First-principles study on alloying stability, electronic structure, and mechanical properties of Al-based intermetallics

First-principles calculations were performed to study on alloying stability, electronic structure, and mechanical properties of Al-based intermetallic compounds (AlCu₃, AlCu₂Zr, and AlZr₃). The calculated results show that the lattice parameters obtained after full relaxation of crystalline cells are consistent with experimental data. The calculation of cohesive energies indicated that the structure stability of these Al-based intermetallics will become higher with increasing Zr element in crystal. The calculations of formation energies showed that AlCu₂Zr has the strongest alloying ability, followed by AlZr₃ and finally the AlCu₃. The further analysis find out that single-crystal elastic constants at zero-pressure satisfy the requirement of mechanical stability for cubic crystals. The calculations on the ratio of bulk modulus to shear modulus reveal that AlCu₂Zr can exhibit a good ductility, followed by AlCu₃, whereas AlZr₃ can have a poor ductility; however, for stiffness, these intermetallics show a converse order. The calculations on Poisson's ratio show that AlCu₃ is much more anisotropic than the other two intermetallics. In addition, calculations on densities of states indicate that the valence bonds of these intermetallics are attributed to the valence electrons of Cu 3d states for AlCu₃, Cu 3d, and Zr 4d states for AlCu₂Zr, and Al 3s, Zr 5s and 4d states for AlZr₃, respectively; in particular, the electronic structure of the AlZr₃ shows the strongest hybridization, leading to the worst ductility.     

Structural, elastic and electronic properties of transition metal carbides TMC (TM=Ti, Zr, Hf and Ta) from first-principles calculations

The structural, elastic and electronic properties of TiC, ZrC, HfC and TaC have been investigated by first-principles calculations using the plane-wave pseudopotential method. Different exchange-correlation functionals regarding the local density approximation and the PBE, RPBE and PW91 forms of generalized gradient approximation are taken into account. The NaCl-type cubic structures of TMC (TM=Ti, Zr, Hf and Ta) are optimized and confirmed to be mechanically stable. The elastic properties such as the elastic constants, bulk modulus, shear modulus, Young’s modulus and Poisson’s ratio of TMC are investigated, and the performances of LDA and GGA are discussed. The electronic density of state, electron charge density and Mulliken population analysis have been explored to discuss the electronic properties and bonding behaviors of TMC. The present calculation results compare satisfactorily with the experimental data and previous theoretical calculations.     

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.     

Prediction study of structural and elastic properties under pressure effect of M2SnC (M=Ti, Zr, Nb, Hf)

Using first-principles calculations, we have studied the structural and elastic properties of M₂SnC, with M=Ti, Zr, Nb and Hf. Geometrical optimization of the unit cell is in good agreement with the available experimental data. The effect of high pressures, up to 20 GPa, on the lattice constants shows that the contractions along the a-axis were higher than those along the c-axis. We have observed a quadratic dependence of the lattice parameters versus the applied pressure. The elastic constants and their pressure dependence are calculated using the static finite strain technique. A linear dependence of the elastic stiffnesses on the pressure is found. We derived the bulk and shear moduli, Young's moduli and Poisson's ratio for ideal polycrystalline M₂SnC aggregates. We estimated the Debye temperature of M₂SnC from the average sound velocity. This is the first quantitative theoretical prediction of the elastic properties of Ti₂SnC, Zr₂SnC, Nb₂SnC, and Hf₂SnC compounds.     

Structural, electronic and elastic properties of M2SC (M = Ti, Zr, Hf) compounds

Using ab initio calculations, we have studied the structural, electronic and elastic properties of M₂SC, with M = Ti, Zr and Hf. Geometrical optimization of the unit cell are in good agreement with the available experimental data. The band structures show that all three materials are conducting. The analysis of the site and momentum projected densities shows that the bonding is achieved through a hybridization of M-atom d states with S and C-atom p states. The Md-Sp bonds are lower in energy and are stiffer than Md-Cp bonds. The elastic constants are calculated using the static finite strain technique. We derived the bulk and shear moduli, Young's moduli and Poisson's ratio for ideal polycrystalline M₂SC aggregates. We estimated the Debye temperature of M₂SC from the average sound velocity. This is a quantitative theoretical prediction of the elastic properties of Ti₂SC, Zr₂SC, and Hf₂SC compounds, and it still awaits experimental confirmation.     

