First-principles predictions of anisotropies in elasticity and sound velocities of CsCl-type refractory intermetallics: TiTM,ZrTM and HfTM (TM = Fe,Ru, Os)

ABSTRACT

Structural properties, elastic properties, sound velocities and Debye temperatures of CsCl-type refractory TiTM, ZrTM and HfTM (TM?=?Fe, Ru, Os) intermetallics were investigated using first-principles calculations. The calculated equilibrium lattice parameters are coincided with the reported experimental and theoretical data. Based on single-crystal elastic constants, polycrystalline elastic moduli, Poisson’s ratios, sound velocities and Debye temperatures were evaluated. Anisotropies in elastic moduli of these CsCl-type intermetallics were discussed by elastic anisotropy indexes, three-dimensional surface constructions and their projections, and directional elastic modulus. The results showed that ZrFe has the highest elastic anisotropy and ZrOs presents the lowest one. Finally, sound velocities, Debye temperatures and their anisotropies were also calculated and discussed.     

Phase stability,anisotropic elastic properties and electronic structures of C15-type Laves phases ZrM2 (M = Cr,Mo and W) from first-principles calculations

Abstract

Systematic investigations of phase stability and mechanical properties of C15-type ZrM₂ (M = Cr, Mo and W) Laves phases were performed using first-principles calculations. The formation enthalpies of ZrM₂ are in good agreement with the theoretical and experimental values. The elastic properties, including elastic constants and moduli, Poisson’s ratio and B/G, were discussed. The elastic anisotropy was also investigated via the anisotropy indexes (A^U, A^Z, A_shear and A_comp), the anisotropy of shear modulus and the 3D construction of bulk and Young’s moduli. The elastic anisotropy of ZrM₂ is in order of ZrCr₂ < ZrMo₂ < ZrW₂. The variations in the shear modulus and hardness show similar trends with increasing values from ZrCr₂ to ZrW₂. The electronic structures for these C15-type Laves phases were analysed to obtain deeper understanding of chemical bonds and phase stabilities. Finally, the sound velocities and Debye temperatures were also investigated.     

A first-principles study on structural stability and mechanical properties of polar intermetallic phases CaZn2 and SrZn2

Structural stability and electronic properties of polar intermetallic CaZn₂ and SrZn₂ in both CeCu₂-type and MgZn₂-type structures have been investigated using first-principles method. The calculated equilibrium lattice parameters agree closely with the available experimental and other theoretical results. In terms of formation enthalpy, it is discovered that the present compounds with CeCu₂-type structure are energetically more stable than that with MgZn₂-type. They are all mechanically stable according to the criteria of elastic stability. In particular, we have investigated the pressure effect on the compressive behaviour and structural stability of each compound. Subsequently, the bulk modulus, shear modulus, Young’s modulus, theoretical hardness, Poisson’s ratio and Debye temperature in the ground state can be estimated using Voigt–Reuss–Hill homogenization method. Mechanical anisotropy is characterized by the anisotropic factors and direction-dependent Young’s modulus. Finally, the electronic structures are determined to reveal the bonding characteristics of considered phases.     

Elastic,dynamical, and electronic properties of LiHg and Li<Subscript>3</Subscript>Hg: First-principles study

The elastic, dynamical, and electronic properties of cubic LiHg and Li₃Hg were investigated based on first-principles methods. The elastic constants and phonon spectral calculations confirmed the mechanical and dynamical stability of the materials at ambient conditions. The obtained elastic moduli of LiHg are slightly larger than those of Li₃Hg. Both LiHg and Li₃Hg are ductile materials with strong shear anisotropy as metals with mixed ionic, covalent, and metallic interactions. The calculated Debye temperatures are 223.5 K and 230.6 K for LiHg and Li₃Hg, respectively. The calculated phonon frequency of the T_2g mode in Li₃Hg is 326.8 cm^?1. The p states from the Hg and Li atoms dominate the electronic structure near the Fermi level. These findings may inspire further experimental and theoretical study on the potential technical and engineering applications of similar alkali metal-based intermetallic compounds.     

