Elastic properties, thermal expansion coefficients and electronic structures of Ti0.75X0.25C carbides

Elastic properties, thermal expansion coefficients and electronic structures of Ti_0.75X_0.25C carbides (X=W, Mo, Ta, Nb, V, Hf, Zr, Cr and Al) were systematically investigated using ab initio density functional theory (DFT) calculations. The calculated elastic moduli, electronic structures and thermal expansion coefficients α(T) of pure TiC are in good agreement with experimental data and other DFT calculations. Based on a phenomenological formula, the trends of elastic properties and ductile/brittle behavior of Ti_0.75X_0.25C were analyzed. It was found that alloying elements W, Mo, Ta, Nb, V and Hf can increase elastic moduli, while Zr, Cr and Al reduce moduli. The nearly free electron model and Debye approximation were applied in the evaluation of α(T). The anharmonic effect was taken into account by including volume-dependent elastic moduli and Debye temperature. Results show that alloying additions of 3d V, 4d Zr and Mo slightly reduce α(T), while 3d Cr increases α(T), Al, 4d Nb, 5d Hf and W almost keep α(T) unchanged in Ti_0.75X_0.25C at high temperatures. The electronic structures of Ti_0.75X_0.25C were calculated and analyzed, and the electronic density of states was used to interpret variations of elastic properties and ductile/brittle behavior induced by alloying additions.     

Calculated elastic constants of dilute alloys based on bcc metals

The elastic constants of dilute alloys based on bcc metals have been calculated using the Green’s function method obtaining explicit expressions for change in elastic constants in terms oft-matrix. The crystal impurity problem is discussed within an impurity model containing central and non-central force constant changes extended up to second neighbours of the impurity. The effect of volume change on elastic constants and a contribution from electron pressure term are considered. Numerical results for changes in three elastic moduli have been presented for a number of dilute alloys based on Mo, Nb, W, Ta and V.     

理论研究VTiTaNbAlx高熵合金的结构与弹性力学性质

实验已证明VTiTaNbAlx高熵合金(HEAs)为单相固溶体,它采用了体心立方结构. 在这篇文章中,我们使用基于密度泛函理论的饼模轨道(EMTO)结合相干势近似(CPA)方法,计算并分析了此高熵合金体系的平衡体性质,弹性常数及多晶弹性模量. 结果表明：此系列高熵合金符合单相高熵合金的理论判据,具有较好的内在塑性,等摩尔比的VTiTaNb高熵合金趋于弹性各向同性. 随着Al含量的增加,此系列高熵合金的弹性各向异性趋于增大,但对多晶弹性模量几乎没有影响;同时讨论了基于弹性常数计算的德拜温度.     

理论研究VTiTaNbAl_x高熵合金的结构与弹性力学性质

实验已证明VTiTaNbAl_x高熵合金(HEAs)为单相固溶体,它采用了体心立方结构.在本文中,我们使用基于密度泛函理论的饼模轨道(EMTO)结合相干势近似(CPA)方法,计算并分析了此高熵合金体系的平衡体性质,弹性常数及多晶弹性模量.结果表明:此系列高熵合金符合单相高熵合金的理论判据,具有较好的内在塑性,等摩尔比的VTiTaNb高熵合金趋于弹性各向同性.随着Al含量的增加,此系列高熵合金的弹性各向异性趋于增大,但对多晶弹性模量几乎没有影响;同时讨论了基于弹性常数计算的德拜温度.     

过渡族BCC金属晶格动力学的改进分析型EAM模型

应用改进分析型EAM多体势,运用晶格动力学理论,具体计算了7种过渡族bcc金属(Cr,Fe,W,Mo,Ta,V,Nb)的[100],[110]和[111]三个晶向声子谱和比热.将计算结果与实验值进行了比较,较Johnson势有很大提高;并从方向性键合角度对符合情况进行了分析.     

