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.     

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.     

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.     

Supreme shear modulus predicted in the monocarbide system: the Rex W1–x C alloy

The energetic, mechanical and electronic properties as a function of composition for Re_x W_1–x C alloys in the WC structure have been investigated. It has been demonstrated that the shear modulus of WC can be enhanced by alloying with a small amount of Re, to a maximum shear modulus of 311 GPa at x = 0.23. The designed alloy is energetically stable and could be expected to be a potential extremely hard transition‐metal monocarbide, which is attributed to the strong metal–metalloid interaction with modulated valence electron concentration with respect to WC. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

非晶态合金FeTmB的磁矩和居里温度

本文系统地报道单辊液淬方法制备FeTmB(Tm=Ti,V,Cr,Mn,Zr,Nb,Mo,Ta,W)非晶态合金的磁性,讨论了3d,4d,5d元素的加入对非晶态FeB合金的磁矩和居里温度的影响。实验结果表明在非晶态FeTmB合金系中Fe原子磁矩都在2.0μ_B左右。Tm原子在非晶态Fe基合金中比在相应的晶态合金中显示更强的局域特性。Tm原子的磁矩与元素的外层电子数有关,IVB(Ti),VB(V),VIB(Cr),VIIB(Mn)族原子的磁矩分别约为4,5,4,3μ_B,Tm的磁矩与铁原子磁矩反平行耦合。合金磁矩随Tm含量的变化率dμ/dx与混合模型的计算值相符合。用虚拟束缚态讨论,得到IVB(Ti),VB(V)族元素的虚拟束缚态在费密面以上,VIB(Cr),VIIB(Mn)族元素的虚拟束缚态与费密面交迭。 关键词：     

Lattice mechanical properties of alkaline earth metals in bcc and fcc phases

A model pseudopotential depending on an effective core radius treated as a parameter is used for alkaline earth metals in bcc and fcc phases to study the Binding energy, Interatomic interactions, phonon dispersion curves, Phonon density of states, Debye-Waller factor, mean square displacement, Debye-Waller temperature parameters, dynamical elastic constants (C₁₁, C₁₂ and C₄₄), bulk modulus (B), shear modulus (C′), deviation from Cauchy relation (C₁₂−C₄₄), Poisson's ratio (σ), Young's modulus (Y), behavior of phonon frequencies in the elastic limit independent of the direction (Y₁), limiting value in the [1 1 0] direction (Y₂), degree of elastic anisotropy (A) and propagation velocities of the elastic waves. The contribution of s-like electrons is incorporated through the second-order perturbation theory due to model potential. The theoretical results are compared with the existing experimental data. A good agreement between theoretical investigations and experimental findings has confirmed the ability of our potential to yield large numbers of lattice mechanical properties of certain alkaline earth metals.     

A neutron diffraction and magnetization study of Heusler alloys containing Co and Zr,Hf, V or Nb

Neutron diffraction, X-ray diffraction and saturation magnetization measurements have been made on a series of ferromagnetic alloys at the composition Co₂YZ, where Y is a group IVA or VA element and Z is a group IIIB or IVB element. The alloys are mainly ordered in the Heusler L2₁ type chemical structure, but some show the presence of a small amount of additional phase, or some preferential disorder.The magnetic results form two distinct groups in which the moments are confined to the Co sites but their magnitude depends on the electron concentration determined by the Y and Z atoms. Although the magnetic moments and Curie temperatures of the alloys in the same group are similar, their lattice parameters differ according to whether Z is a group IIIB or IVB element. Such behaviour indicates that, as in other alloy series with the Heusler structure, a change in lattice parameter has little effect on the magnetic properties in comparison with the effect of a change in electron concentration.     

Ab initio study of Nb2SC and Nb2S2C: Differences in coupling between the S and Nb-C layers

Using ab initio calculations, we have studied the structurally related compounds Nb₂SC and Nb₂S₂C. In Nb₂S₂C (space group , prototype Bi₂Te₃), S atoms are nearest neighbours, while in Nb₂SC (space group P6₃/mmc, prototype Cr₂AlC) this is not the case. The calculated equilibrium volume for these two phases deviates by 1.6-3.7% to previously-published experimental data and the bulk modulus-to-c₄₄ ratios obtained are 1.5 and 5.9, respectively. These results indicate a resemblance of Nb₂S₂C to hexagonal BN and graphite. Furthermore, we have demonstrated that the uniform compression method is adequate for estimating the elastic properties of Nb₂SC, a so-called MAX phase. It is our ambition that these calculations will stimulate further experimental research on these compounds.     

