Pressure-dependence of mechanical and thermodynamic properties of Al3Zr in Al–Li alloys from first-principles calculations

The pressure-dependence of mechanical, electronic and thermodynamic properties of metastable (L1₂ type) and stable (D0₂₃ type) Al₃Zr precipitations in Al–Li alloys were investigated by employing the first-principle calculations. The calculated equilibrium parameters are in good agreement with experimental and previous calculation results available. Elastic properties including bulk modulus, shear modulus, Young’s modulus, Poisson’s ratio and universal anisotropic index are determined by Voigt–Reuss–Hill approximation. It is found that for both phases, external pressure can improve the mechanical stability, ductility and plasticity. The electronic structures are determined to reveal the bonding characteristics of both phases. In addition, both phonon method and Gibbs program have been proposed to predict thermodynamic properties of two phases. All of these results can help to have a better understanding of the physical and chemical properties of Al₃Zr precipitations in Al–Li alloy. And can offer theoretical guidance for the weight lighting, energy conservation and emissions reduction in the design of new aluminium alloys.     

First-principles investigation on vibrational,anisotropic elastic and thermodynamic properties for L12 structure of Al3Er and Al3Yb under high pressure

To better clarify the physical properties for Al₃RE precipitates, first-principles calculations are performed to investigate the vibrational, anisotropic elastic and thermodynamic properties of Al₃Er and Al₃Yb. The calculated results agree well with available experimental and theoretical ones. The vibrational properties indicate that Al₃Er and Al₃Yb will keep their dynamical stabilities with L1₂ structure up to 100 GPa. The elastic constants are satisfied with mechanical stability criteria up to the external pressure of 100 GPa. The mechanical anisotropy is predicted by anisotropic constants A^G, A^U, A^Z and 3D curved surface of Young’s modulus. The calculated results show that both Al₃Er and Al₃Yb are isotropic at zero pressure and obviously anisotropic under high pressure. Further, we systematically investigate the thermodynamic properties and provide the relationships between thermal parameters and pressure. Finally, the pressure-dependent behaviours of density of states, Mulliken charge and bond length are discussed.     

L12型铝合金的结构、弹性和电子性质的第一性原理研究

运用第一性原理方法研究了L1₂型铝合金相Al₃Sc和Al₃Zr的晶体结构、电子结构和弹性.结合能和形成能的计算表明,两种合金具有较强的合金化能力,且Al₃Zr较Al₃Sc具有更强的结构稳定性.电子结构分析表明,费米能级以下较多的价电子数决定了Al₃Zr具有较强的结构稳定性.计算并分析比较了两种合金相的单晶弹性常数（C₁₁,C₁₂和C₄₄）以及多晶弹性模量（体弹性模量B、剪切模量G、杨氏模量Y、泊松比ν和各向异性因子A）.通过对比实验和其他理论计算结果,进一步分析和解释了两种合金相的力学性质. 关键词： 铝合金 第一性原理 结构和电子性质 弹性     

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.     

Effects of Ca/Al ratio and extrusion process on Mg–Al–Ca alloys to produce a high toughness in-situ composite

The microstructures and tensile properties of Mg–Al₂Ca–Mg₂Ca in situ composites (Mg–17Al–8Ca, Mg–14Al–11Ca and Mg–12.5Al–12.5Ca) with different Ca/Al ratios have been studied in both as-cast and extruded conditions. The results indicated that by increasing Ca/Al ratio, new Mg₂Ca intermetallic introduces to the Al₂Ca phase in eutectic structure. Computer-aided cooling curve analysis confirmed the formation of these phases during solidification. Extrusion process not only altered the size of large bulk Al₂Ca intermetallic, but also changed the size and morphology of intermetallics in eutectic structure considerably. The results showed that with increasing Ca/Al ratio, tensile properties of cast composites changes slightly, but significant enhancement is observed after extrusion process. The strength and elongation values of Mg–12.5Al–12.5Ca (Ca/Al = 1) alloy improved from 166 MPa and 2% in as-cast condition to 465 MPa and 12% in hot-extruded condition. The reason for the improved toughness may be attributed to the formation of finer and well-dispersed distribution of hard (Al₂Ca) and ductile (Mg₂Ca) phases. It was found that hot extrusion easily deforms ductile Mg₂Ca phase in comparison with Al₂Ca phase. In as-extruded condition, there are more very fine dimples than as-casted condition because extrusion process leads to formation of fragmented tiny particles and more uniformity distribution of Al₂Ca particles.     

