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.     

First-principles study of elastic and electronic properties of layered ternary nitride SrZrN2 under pressure

The structural, elastic, and electronic properties of SrZrN₂ under pressure up to 100?GPa have been carried out with first-principles calculations based on density functional theory. The calculated lattice parameters at 0?GPa and 0?K by using the GGA-PW91-ultrasoft method are in good agreement with the available experimental data and other previous theoretical calculations. The pressure dependence of the elastic constants and the elastic-dependent properties of SrZrN₂, such as bulk modulus B, shear modulus G, Young's modulus E, Debye temperature Θ, shear and longitudinal wave velocity V_S and V_L, are also successfully obtained. It is found that all elastic constants increase monotonically with pressure. When the pressure increases up to 140?GPa, the obtained elastic constants do not satisfy the mechanical stability criteria and a phase transition might has occurred. Moreover, the anisotropy of the directional-dependent Young's modulus and the linear compressibility under different pressures are analysed for the first time. Finally, the pressure dependence of the total and partial densities of states and the bonding property of SrZrN₂ are also investigated.     

Structural, elastic and electronic properties of a new ternary-layered Ti2SiN

The structural, elastic and electronic properties of Ti₂SiN were studied by first-principle calculations. The calculated bond lengths of Ti-Si and Ti-C are 2.65 and 2.09 Å, respectively. The results show Ti₂SiN is mechanically stable, and its bulk modulus B, shear modulus G, Young's modulus E, Poisson's ratio μ and anisotropy factor A are determined to be 182 GPa, 118 GPa, 291 GPa, 0.233 and 1.57, respectively. The calculated electronic structure indicates that Ti₂SiN is anisotropic and conductive.     

Fluoride-doped MWCNT/Si3N4 composite with improved mechanical and structural properties

The addition of carbon nanotubes (CNT) in ceramic composites has stimulated a substantial interest due to their high mechanical, thermal and electrical properties. This approach used fluoride additives (AlF₃ and MgF₂) to prepare multi-walled carbon nanotubes/silicon nitride (MWCNT/Si₃N₄) composite densified at 1700 °C for 1 h by hot press (HP) sintering. The microstructural analyses of MWCNT/Si₃N₄ composites indicate that the fluoride additives have substantially improved densification and the transformation of α-Si₃N₄ to β-Si₃N₄. As observed, the mechanical properties, i.e. flexural strength, fracture toughness, Young's modulus and hardness of MWCNT/Si₃N₄ composites are improved with an increasing concentration of MWCNT. These results attributed to the highly dense composites, strong interfacial interaction and the pull-out mechanism of MWCNT and β-Si₃N₄. The maximum values of fracture toughness flexural strength, Young's modulus, and hardness were 12.76 ± 1.15 MPa.m^0.5, 883 ±46 MPa, 260 ±9 GPa, and 26.4 ± 1.3 GPa, respectively. The improved mechanical properties also ascribed to the synergistic strengthening and toughening influence of MWCNT and β-Si₃N₄.     

Young's modulus as a function of composition for an n-type lead–antimony–silver–telluride (LAST) thermoelectric material

For 17 cast lead–antimony–silver–telluride (LAST) thermoelectric specimens (representing 14 different chemical compositions), a combination of Vickers and Knoop microindentation techniques were used to determine the composition-dependent Young's modulus, E, which ranged from 24 to 68?GPa. Following microindentation, independent nanoindentation measurements were also performed on 10 of the 17 specimens. In the literature, for pseudobinary joins in ternary or quaternary compounds (with the compositions A _x B_{1– x} C or A _x B_{1– x} CD, respectively), changes in the Young's modulus have been expressed as quadratic functions of the compositional parameter x. In this study, we extend the quadratic functional form to a paraboloid in four composition variables to describe composition-dependent changes in E for the LAST compounds. Also, the composition-dependent changes in LAST are compared to the trends observed in the literature for E and bulk modulus for systems described by a single compositional variable.     

First-principles study of structural and elastic properties of CrO2 at high pressure

The structural and elastic properties of CrO₂ in the rutile phase under high pressures have been investigated using pseudopotential plane-wave method based on density functional theory. The optimized lattice parameters and the bulk modulus at zero pressure agree well with available experimental and theoretical data. The elastic constants C ₁₁, C ₁₂, C ₄₄, C ₃₃, C ₁₃, and C ₆₆ at zero pressure are calculated to be 359.91, 264.69, 143.28, 309.45, 218.45, and 260.74 GPa, respectively. Elastic constants, bulk modulus, shear modulus, Young's modulus, and Poisson's ratio under pressures are obtained. Our results indicate that the rutile phase is mechanically stable below 11.99 GPa. The elastic anisotropy of rutile phase under pressures has also been predicted.     