Static and vibrational properties of equiatomic Na-based binary alloys

The computations of the static and vibrational properties of four equiatomic Na-based binary alloys viz. Na_0.5Li_0.5, Na_0.5K_0.5, Na_0.5Rb_0.5 and Na_0.5Cs_0.5, to second order in local model potential is discussed in terms of real-space sum of Born von Karman central force constants. The local field correlation functions due to Hartree (H), Ichimaru-Utsumi (IU) and Sarkar et al. (S) are used to investigate the influence of the screening effects on the aforesaid properties. Results for the lattice constants C₁₁, C₁₂, C₄₄, C₁₂-C₄₄, C₁₂/C₄₄ and bulk modulus B obtained using the H-local field correction function have higher values in comparison with the results obtained for the same properties using IU- and S-local field correction functions. The results for the Shear modulus (C′), deviation from Cauchy's relation, Poisson's ratio σ, Young modulus Y, propagation velocity of elastic waves, phonon dispersion curves and degree of anisotropy A are highly appreciable for the four equiatomic Na-based binary alloys.     

Electronic structure of Sc2AC (A=Al, Ga, In, Tl)

Using ab initio calculations, we have studied Sc₂AC with A=Al, Ga, In and Tl. We show that C 2p and Sc 3d as well as A p and Sc 3d states are hybridized, but the antibonding states in the vicinity of the Fermi level weaken the overall bonding. In terms of the chemical bonding, the influence of the size of the A element is minute. Furthermore, the bulk modulus of the corresponding binary transition metal carbide is not conserved in these phases. Therefore, Sc₂AC can be classified as weakly coupled MAX phases according to Sun and co-workers [Z. Sun, D. Music, R. Ahuja, S. Li, J.M. Schneider, Phys. Rev. B 70 (2004) 092102]. It is our ambition that these calculations will stimulate experimental research on these compounds.     

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.     

A theoretical study on the excited states of MC3 (M = Sc, V, and Cr)

The ground state structures of MC₃ (M = Sc, V, and Cr) and their anions have been investigated, employing the first-principles DFT at the B3LYP level. The calculations predict that the equilibrium geometries of both neutral MC₃ and their anions are cyclic structures with C_2v symmetry. The Mulliken charge and spin populations of MC₃ and their anions have also been calculated, and it is found the electron charge changes mainly take place on the M atoms from anions to neutral molecules. The low-lying excited states for the clusters are calculated with time-dependent DFT to assign the features of the photoelectron spectra. Our results agree well with the available experimental and theoretical data.     

Pressure dependence of elastic constants in zinc-blende GaN and InN and their influence on the pressure coefficients of the light emission in cubic InGaN/GaN quantum wells

We have studied the influence of nonlinear elastic effects on the pressure coefficients of light emission, dE_E/dP, in cubic InGaN/GaN quantum wells. By means of ab-initio calculations, we have determined the pressure dependences of the elastic constants, C₁₁, C₁₂ and C₄₄ in zinc-blende InN and GaN. Further, we show that the pressure dependence of the elastic constants results in significant reduction of dE_E/dP in cubic InGaN/GaN quantum wells and essentially improves the agreement between experimental and theoretical values.     

Ab initio study of the electronic structure and elastic properties of Al5C3N

We investigate the electronic structure, chemical bonding and elastic properties of the hexagonal aluminum carbonitride, Al₅C₃N, by ab initio calculations. Al₅C₃N is a semiconductor with a narrow indirect gap of 0.81 eV. The valence bands below the Fermi level (E_F) originate from the hybridized Al p-C p and Al p-N p states. The calculated bulk and Young's moduli are 201 GPa and 292 GPa, which are slightly lower than those of Ti₃SiC₂. The values of the bulk-to-shear-modulus and bulk-modulus-to-c44 are 1.73 and 1.97, respectively, which are higher than those of Ti₂AlC and Ti2AlN, indicating that Al₅C₃N is a ductile ceramic.     