金属钒弹性波速与热力学函数的理论计算

在全电子水平上,基于广义梯度近似(GGA)的密度泛函理论和全势能线性缀加平面波方法(FLAPW)计算了钒的晶格参数,弹性波速和格临爱森参数.在德拜模型的基础上,利用弹性波速方法和原子位移方法分别计算了钒的德拜频率,以及在标准条件下(298.15 K,1atm)的热容,熵等热力学函数,并与实验值进行了比较.     

First-principles investigations on structural stability,mechanical, and thermodynamic properties of LaT_2Al_(20)(T = Ti,V,Cr,Nb,and Ta) intermetallic cage compounds

First principles calculations were used to explore the structural stability, mechanical properties, and thermodynamic properties of LaT_2 Al_(20)(T = Ti, V, Cr, Nb, and Ta) intermetallics. The calculated formation enthalpy and phonon frequencies indicate that LaT_2Al_(20) intermetallics exhibit the structural stability. The elastic moduli(B, G, E, and Hv) indicate that these intermetallics possess the better elastic properties than pure Al. The values of Poisson's ratio v and B/G demonstrate that LaT_2Al_(20) intermetallics are all brittle materials. The anisotropy of elasticity and Young's modulus(three-and two-dimensional figures) indicate that LaT_2Al_(20) compounds are anisotropic. Importantly, the calculated thermal quantities demonstrate that LaT_2Al_(20) intermetallics possess the better thermal physical properties than pure Al at high temperatures.     

Mechanical properties of bcc Fe-Cr alloys by first-principles simulations

The effect of chromium content on the fundamental mechanical properties of Fe-Cr alloys has been studied by first-principles calculations. Within a random solid solution model, the lattice constants and the elastic constants of ferromagnetic bcc Fe_1?x Cr _x (0? · ?0.156) alloys were calculated for different compositions. With addition of Cr content, the lattice parameters of Fe-Cr alloys are larger than that of pure Fe solid, and the corresponding Young??s modulus and shear modulus rise nonmonotonically with the increasing Cr content. All alloys (except 9.4 at% Cr) exhibit less ductile behavior compared with pure bcc Fe. For the Fe_1?x Cr _x (0? · ?0.156) alloys, the average magnetic moment per atom decreases linearly with the increasing Cr concentration.     

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.     

Nb掺杂γ-TiAl金属间化合物的电子结构与力学性能

运用基于密度泛函理论的第一性原理方法计算了Nb掺杂γ-TiAl金属间化合物的结构参数、能带结构、电子态密度及弹性常数.结果表明:Nb替代Ti掺杂相比Nb替代Al掺杂的形成能低,Nb在替位掺杂时更倾向于取代Ti原子形成稳定的结构,Nb替代Ti掺杂能够提高γ-TiAl金属间化合物的抵御塑性变形能力、断裂强度和延展性;与Nb替代Ti掺杂相比,Nb替代Al掺杂同样增强γ-TiAl金属间化合物的断裂强度且其增强延展性的效果更好,但抵御塑性变形的能力有所削弱.     

Structural,electronic and vibrational properties of ordered intermetallic alloys CoZ (Z = Al,Be, Sc and Zr) from first-principles total-energy calculations

Self-consistent band calculations on four intermetallic compounds of the CsCl structure are presented. The calculations were performed employing the self-consistent ultrasoft pseudopotential method based on the density functional theory, within the local density approximation and the generalized gradient approximation. The calculations predicted that the equilibrium lattice constants are in excellent agreement with the experiment for CoAl and are 1% smaller than experimental values for CoBe, CoSc and CoZr, respectively. In the present study, ordered CoAl do not show any magnetic moment, whereas the other three compounds have moderate magnetic moments of about 0.2 and 0.7 Bohr magnetons (μ_B ) per atom. The elastic constants are calculated using two approaches, the energy-strain method and the use of phonon dispersion curves. The values obtained from the two methods are in reasonable agreement for the studied intermetallic compounds CoZ (Z?=?Al, Be, Sc and Zr). The brittleness and ductility properties of CoZ (Z?=?Al, Be, Sc and Zr) are determined by Poisson’s ratio σ criterion and Pugh’s criterion. The calculated elastic constants satisfy the mechanical stability criterion and the ductility of CoZr and CoSc is predicted by Pugh’s criterion. The band structure and density of states, and phonon dispersion curves have been obtained and compared with the available experimental results as well as with existing theoretical calculations. We studied and discussed the position of Fermi level for the selected four intermetallic compounds.     