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.     

Mg NMR site analysis in metals and intermetallics

Nuclear magnetic resonance (NMR) of the low abundance and low gyromagnetic ratio isotope ²⁵Mg, I=5/2, 2.606 MHz/T, 10% abundant, is shown here to provide an informative probe for phase identification, site symmetry and site multiplicity of the intermetallic compounds which occur as strengthening precipitate phases in lightweight alloys. The intermetallics discussed here, Mg₁₇Al₁₂, MgZn₂, Mg₂Al₃ and Al₂CuMg, are the final equilibrium precipitate phases in a number of Mg- and Al-based heat-treatable alloys. The ²⁵Mg spectra of Mg in Al–10 at%Mg alloy show the progressive precipitation of Mg₂Al₃ from Mg in solid solution as a function of annealing time at 150 °C. Also reported are ²⁵Mg spectra for CuMg₂, Mg₄₄Al₁₅Zn₄₁ and Mg₂Sn, along with the counter atom ⁶⁷Zn and ⁶³Cu NMR spectra for MgZn₂ and CuMg₂. All spectra are simulated to determine nuclear interaction parameters and confirm site occupancy.     

Control Al/Mg intermetallic compound formation during ultrasonic-assisted soldering Mg to Al

To prevent the formation of Al/Mg intermetallic compounds (IMCs) of Al₃Mg₂ and Al₁₂Mg₁₇, dissimilar Al/Mg were ultrasonic-assisted soldered using Sn-based filler metals. A new IMC of Mg₂Sn formed in the soldered joints during this process and it was prone to crack at large thickness. The thickness of Mg₂Sn was reduced to 22 μm at 285 °C when using Sn-3Cu as the filler metal. Cracks were still observed inside the blocky Mg₂Sn. The thickness of Mg₂Sn was significantly reduced when using Sn-9Zn as the filler metal. A 17 μm Mg₂Sn layer without crack was obtained at a temperature of 200 °C, ultrasonic power of Mode I, and ultrasonic time of 2 s. The shear strengths of the joints using Sn-9Zn was much higher than those using Sn-3Cu because of the thinner Mg₂Sn layer in the former joints. Sn whiskers were prevented by using Sn-9Zn. A cavitation model during ultrasonic assisted soldering was proposed.     

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.     

Ordering effect on the mechanical,electronic and magnetic properties of the β-based non-canonical approximant phases: β-Al50Cu33Fe17, η-Al50Cu44Fe6 and φ-Al47.5Cu49.5Fe3

Abstract

Using transmission electron microscopy and X-ray diffraction, we established that the ordered η1-Al₅₀Cu₄₄Fe₆ and φ-Al_47.5Cu_49.5Fe₃ (Fmm2) alloys with nano-sized domain structure are formed by slowly cooling, whereas β-solid solutions with a short-range order were found in quenched states. The φ′-modification which exhibits the additional long-period superstructure was also observed in Al_47.5Cu_49.5Fe₃. The studies of low temperature magnetic susceptibility and heat capacity did not reveal any another phase transitions in these alloys. The indentation test showed that hardness and Young’s modulus consistently grow as β-Al₅₀Cu₃₃Fe₁₇ → η1-Al₅₀Cu₄₄Fe₆ → (φ+φ′)-Al_47.5Cu_49.5Fe₃ and approach to those in icosahedral phase. The same trend in the Young’s modulus was obtained for alloys containing β-solid solution with a short-range order. Ab initio calculations, however, predicted the opposite tendency in cubic β-Al₅₀Cu_50?xFe_x with a decrease in x, which was explained by the weakening of the covalent Fe 3d – Al sp bonding. This discrepancy between the results for β- and ordered phases, we related to a crucial effect of ordering which is accompanied by a progressive distortion of cubic local structure in the series β-Al₅₀Cu₃₃Fe₁₇ → η1-Al₅₀Cu₄₄Fe₆ → φ-Al_47.5Cu_49.5Fe_3. As we demonstrated for η-Al(Cu, Fe), these distortions lead to the strengthening of the both covalent Fe–Al and Cu–Al bonds and the higher modules.     