Forming abilities of monatomic chains of several fcc and bcc metals in different crystallographic orientations

The forming abilities of monatomic chains (MC) of several fcc and bcc metals stretched in three principal crystallographic orientations of [1 1 1], [1 0 0] and [1 1 0] are analyzed in terms of a ratio between Peierls stress of a bulk crystal with dislocations (τ_p) and theoretical shear stress of a monatomic chain (τ_m). It is found that the structure and orientation dependent τ_m/τ_p values are proportional to the forming abilities of MC while τ_m/τ_p is a function of Possion's ratio ν. The above considerations are in agreement with known experimental and simulation results of Au. In addition, Nb as a candidate for MC formation is suggested.     

Theoretical investigations on the elastic and thermodynamic properties of Ti2AlC0.5N0.5 solid solution

We have performed theoretical studies on the elastic and thermodynamic properties of the solid solution: Ti₂AlC_0.5N_0.5. The lattice parameters, elastic constants, bulk, shear, Young's moduli, Poisson's ratio and Debye temperature were calculated and compared with those of the end members, Ti₂AlC and Ti₂AlN. The temperature dependence of the bulk moduli, thermal expansion coefficient and specific heats of Ti₂AlC_0.5N_0.5 were obtained from the quasi-harmonic Debye model. The calculated elastic and thermodynamic properties were compared with experimental data.     

First-Principles Study on Magnetic Properties of V-Doped ZnO Nanotubes

Electronic and magnetic properties of V-doped ZnO nanotubes in which one of Zn^2＋ ions is substituted by V^2＋ ions are studied by the first-principles calculations of plane wave ultra-soft pseudo-potential technology based on the spin-density function theory. The computational results reveal that spontaneous magnetization in Vdoped （9,0） ZnO nanotubes can be induced without p-type or n-type doping treatment, and the ferromagnetism is isotropic and independent of the chirality and diameter of the nanotubes. It is found that V-doped ZnO nanotubes have large magnetic moments and are ferromagnetic half-metal materials. Moreover, the ferromagnetic coupling among V atoms is generated by O 2p electron spins and V 3d electron spins localized at the exchanging interactions between magnetic transitional metal （TM） impurities. The appearance of ferromagnetism in V-doped ZnO nanotubes gives some reference to fabrication of a transparent ferromagnet which may have a great impact on industrial applications in magneto-optical devices.     

Mechanical Properties and Electronic Structures of Cotunnite TiO2

Based on the first-principles plane-wave basis pseudopotential calculations, we investigate mechanical properties and electronic structures of the hardest known oxide, cotunnite TiO2. The calculated results show that cotunnite TiO2 has the highest bulk modulus （348 GPa） and hardness （32 GPa） among the high-pressure phases of TiO2, but its mechanical properties are not superior to those of c-BN. Moreover, the high hardness of cotunnite TiO2 can be understood from both the dense crystal structure （high valence electron density and short bond lengths） and the unusual mixtures of covalent and ionic bonding of Ti-O.     

Crystal and electronic structure of solid C76

The crystal and electronic structure of solidC ₇₆ has been studied using transmission electron microscopy and electron energy-loss spectroscopy in transmission. C₇₆ forms a close packed structure with an average facecentred cubic symmetry. From valence band and core electron excitations information on the dielectric function and the unoccupied density of states has been obtained.     

Formation of metallofullerenes by laser ablation of externally doped fullerenes C60Mx (M=Sm, Pt and Ni)

Photofragmentation of metal fullerides C₆₀M_x (M=Sm, Pt and Ni) has been studied by excimer laser ablation–TOF mass spectrometry. Metallofullerenes of the type C_nM (n<60) have been observed in both the positive and negative ionic modes, with C₅₉M being the most prominent species. It is supposed that the metal atom is incorporated into the network of the fullerene cage to replace one carbon atom of the cage, forming substitutional metallofullerene. The occurrence of the C₅₉M, C₅₈M, C₅₇M clusters in the mass spectra is confirmed by the coincidence of the intensity distribution of the mass peaks with the isotopic abundance pattern calculated from the natural abundance of isotopes of C and M. Odd-numbered high-carbon clusters are observed in our laser ablation study of all the metal fullerides in the negative ion channel. The evolution of the mass spectra of these samples with laser irradiation shots indicates that the transformation process from an externally doped fullerene to the substitutionally doped fullerene involves the loss of metal carbide, MC. The structures of metallofullerenes C_2n+1M and C_2nM with even and odd total numbers of atoms respectively are discussed. Formation mechanisms with the participation of odd-numbered all-carbon fullerene clusters as intermediates are supposed. Received: 18 June 2001 / Accepted: 28 September 2001 / Published online: 2 May 2002