高压下钨弹性和热力学性质的第一性原理研究

本文利用密度泛函理论研究了高压下bcc结构钨的弹性和热力学性质,计算得到钨的晶格常数、体弹模量以及其对压强的一阶偏导与实验值符合较好;在常压下弹性常数计算值与实验值符合较好的基础上,预测了其高压数据.针对钨的固相结构稳定性问题,根据力学稳定判断标准得到0~600 GPa范围内bcc结构是力学稳定的.此外,通过体模量和剪切模量的计算得到bcc结构钨在压力低于600 GPa时的力学性能表现为韧性.最后,基于准简谐德拜模型,成功预测了钨的热膨胀系数、等压热容、等容热容和熵随着压强和温度的变化关系,为钨及其合金的进一步设计及应用提供参考.     

Site preference and elastic properties of ternary alloying additions in B2 YAg alloys by first-principles calculations

First-principles calculations were preformed to study the site preference behavior and elastic properties of 3d (Ti–Cu) transition-metal elements in B2 ductility YAg alloy. In YAg, Ti is found to occupy the Y sublattice whereas V, Cr, Co, Fe, Ni and Cu tend to substitute for Ag sublattice. Due to the addition of 3d transition metals, the lattice parameters of YAg is decreased in the order: V<Cu<Cr<Ni<Co<Fe<Ti. The calculated elastic constants show that Cr, Fe, Co and Cu can improve the ductility of YAg alloy, and Fe is the most effective element to improve the ductility of YAg, while Ti, Ni and V alloying elements can reduce the ductility of YAg alloy, especially, V transforms ductile into brittle for YAg alloy. In addition, both V and Ni alloying elements can increase the hardness of YAg alloy, and Y₈Ag₇V is harder than Y₈Ag₇Ni.     

高压下钨弹性和热力学性质的第一性原理研究

本文利用密度泛函理论研究了高压下bcc结构钨的弹性和热力学性质,计算得到钨的晶格常数、体弹模量以及其对压强的一阶偏导与实验值符合较好;在常压下弹性常数计算值与实验值符合较好的基础上,预测了其高压数据.针对钨的固相结构稳定性问题,根据力学稳定判断标准得到0~600 GPa范围内bcc结构是力学稳定的.此外,通过体模量和剪切模量的计算得到bcc结构钨在压力低于600 GPa时的力学性能表现为韧性.最后,基于准简谐德拜模型,成功预测了钨的热膨胀系数、等压热容、等容热容和熵随着压强和温度的变化关系,为钨及其合金的进一步设计及应用提供参考.     

A simple analytical EAM model for bcc metals including Cr and its application

An analytical embedded atom method (EAM) model, which can treat bcc transition metal Chromium, has been developed. In this model, a new potential was presented, and a modified term has been introduced to fit the negative Cauchy pressure P _c=(C₁₂-C₄₄)/2 for element Cr. The new model was applied to calculating the thermodynamic properties of binary alloys of all bcc transition metals V, Nb, Ta, Cr, Mo, W and Fe. The calculated dilute-solution enthalpies and formation enthalpies of random alloys are in good agreement with the experimental data available, the results from the first-principles calculations, and the results of thermodynamic calculations.     