Electronic structural, elastic properties and thermodynamics of Mg17Al12, Mg2Si and Al2Y phases from first-principles calculations

Electronic structures, elastic properties and thermal stabilities of Mg₁₇Al₁₂, Mg₂Si and Al₂Y have been determined from first-principle calculations. The calculated heats of formation and cohesive energies show that Al₂Y has the strongest alloying ability and structural stability. The brittle behavior and structural stability mechanism is also explained through the electronic structures of these intermetallic compounds. The elastic constants are calculated, the bulk moduli, shear moduli, Young's moduli and Poisson ratio value are derived, the brittleness and plasticity of these phases are discussed. Gibbs free energy, Debye temperature and heat capacity are calculated and discussed.     

Effect of Zr concentration on the mechanical and thermodynamic properties of NbIr3 intermetallic compounds from theoretical estimations

ABSTRACT

The iridium is an important metal which has excellent resistance to corrosion at high temperature. L1₂ intermetallic compounds i.e. Ir₃Nb and Ir₃Zr, with similar lattice parameters are ideal for working at high temperature. They are fully soluble due to their low lattice misfit. A first-principle investigation into the effect of doping Zr with different concentrations on the electronic structure, mechanical and thermodynamic properties of NbIr₃ has been studied to prompt the development of novel high-temperature materials. Nine Zr_xNb_8?xIr₂₄ compounds are carefully considered. The results show that adding Zr into these compounds can strengthen their structural stability and ductility. Nevertheless, it reduces the elastic modulus and elastic stiffness. Simultaneously, with the increase of Zr content, the thermodynamic properties of these compounds decrease. It is also found that the changes of elastic modulus are mainly attributed to the variations of bonds in these compounds.     

First-principles study on the structural,elastic, and thermodynamics properties of Ni3X (X: Al,Mo, Ti,Pt, Si,Nb, V,and Zr) intermetallic compounds

In the present study, the ground-state properties of Ni₃X intermetallic compounds were analyzed by means of the first-principles pseudo-potential method using the Cambridge serial total energy package code. The calculated lattice parameters of Ni₃X intermetallic compounds are in good agreement with the experimental and other theoretical data. The single-crystal elastic constants were calculated; the hardness, ductile, and plasticity of materials were analyzed. The calculated enthalpies of formation showed that all of intermetallic compounds were thermodynamically stable; Debye temperature and heat capacity are calculated and discussed. Moreover, the chemical bonding in these intermetallic compounds was interpreted by calculating the density of states, electron density difference distribution, and Mulliken analysis; magnetism properties were briefly analyzed.     

高温高压下Ag-Mg-Zn合金中金属间化合物的微观结构与热动力学性质的第一性原理计算

采用基于密度泛函理论的第一性原理计算方法,研究了Ag-Mg-Zn合金中金属间化合物AgMg,Mg4Zn8和Ag8Mg4Zn4在高温高压下的结构稳定性、弹性性能和热动力学性质.理论计算结果与实验值和其他的理论结果符合得非常好.研究表明:金属间化合物AgMg,Mg4Zn8和Ag8Mg4Zn4在零温零压下是力学稳定的;Mg4Zn8和Ag8Mg4Zn4为延性相,而AgMg则为脆性相;在这三种金属间化合物中,Ag8Mg4Zn4的塑性最好,AgMg的塑性最差.利用准谐Debye模型,讨论了高温高压下Ag-Mg-Zn合金中金属间化合物的摩尔振动内能Uvib,m,摩尔Helmholtz振动自由能Avib,m,摩尔振动熵Svib,m,摩尔定容热容Cv,m,摩尔定压热容Cp,m,热膨胀系数α,Griüneisen 参量γ和Debye温度(O).     

Temperature dependence of the elastic constants and Debye temperatures of NaCl and KCl single crystals

A pulsed ultrasonic method has been used to measure the temperature dependences of the elastic moduli, the constants C_ik and S_ik , the anisotropy factors, the bulk moduli, and the Poisson ratios over the temperature range 300-120 ° K for NaCl and over the range 300-80 ° K for KCl. The Debye temperatures of these compounds are calculated from the elastic constants extrapolated to 0 ° K.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 6, pp. 22–28, June, 1970.     