A first-principle study of Os-based compounds: Electronic structure and vibrational properties

The electronic structure, elastic, and phonon properties of OsM (M=Hf, Ti, Y and Zr) compounds are studied using first-principles calculations. Elastic constants of OsY and specific heat capacity of OsM (M=Hf, Ti, Y, and Zr) are reported for the first time. The predicted equilibrium lattice constants are in excellent agreement with experiment. The calculated values of bulk moduli are considerably high but are much smaller than that of Osmium, which is around 400 GPa. The phase stability of the OsM (M=Hf, Ti, Y and Zr) compounds were studied by DOS calculations and the results suggest that OsY is unstable in the B2 phase. The brittleness and ductility properties of OsM (M=Hf, Ti, Y and Zr) are determined. OsM (M=Hf, Ti, Y and Zr) compounds are predicted to be ductile materials. The electronic structure and phonon frequency curves of OsM (M=Hf, Ti, Y and Zr) compounds are obtained. The position of Fermi level of these systems was calculated and discussed in terms of the pseudo gaps. The finite and small DOS at the Fermi level 0.335, 0.375, 1.063, and 0.383 electrons/eV for OsHf, OsTi, OsY, and OsZr, respectively, suggest that OsM (M=Hf, Ti, Y and Zr) compounds are weak metals.     

Structural, electronic and elastic properties of Ti2TlC, Zr2TlC and Hf2TlC

Using First-principle calculations, we have studied the structural, electronic and elastic properties of M₂TlC, with M = Ti, Zr and Hf. Geometrical optimization of the unit cell is in good agreement with the available experimental data. The effect of high pressures, up to 20 GPa, on the lattice constants shows that the contractions are higher along the c-axis than along the a axis. We have observed a quadratic dependence of the lattice parameters versus the applied pressure. The band structures show that all three 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-Tl p hybridizations. The M d-C p bonds are lower in energy and stiffer than M d-Tl p bonds. The elastic constants are calculated using the static finite strain technique. We derived the bulk and shear moduli, Young’s modulus and Poisson’s ratio for ideal polycrystalline M₂TlC aggregates. We estimated the Debye temperature of M₂TlC from the average sound velocity. This is the first quantitative theoretical prediction of the elastic properties of Ti₂TlC, Zr₂TlC, and Hf₂TlC compounds that requires experimental confirmation.      

三元层状陶瓷M-Al-N(M=Ti,Zr,Hf)的结构及力学性质的第一性原理模拟

基于第一性原理方法，探索M-Al-N（M=Ti，Zr，Hf）结构的稳定性，计算其力学性质.计算M-Al-N化合物的能量，发现除实验已知的结构Ti₂AlN和Ti₄AlN₃、Zr₂AlN、Hf₂AlN外，还存在两种新的热力学稳定结构Zr₄AlN₃、Hf₄AlN₃.弹性常数和声子谱的计算，表明这两个结构是力学稳定和晶格动力学稳定的.计算M₂AlN和M₄AlN₃的力学性质，发现它们具有高的体模量、剪切模量、弹性模量、维氏硬度等；分析其力学性质随组分比例、组成元素的变化规律，为该类材料的选择和应用提供理论依据.最后计算M₂AlN和M₄AlN₃的电子态密度和分态密度、电子密度分布、Mulliken群分析等.     

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.     

Calculated elastic properties of M2AlC (M=Ti, V, Cr, Nb and Ta)

M₂AlC phases, where M is a transition metal, are layered ternary compounds that possess unusual properties. In this paper, we have calculated the elastic properties of M₂AlC, with M=Ti, V, Cr, Nb and Ta, by means of ab initio total energy calculations using the projector augmented-wave method. We have derived the bulk and shear moduli, Young's moduli and Poisson's ratio for ideal polycrystalline M₂AlC aggregates. We have estimated the elastic modulus of Cr₂AlC with 357.7 GPa while the values of all other phases are in the range 309±10 GPa. We suggest that this can be understood based on the calculated bond energies for the M-C bonds. Furthermore, our results indicate a profound elastic anisotropy of M₂AlC even compared to materials with a well-established anisotropic character such as α-alumina. Finally, we have estimated the Debye temperatures of M₂AlC from the average sound velocity.     

