₂ become from brittle to ductile with pressure rise. The Debye temperature rises as pressure increase. With increasing N content, the enhancement of covalent interactions and decline of metallicity lead to the increase of the micro-hardness. Their constant volume heat capacities increase rapidly in the lower temperature, at a given pressure. At higher temperature, the heat capacities are close to the Dulong–Petit limit, and the heat capacities of TiN and Ti₂N are larger than that of c-BN. The thermal expansion coefficients of titanium nitrides are slightly larger than that of c-BN. The band structure and the total Density of States (DOS) are calculated at 0 GPa and 50 GPa. The results show that TiN and Ti₂N present metallic character. Ti₃N₂ present semiconducting character. The band structures have some discrepancies between 0 GPa and 50 GPa. The extent of energy dispersion increases slightly at 50 GPa, which means that the itinerant character of electrons becomes stronger at 50 GPa. The main bonding peaks of TiN, Ti₂N and Ti₃N₂ locate in the range from −10 to 10 eV, which originate from the contribution of valance electron numbers of Ti s, Ti p, Ti d, N s and N p orbits. We can also find that the pressure makes that the total DOS decrease at the Fermi level for Ti₂N. The bonding behavior of N–Ti compounds is a combination of covalent and ionic nature. As N content increases, valence band broadens, valence electron concentration increases, and covalent interactions become stronger. This is reflected in shortening of Ti–N bonds.     

Elasticity of single-crystal phase D (a dense hydrous magnesium silicate) by Brillouin spectroscopy

Phase D (MgSi₂O₆H₂) is the only hydrous magnesium silicate, where all Si atoms are octahedrally coordinated. The single-crystal elastic constants of phase D have been measured by Brillouin spectroscopy at ambient conditions. The elastic constants C₁₁, C₃₃, C₄₄, C₁₂, C₁₃ and C₁₄, based on a trigonal unit cell, are 284.4±3.0, 339.4±9.1, 120.7±1.9, 89.4±4.2, 126.6±3.1 and −4.7±1.4 GPa, respectively. The aggregate adiabatic bulk modulus, using the Voigt-Reuss-Hill (VRH) scheme, is 175.3±14.8 GPa and the shear modulus is 104.4±13.6 GPa. These data yield the compressional-wave velocity, V_p=9.70±0.51 km/s, and the shear-wave velocity, V_s=5.59±0.36 km/s, at ambient conditions. Thus, phase D is not only the most closely packed but the least compressible hydrous magnesium silicate known to date.     

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 studies of the electronic and elastic properties of Ti2GeC

We have performed first-principles studies on electronic structure and elastic properties of Ti₂GeC. The calculated band structure shows that this compound is electrical conductor. From the pressure dependence of elastic constants, we find that Ti₂GeC is most stable in the pressure range from 0 to 100 GPa. The strong Ti 3d, Ge 4p and C 2p hybridization may stabilize the structure of Ti₂GeC. By analyzing the ratio between the bulk and shear moduli, we conclude that Ti₂GeC is brittle in nature, and the brittleness of Ti₂GeC originated from the large value of Ti atom occupying the internal parameter z.     

Elasticity, electronic structure, chemical bonding and optical properties of monoclinic ZrO2 from first-principles

Structural parameters as well as elastic, electronic, bonding and optical properties of monoclinic ZrO₂ were investigated using the plane-wave ultrasoft pseudopotential technique based on the first-principles density-functional theory (DFT). The calculated structural properties and independent elastic constants of monoclinic ZrO₂ are in favorable agreement with previous work. We have derived the bulk and shear moduli, Young’s modulus and Poisson coefficients for monoclinic ZrO₂ and estimated the Debye temperature of monoclinic ZrO₂ from acoustic velocity. Electronic and bonding properties are studied from the calculation of band structure, densities of states and charge densities. Furthermore, in order to clarify the mechanism of optical transitions in monoclinic ZrO₂, the dielectric functions are calculated and analyzed by means of the electronic structure, which shows significant optical anisotropy in the components of polarization directions (1 0 0), (0 1 0) and (0 0 1).     

Characterization of Zr-Si-N films deposited by cathodic vacuum arc with different N2/SiH4 flow rates

Zr-Si-N films were deposited on silicon and steel substrates by cathodic vacuum arc with different N₂/SiH₄ flow rates. The N₂/SiH₄ flow rates were adjusted at the range from 0 to 12 sccm. The films were characterized by X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS), scanning electron microscope (SEM), hardness and wear tests. The structure and the mechanical properties of Zr-Si-N films were compared to those of ZrN films. The results of XRD and XPS showed that Zr-Si-N films consisted of ZrN crystallites and SiN_x amorphous phase. With increasing N₂/SiH₄ flow rates, the orientation of Zr-Si-N films became to a mixture of (1 1 1) and (2 0 0). The column width became smaller, and then appeared to vanish with the increase in N₂/SiH₄ flow rates. The hardness and Young's modulus of Zr-Si-N films increased with the N₂/SiH₄ flow rates, reached a maximum value of 36 GPa and 320 GPa at 9 sccm, and then decreased 32 GPa and 305 GPa at 12 sccm, respectively. A low and stable of friction coefficient was obtained for the Zr-Si-N films. Friction coefficient was about 0.1.     

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.