DFT - based study of electronic structures and mechanical properties of LiTaO3: ferroelectric and paraelectric phases

Abstract

By applying ab initio calculation within density functional theory (DFT), we study the structure parameters, electronic band structure, elastic coefficients, polycrystalline elastic properties, anisotropy factors and Debye temperature of ferroelectric and paraelectric phases of LiTaO₃ within the generalised gradient approximation at ambient pressure. The atomic structure in both phases is fully relaxed and the lattice constant, angle and atomic positions are well consistent with experimental values. The computed single-crystal elastic coefficients indicate that mechanical stability of LiTaO₃ in both phases is confirmed using the generalised Born criteria. The shear, bulk and Young’s modulus, Poisson’s ratio, and Vickers hardness were computed according to theoretical elastic constants by Voight–Reuss–Hill method. Several anisotropy factors and indexes are computed to illustrate mechanical anisotropy. Both phases are shown to be weakly anisotropic. The Debye temperature is estimated using the longitude and transverse elastic wave velocity of the ideal polycrystalline LiTaO₃ aggregates. We have found that LiTaO₃ in both phases has an indirect energy band gap. The differences in the electronic structure and density of states for both phases are quite small. Our results indicate that the mechanical and bonding properties of both phases are very similar. The obtained results were compared with the available experimental and theoretical values.     

Evaluation of the biquadratic pair coupling from the magnetic anisotropy in rare earth intermetallic compounds : HoAl2

It is shown that the two-ion biquadratic pair coupling,which is usually determined from spin-wave spectra or from studies of crystallographic phase transition and variation of the elastic constants with temperature in rare earth intermetallic compounds, can as well be estimated from the anisotropy of the magnetic energy. This method is particularly useful for systems which do not indicate any significant distortion e.g. in HoAl₂.     

Theoretical study on the phase stability,elasticity, hardness and electronic structures of Ni–P compounds

A systematic investigation concerned with phase stability, elastic properties, hardness and relevant electronic structure of Ni–P compounds (Ni₃P, Ni₁₂P₅, Ni₂P, Ni₅P₄, NiP, NiP₂ and NiP₃) was carried out using first principles calculations. The calculated results show that the Ni–P compounds have strong hardness, ranging from 7.80–14.54 GPa. Also, the hardness values gradually increase with the P content. Electronic structure analysis shows that the strong Ni–P and part of P–P hybrid orbitals play important roles in the hardness of these compounds. The calculated elastic constants indicated that the Ni₃P, Ni₁₂P₅ and NiP₂ phases are significantly anisotropic, the NiP and Ni₂P exhibit some anisotropy, while the Ni₅P₄ and NiP₃ show a relatively isotropic character. At last, the properties of these Ni–P compounds including lattice constants, thermodynamic stability, elastic constants C_ij, bulk modulus B, shear modulus G, Young's modulus E and Poisson's ratio ν have been calculated.     

Stability and elastic properties of B2 CoX (X = Ti,Zr and Hf) intermetallic compounds as a function of pressure

By means of first-principles calculations within the generalised gradient approximation (GGA), phase stability, elastic properties and electronic structures of B2 CoX (X = Ti, Zr and Hf) compounds as a function of pressure have been investigated. The formation energy indicates that CoTi is the most stable phase in these three B2 phases under different pressures. The elastic properties of B2 Co (X = Ti, Zr and Hf), calculated via the Voigt–Reuss–Hill (VRH) approximation, increase with increasing pressure. The mechanical anisotropies are characterised by the universal anisotropy index (A^U) and the Zener anisotropy index (A^Z). The sound velocities, Debye temperatures and melting temperature under applied pressure are also evaluated. Electronic structure show that the changes in the charge distribution are moderate under applied pressure, resulting in the general characteristics of the bonding between X (X = Ti, Zr and Hf) and Co remain unchanged.     

Structural properties,phase stability,elastic properties and electronic structures of Cu–Ti intermetallics

The structural properties, phase stabilities, anisotropic elastic properties and electronic structures of Cu–Ti intermetallics have been systematically investigated using first principles based on the density functional theory. The calculated equilibrium structural parameters agree well with available experimental data. The ground-state convex hull of formation enthalpies as a function of Cu content is slightly symmetrical at CuTi with a minimal formation enthalpy (–13.861 kJ/mol of atoms), which indicates that CuTi is the most stable phase. The mechanical properties, including elastic constants, polycrystalline moduli and anisotropic indexes, were evaluated. G/B is more pertinent to hardness than to the shear modulus G due to the high power indexes of 1.137 for G/B. The mechanical anisotropy was also characterized by describing the three-dimensional (3D) surface constructions. The order of elastic anisotropy is Cu₄Ti₃ > Cu₃Ti₂ > α-Cu₄Ti > Cu₂Ti > CuTi > β-Cu₄Ti > CuTi₂. Finally, the electronic structures were discussed and Cu₂Ti is a semiconductor.     