Structural,elastic and electronic properties of ACTi3 (A=Al,In and Tl) antiperovskite

First principle calculations were performed to investigate the structural, elastic and electronic properties of unexplored antiperovskite ACTi₃, with A=Al, In and Tl. The calculated structural parameters were found to be in good agreement with the available experimental data, with deviations being less than 2.7%. The bulk modulus was found to be equal to 155 GPa for AlCTi₃ and to a value 5% lower, 147 GPa, for TlCTi₃. For values of applied pressures up to 40 GPa, elastic moduli were calculated and the mechanical stability criteria were verified. The band structure of these compounds has been found to display a metallic character, with strong ionic–covalent bonds between Ti and C atoms, and ionic bonds along A and Ti atoms. The overlap population analysis showed that the stiffness decreases with an increase in the antibonding state between Ti and A atoms.     

The first principle study of magnetic properties of Mn2WSn,Fe2YSn (Y=Ti,V), Co2YSn (Y=Ti,Zr, Hf,V, Mn) and Ni2YSn (Y=Ti,Zr, Hf,V, Mn) heusler alloys

The spin polarized electronic band structures, density of states (DOS) and magnetic properties of Mn₂WSn, Fe₂YSn (Y=Ti, V), Co₂YSn (Y=Ti, Zr, Hf, V, Mn) and Ni₂YSn (Y=Ti, Zr, Hf, V, Mn) huesler compounds are reported. The calculations are performed by using full-potential linearized augmented plane wave method (FP-LAPW) within density functional theory. The magnetic trend in these compounds is studied using values of magnetic moments, exchange interaction and calculated band gap. The results reveal that Mn₂WSn and Ni₂VSn show 100% spin polarization, Co₂YSn (Y=Ti, Zr, Hf, Mn), Fe₂YSn (Y=Ti, V), and Ni₂MnSn exhibit metallic nature and Ni₂YSn (Y=Ti, Zr, Hf) and Co₂VSn show semi-conducting behavior.     

金属氢化物力学性能的第一性原理研究

采用第一性原理方法详细研究了氟化钙结构的多种金属氢化物MH₂ (M= La, Nd, Gd, Tb, Y, Dy, Ho, Er, Lu, Sc, Ti, Zr, Hf)的力学性质(弹性常数、体弹模量、剪切模量、杨氏模量).计算结果表明, MH₂ (M= La, Nd, Gd, Tb, Y, Dy, Ho, Er, Lu, Sc)在低温下具有稳定的氟化钙结构,其抵抗体积形变, 切应变和拉伸(或压缩)形变的能力从LaH₂, NdH₂, GdH₂, TbH₂, YH₂, DyH₂, HoH₂, ErH₂, LuH₂到ScH₂逐次递增, 而MH₂ (M= Ti, Zr, Hf)在低温下的氟化钙结构不稳定.通过对两种稳定的氢化物(TbH₂, ErH₂) 和两种不稳定的氢化物(TiH₂, HfH₂)的电子态密度以及差分电荷密度进行对比, 发现它们的稳定性与金属和氢之间的相互作用有密切关系.     

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).     

Insight into the structural,elastic, electronic,thermoelectric, thermodynamic and optical properties of MRhSb (M = Ti,Zr, Hf) half-Heuslers from ab initio calculations

A detailed theoretical investigation on the structural, elastic, electronic, thermoelectric, thermodynamic and optical properties of half-Heusler MRhSb (M = Ti, Zr, Hf) compounds is presented. The computations are carried out using the full potential linear augmented plane wave method (FP-LAPW) within density functional theory (DFT). The optimized lattice parameters are in fairly good agreement with available experimental data. The computed elastic constants (C_ij) and their related elastic moduli confirm the stability of the studied compounds in the cubic phase and highlight their ductile nature. Analysis of band structures and densities of states (DOS) profiles reveal the semiconducting nature with an indirect energy band gap (Γ-X). The bonding nature discussed via the electron charge density plot shows a mixture of covalent and ionic character. The evaluation of Seebeck coefficient leads to thermopower S ≥ 500 µeV which is very benefic for thermoelectric applications. Estimated thermodynamic characteristic within the quasi-harmonic approximation shows similar behavior for the three compounds. Finally, some optical spectra such as the complex dielectric function, refractive index, reflectivity, energy loss function and absorption are presented.     

Study of elastic properties of CeO2 by statistical moment method

The purpose of the present paper is to investigate the temperature and pressure dependences of the elastic properties of cerium dioxide using the statistical moment method (SMM). The equation of states of bulk CeO₂ is derived from the Helmholtz free energy, and the pressure dependences of the elastic moduli like the bulk modulus, B_T, shear modulus, G, Young’s modulus, E, and elastic constants (C11, C12, and C44) are presented taking into account the anharmonicity effects of the thermal lattice vibrations. In the present study, the influence of temperature and pressure on the elastic moduli and elastic constants of CeO₂ has also been studied, using three different interatomic potentials. We compare the results of the present calculations with those of the previous theoretical calculations as well as with the available experiments.     