The different influences of the two incorporation sites of B atoms on the mechanical and thermodynamic properties of B2–ZrCu compounds: a first-principle calculation

We applied a first-principle calculation to investigate the different influences of the two incorporation sites of B atoms on the mechanical and thermodynamic properties of the near-equiatomic B2–ZrCu compound. The alloying B atoms have two possible incorporation sites, namely, octahedral interstices and Cu sites. When the concentration of B atoms is lower than 5.882 at.%, interstitial B atoms will be effective at improving the bulk modulus (B), shear modulus (G) and Young’s modulus (E) of the B2–ZrCu parent. When the concentration of the substitutional B atoms is lower than 12.5 at.%, the ductility of the parent will be strengthened. The interstitial B atoms that are located at octahedral interstices in the 〈110〉 direction can remarkably improve the Debye temperature (Θ_D) of the substituted Zr₈Cu_8?zB_z phase. The prediction for the melting point shows that the high-temperature stability is strengthened with the increase of the B concentration. Interstitial B atoms are beneficial to the minimum thermal conductivity. Finally, the electronic properties are discussed in detail to further understand the mechanical properties.     

Pb-Mg-Al合金腐蚀机理的电子理论研究

为了了解Pb-Mg-Al合金腐蚀的物理本质, 本文采用基于第一性原理的赝势平面波方法系统地计算了Pb-Mg-Al合金中各物相的结合能、费米能级和局域态密度等电子结构参数, 分析了合金的电化学腐蚀机理. 计算结果表明：Pb-Mg-Al合金中各主要组成物相稳定性大小关系为 Mg₁₇Al₁₂>Mg₂Pb>Mg;Mg,Mg₂Pb和Mg₁₇Al₁₂的费米能级存在E_f(Mg)>E_f(Mg₂Pb)>E_f(Mg₁₇Al₁₂)的关系, 说明Mg最容易失去电子, Mg₂Pb次之, Mg₁₇Al₁₂最难;局域态密度表明, 在同样的外界条件下, 体系中Mg相和Mg₂Pb相对于Mg₁₇Al₁₂均处于不稳定的状态, 容易失去电子, 即容易发生腐蚀. Pb-Mg-Al合金体系中不同物相的费米能级差构成了电化学腐蚀的电动势, 导致电子从费米能级高的Mg相和Mg₂Pb相流向费米能级低的Mg₁₇Al₁₂相, 使Pb-Mg-Al合金发生腐蚀.     

First-principles investigations on structural,elastic, electronic properties and Debye temperature of orthorhombic Ni3Ta under pressure

The structural, elastic, electronic properties and Debye temperature of Ni₃Ta under different pressures are investigated using the first-principles method based on density functional theory. Our calculated equilibrium lattice parameters at 0 GPa well agree with the experimental and previous theoretical results. The calculated negative formation enthalpies and elastic constants both indicate that Ni₃Ta is stable under different pressures. The bulk modulus B, shear modulus G, Young’s modulus E and Poisson’s ratio ν are calculated by the Voigt–Reuss–Hill method. The bigger ratio of B/G indicates Ni₃Ta is ductile and the pressure can improve the ductility of Ni₃Ta. In addition, the results of density of states and the charge density difference show that the stability of Ni₃Ta is improved by the increasing pressure. The Debye temperature Θ _D calculated from elastic modulus increases along with the pressure.     

Structural,elastic, thermodynamic and electronic properties of LuX (X = N,Bi and Sb) compounds: first principles calculations

ABSTRACT

The structural, electronic, elastic and thermodynamic properties of LuX (X = N, Bi and Sb) based on rare earth into phases, Rocksalt (B1) and CsCl (B2) have been investigated using full-potential linearized muffin-tin orbital method (FP-LMTO) within density functional theory. Local density approximation (LDA) for exchange-correlation potential and local spin density approximation (LSDA) are employed. The structural parameters as lattice parameters a₀, bulk modulus B, its pressure derivate B’ and cut-off energy (E_c) within LDA and LSDA are presented. The elastic constants were derived from the stress–strain relation at 0 K. The thermodynamic properties for LuX using the quasi-harmonic Debye model are studied. The temperature and pressure variation of volume, bulk modulus, thermal expansion coefficient, heat capacities, Debye temperature and Gibbs free energy at different pressures (0–50 GPa) and temperatures (0–1600 K) are predicted. The calculated results are in accordance with other data.     