第一原理研究铝锂金属间化合物

运用密度泛函理论系统地研究了二元铝锂金属间化合物Al₃Li、AlLi、Al₂Li₃和Al₄Li₉的结构、形成热、弹性和电子结构.通过计算四种金属间化合物的形成热,证明了金属间化合物中铝和锂之间具有强烈的化学作用. 在富锂金属间化合物中,随着锂的含量的增加,金属间化合物热力学稳定性呈线性减弱. 计算金属间化合物的单晶弹性常数可以得出四种金属间化合物都是机械稳定的. 运用Voigt-Reuss-Hil     

First-principles investigation of the structural,dynamical, electronic,and elastic properties of WGe2 and W5Ge3

ABSTRACT

We have investigated the structural, dynamical, elastic, and electronic properties of WGe₂ and W₅Ge₃ compounds in different phases. We have considered the C11_b (tetragonal, space group I4/mmm) and C23 (orthorhombic, space group Pnma) strukturbericht phases for WGe₂ compound and D8₁ (tetragonal, space group I4/mcm), D8_m (tetragonal space group I4/mcm) strukturbericht phases for W₅Ge₃ compound. The structural parameters, formation enthalpies, phonon dispersion curves, elastic constants, mechanical modulus, anisotropic factors, thermal conductivities, and electronic structures have been investigated using generalised gradient approximation within in the plane wave pseudopotential density functional theory. The calculated lattice constants are in a good agreement with the experimental data. The considered phases for WGe₂ and W₅Ge₃ compounds have a metallic character. The results indicated that all phases for compounds are both mechanically stable and dynamically stable except for W₅Ge₃-D8₁. The anisotropy in some mechanical modulus has been investigated using several elastic anisotropy indexes and directional dependence of compressibility, Young’s moduli, shear moduli, and Poisson’s ratio.     

Insight into structural,mechanical, electronic and thermodynamic properties of intermetallic phases in Zr–Sn system from first-principles calculations

The structural, phase stabilities, mechanical, electronic and thermodynamic properties of intermetallic phases in Zr–Sn system are investigated by using first-principles method. The equilibrium lattice constants, enthalpy of formation (ΔH^form) and elastic constants are obtained and compared with available experimental and theoretical data. The configuration of Zr₄Sn is measured with reasonable precision. The ΔH^form of five hypothetical structures are obtained in order to find possible metastable phase for Zr–Sn system. The mechanical properties, including bulk modulus, shear modulus, Young's modulus and Poisson's ratio, are calculated by Voigt–Reuss–Hill approximation and the Zr₅Sn₄ and Zr₅Sn₃ show excellent mechanical properties. The electronic density of states for Zr₅Sn₄, Zr₅Sn₃ and cP8-Zr₃Sn are calculated to further investigate the stability of intermetallic compounds. Through the quasi-harmonic Debye model, the Debye temperature, heat capacity and thermal expansion coefficient under temperature of 0–300 K and pressure of 0–50 GPa for Zr₅Sn₃ and Zr₅Sn₄ are deeply investigated.     

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.     

Ab initio calculation of the phase stability,mechanical properties and electronic structure of ZrCr2 Laves phase compounds

Ab initio calculations have been used to investigate the phase stability, mechanical properties and electronic structure of ZrCr₂ Laves phase compounds, based on the method of augmented plane waves plus local orbitals with the generalized gradient approximation. The calculated lattice constants for the C15, C36 and C14 structures are in good agreement with experimental values. The calculation of heats of formation showed that C15 is a ground-state phase, whereas C36 is an intermediate phase and C14 the high-temperature phase. The elastic constants and elastic moduli for the C15 structure were calculated systematically and compared with experiments and previous theoretical calculations. The intrinsic and extrinsic stacking fault energies are found to be 112 and 98?mJ?m^?2, respectively. The equilibrium separations between Schockley are also predicted using the calculated elastic moduli and stacking fault energies. Finally, the calculated electronic structures of these Laves phases are discussed based on these results.