Structural and anisotropic elastic properties of hexagonal MP (M = Ti,Zr, Hf) monophosphides determined by first-principles calculations

First-principles calculations were performed to investigate the structural properties, phase stabilities, elastic properties and thermal conductivities of MP (M = Ti, Zr, Hf) monophosphides. These monophosphides are thermodynamically and mechanically stable. Values for the bulk modulus B, shear modulus G, Young’s modulus E and Poisson’s ratio ν were calculated by Voigt–Reuss–Hill approximation. The mechanical anisotropy was discussed via several anisotropy indices and three-dimensional (3D) surface constructions. The order of elastic anisotropy is ZrP > HfP > TiP. The minimum thermal conductivities of these monophosphides were investigated using Clarke’s model and Cahill’s model. The results revealed that these monophosphides are suitable for use as thermal insulating materials and that their minimum thermal conductivities are anisotropic.     

Structural and elastic properties of antiperovskites XNBa3 (X=As, Sb) under pressure effect

First-principle calculations of structural, elastic and high pressure properties of antiperovskites XNBa₃ (X=As, Sb) are performed, using the full-potential linear muffin-tin orbital (FP-LMTO) method. The local density approximation (LDA) is used for the exchange-correlation (XC) potential. Results are given for lattice constant, bulk modulus and its pressure derivatives. We have determined the elastic constants C₁₁, C₁₂ and C₄₄ and their pressure dependence. We derived shear moduli, Young's modulus, Poisson's ratio and Lamé's constants for ideal polycrystalline XNBa₃ aggregates. By analyzing the ratio of the bulk to shear moduli, we conclude that XNBa₃ compounds are brittle in nature. We estimated the Debye temperature of XNBa₃ from the average sound velocity. This is the first quantitative theoretical prediction of the elastic properties of AsNBa₃ and SbNBa₃ compounds, and it still awaits experimental confirmation.     

Physical properties of tetragonal transition-metal borides Nb2MB2 (M = Mo,W, Re or Os) with a new superstructure

The mechanical and thermodynamic properties, chemical bonding characteristics and electronic structure of Nb₂MB₂ (M = Mo, W, Re or Os) with a new tetragonal U₃Si₂-type superstructure (space group P4/mnc, no. 128) were studied by means of density functional theory calculations. All Nb₂MB₂ structures studied were demonstrated to be thermodynamically and mechanically stable. The bulk, shear and Young's moduli, Poisson's ratio, Debye temperature and anisotropy factors were derived for ideal polycrystalline Nb₂MB₂ aggregates. Among these compounds, Nb₂WB₂ was found to have the highest shear modulus and hardness. The electronic densities of state and electronic localization function analysis revealed the metallicity and strong covalent B–B, Nb–B and M−B bonding in Nb₂MB₂. Moreover, these results reveal that the covalence between Nb 4d, M nd (n = 4 for Mo and 5 for W, Re and Os) and B 2p states is the cause of the relatively higher elastic modulus and hardness of the Nb-based compounds. Finally, thermodynamic properties, including the bulk modulus, heat capacity and thermal expansion coefficient of Nb₂WB₂ were obtained systematically under high temperature and pressure.     

Structural and elastic properties under pressure effect of the cubic antiperovskite compounds ANCa3 (A = P, As, Sb, and Bi)

Using first-principles density functional calculations, the effect of high pressures, up to 40 GPa, on the structural and elastic properties of ANCa₃, with A = P, As, Sb, and Bi, were studied by means of the pseudo-potential plane-waves method. Calculations were performed within the local density approximation and the generalized gradient approximation for exchange-correlation effects. The lattice constants are in good agreement with the available results. The elastic constants and their pressure dependence are calculated using the static finite strain technique. We derived the bulk and shear moduli, Young's modulus, Poisson's ratio and Lamé's constants for ideal polycrystalline ANCa₃ aggregates. By analysing the ratio between the bulk and shear moduli, we conclude that ANCa₃ compounds are brittle in nature. We estimated the Debye temperature of ANCa₃ from the average sound velocity. This is the first quantitative theoretical prediction of the elastic properties of PNCa₃, AsNCa₃, SbNCa₃, and BiNCa₃ compounds, and it still awaits experimental confirmation.