Structure,bonding and stability of semi-carbides M2C and sub-carbides M4C (M=V,Cr, Nb,Mo, Ta,W): A first principles investigation

Density functional theory within the generalized gradient approximation (GGA) is used to investigate the electronic structure and formation energies of semi-carbides M₂C and sub-carbides M₄C (where M=V, Cr, Nb, Mo, Ta and W). Our results show that M₂C carbides are more stable than M₄C. Total and partial densities of states were obtained and analyzed systematically for these phases. Moreover, the bonding nature of M₂C polymorphs is studied from the point of view of the Quantum Theory of Atoms in Molecules (QTAIM). It is found that inter-atomic interactions in these carbides are of mixed type including ionic, covalent and metallic components.     

First-principles calculations of elastic,phonon and thermodynamic properties of W

We investigate the elastic properties, lattice dynamical, thermal equation of state and thermodynamic properties of bcc phase W under high pressure using density functional theory. The calculated high-pressure elastic constants of bcc phase W agree well with experimental and theoretical data. Under compression, the phonon dispersion curves of bcc phase W do not show any anomaly or instability. Our calculated zero-pressure phonon dispersion curves are in excellent agreement with experiments. Within the quasiharmonic approximation, we predict the thermal equation of state and other properties including the thermal expansion coefficient, adiabatic bulk modulus, specific heat at constant volume and entropy.     

新型石墨插层化合物HfC2结构与性质的第一性原理研究

在高压下,预测一种新型石墨插层化合物HfC₂.采用第一性原理方法对其在0 GPa下的结构和性质进行研究,分别采用GGA-PBESOL、GGA-PW91和LDA方法进行结构优化,得到的晶体学数据基本相同.弹性常数和声子谱计算证实其力学和晶格动力学稳定性,表明HfC₂在0 GPa下能够稳定存在.采用GGA-PBESOL方法计算得到HfC₂的体模量和剪切模量达到265 GPa和118 GPa,Pugh比k<0.57,是一种具有高体模量的韧性材料.HfC₂存在C-C、Hf-C共价作用,且具有金属特性和特殊层状结构,是其具有高体模量和韧性的原因.最后,对HfC₂在0~500 GPa内的键长、体模量、剪切模量、k值等进行研究,探索其力学性质随压力变化的规律.     

Theoretical study of B2 type technetium AB (A=Tc,B=Ti,V, Nb and Ta) intermetallic compounds

The structural, electronic, elastic and thermal properties of the cubic AB type (A=Tc, B=Ti, V, Nb and Ta) technetium intermetallic compounds have been studied using the full potential linearized augmented plane wave (FP-LAPW) method within the generalized gradient approximation (GGA) and local density approximation (LDA) used for the exchange-correlation potential. The calculated lattice parameters agree well with the experimental results. The calculated electronic properties reveal that these compounds are metallic in nature with partial ionic bonding. The elastic constants obey the stability criteria for cubic system. Ductility for these compounds has been analyzed using the Pugh's rule and Cauchy's pressure revealing ductile in nature of all the compounds. Bonding nature is discussed using Fermi surface, band structure and charge density difference plots.     

Structural,elastic and thermodynamic properties of tetragonal and orthorhombic polymorphs of Sr2GeN2: an ab initio investigation

The structural, elastic and thermodynamic properties of the α (tetragonal) and β (orthorhombic) polymorphs of the Sr₂GeN₂ compound have been examined in detail using ab initio density functional theory pseudopotential plane-wave calculations. Apart the structural properties at the ambient conditions, all present reported results are predicted for the first time. The calculated equilibrium lattice parameters and inter-atomic bond-lengths of the considered polymorphs are in good agreement with the available experimental data. It is found that α-Sr₂GeN₂ is energetically more stable than β-Sr₂GeN₂. The two examined polymorphs are very similar in their crystal structures and have almost identical local environments. The single-crystal and polycrystalline elastic parameters and related properties – including elastic constants, bulk, shear and Young’s moduli, Poisson’s ratio, anisotropy indexes, Pugh’s criterion, elastic wave velocities and Debye temperature – have been predicted. Temperature and pressure dependence of some macroscopic properties – including the unit-cell volume, bulk modulus, volume thermal expansion coefficient, heat capacity and Debye temperature – have been evaluated using ab initio calculations combined with the quasi-harmonic Debye model.