Elastic and vibrational properties of Mg2Si1−xSnx alloy from first principles calculations

The structural, elastic and phonon properties of Mg₂Si_1?xSn_x alloy are investigated by performing density functional theory and density functional perturbation theory calculations. The calculated lattice parameter increases with the increase of Sn content obeying Vegard’s Law that is in good agreement with available experimental data. Shear modulus, Young’s modulus and sound velocities are determined from the obtained elastic constants. Phonon dispersion curves show a pronounced softening with increasing of Sn content. The softening mechanism has been discussed based upon the element mass and bond strength. Besides, phonon contribution to the Helmholtz free energy, the entropy and the constant-volume heat capacity are calculated within the harmonic approximation based on the calculated phonon density of states. Results show Mg₂Si_1?xSn_x is thermodynamically more stable with higher Sn content.     

Effect of doping Zn atom on the structural stability,mechanical and thermodynamic properties of AlLi phase in Mg–Li alloys from first-principles calculations

ABSTRACT

This work uses first-principles total energy calculations on the basis of density functional theory to predict the structural stability, mechanical and thermodynamic properties of Zn atom doped AlLi phase in Mg–Li–Al–Zn alloy. The values of the equilibrium lattice parameters and the formation of enthalpy are highly consistent with the experimental and previous calculations results available. Negative enthalpies of formation ΔH are predicted for all AlLi phase doped concentrations which have positive consequences for its structural stability. The elastic modulus is deduced by Voigt–Reuss–Hill arithmetic approximation. The bulk modulus of the Al–Li–Zn compounds increases as the doping concentrations increase, which are larger than the value of the AlLi phase. In particular, the stability and mechanical anisotropy of the Al–Li–Zn compounds are discussed. The charge density cloud map is drawn to reveal the bonding characteristics of four compounds. The changes in thermodynamic properties are derived by the phonon frequencies within the quasi-harmonic approximation.     

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.     

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.     

First-principles study of structural,elastic, electronic and thermodynamic properties of topological insulator Bi2Se3 under pressure

The structural, elastic, electronic and thermodynamic properties of the rhombohedral topological insulator Bi₂Se₃ are investigated by the generalized gradient approximation (GGA) with the Wu–Cohen (WC) exchange-correlation functional. The calculated lattice constants agree well with the available experimental and other theoretical data. Our GGA calculations indicate that Bi₂Se₃ is a 3D topological insulator with a band gap of 0.287 eV, which are well consistent with the experimental value of 0.3 eV. The pressure dependence of the elastic constants C_ij, bulk modulus B, shear modulus G, Young’s modulus E, and Poisson’s ratio σ of Bi₂Se₃ are also obtained successfully. The bulk modulus obtained from elastic constants is 53.5 GPa, which agrees well with the experimental value of 53 GPa. We also investigate the shear sound velocity V_S, longitudinal sound velocity V_L, and Debye temperature Θ_E from our elastic constants, as well as the thermodynamic properties from quasi-harmonic Debye model. We obtain that the heat capacity C_v and the thermal expansion coefficient α at 0 GPa and 300 K are 120.78 J mol^?1 K^?1 and 4.70 × 10^?5 K^?1, respectively.     

Electronic,elastic and dynamical properties of MgSe under pressure: rocksalt and iron silicide phase

The electronic, elastic and dynamical properties of MgSe in the rocksalt (B1) and iron silicide (B28) phase and the effects of pressure on these properties are investigated using first-principles method. The calculated electronic band structure indicates that the B1 phase of MgSe presents an indirect band-gap feature and the band gaps initially increase with pressure and subsequently decrease upon compression. Remarkably, an indirect-to-direct band-gap transition has been observed at the phase transition pressure. The elastic constants, bulk modulus, shear modulus, Young’s modulus, elastic anisotropy and B/G ratio of MgSe in the B1 and B28 phase at high pressure have also been investigated. The bulk modulus, shear modulus and Young’s modulus all increase monotonously with the increasing of pressure for the B1 and B28 phase of MgSe. The calculated phonon frequencies of the B1 phase at zero pressure agree well with available theoretical results. And the transverse acoustic phonon TA(X) mode of this phase completely softening to zero at 82 GPa. The phonon curves of the B28 phase under pressure have also been successfully investigated.