Temperature-dependent elastic moduli of lead telluride-based thermoelectric materials

In the open literature, reports of mechanical properties are limited for semiconducting thermoelectric materials, including the temperature dependence of elastic moduli. In this study, for both cast ingots and hot-pressed billets of Ag-, Sb-, Sn- and S-doped PbTe thermoelectric materials, resonant ultrasound spectroscopy (RUS) was utilized to determine the temperature dependence of elastic moduli, including Young's modulus, shear modulus and Poisson's ratio. This study is the first to determine the temperature-dependent elastic moduli for these PbTe-based thermoelectrics, and among the few determinations of elasticity of any thermoelectric material for temperatures above 300 K. The Young's modulus and Poisson's ratio, measured from room temperature to 773 K during heating and cooling, agreed well. Also, the observed Young's modulus, E, versus temperature, T, relationship, E(T) = E ₀(1–bT), is consistent with predictions for materials in the range well above the Debye temperature. A nanoindentation study of Young's modulus on the specimen faces showed that both the cast and hot-pressed specimens were approximately elastically isotropic.     

Electronic structure,elastic and thermodynamic properties of α-phase Na3N under pressure from first principles

The structural, electronic, elastic and thermodynamic properties of α-phase Na₃N under pressure are investigated by performing first principles calculations within generalized gradient approximation. The elastic constants, bulk modulus, shear modulus, Young's modulus, and Poisson's ratio dependencies on pressure are also calculated. The thermodynamic properties of the α-phase Na₃N are calculated using the quasi-harmonic Debye model. The dependencies of the heat capacity and the thermal expansion coefficient, as well as the Grüneisen parameter on pressure and temperature are investigated systematically in the ranges of 0–1 GPa and 0–100 K.     

DSC and elastic moduli studies on tellurite-vanadate glasses containing antimony oxide

xSb₂O₃-40TeO₂-(60 − x) V₂O₅ glasses with 0 ≤ x ≤ 10 (in mol%) have been prepared by rapid- melt quenching method. DSC curves of these ternary glasses have been investigated. The glass transition properties that have been measured and reported in this paper, include the glass transition temperature (T _g ), glass transition width (ΔT _g ), heat capacity change at glass transition (ΔC _P ) and fragility (F). Thermal stability, Poisson’s ratio, fragility and glass forming tendency of these glasses have been estimated, to determine relationship between chemical composition and the thermal stability or to interpret the structure of glass. In addition, Makishima and Makenzie’s theory was applied for determination of Young’s modulus, bulk modulus and shear modulus, indicating a strong relation between elastic properties and structure of glass. Generally, results of this work show that glass with x = 0 has the highest shear, bulk and Young’s moduli which make it as suitable candidate for the manufacture of strong glass fibers in technological applications; but it should be mentioned that glass with x = 8 has higher handling temperature and super resistance against thermal attack.     

High hardness,low Young's modulus and low friction of nanocrystalline ZrW2 Laves phase and Zr1−xWx thin films

Zr_1?xW_x nanocrystalline films of Zr-W solid solutions and ZrW₂ Laves phase were synthesized by magnetron co-sputtering. Large values of the H/E ratio up to 0.09 are observed for grain sizes in the nanometer range along with a hardness above 10 GPa and Young's modulus below 230 GPa. H/E values are correlated with the developed surface of grain boundaries suggesting an elastic deformation mostly handled by the grain boundaries. This is associated to friction coefficients comparable to those of metallic glass surfaces. In contrast to fragile bulk Laves phases, no cracks were detected at the film surface after indentation and scratch test of nanocrystalline ZrW₂. The friction coefficient of such films against diamond tip was in the range 0.08–0.15, similarly to metallic glass surfaces.     

Theoretical prediction of structural,elastic and electronic properties of Si-doped TiCuGe intermetallics

The structural, elastic and electronic properties of TiCuGe_1?xSi_x alloys (x = 0, 0.25, 0.5, 0.75 and 1) were investigated by means of first-principles calculations within the framework of density functional theory (DFT). The calculated results demonstrate that the partial substitution of Si with Ge in TiCuGe leads to a decrease of lattice constants, and the optimized structural parameters are in agreement with the available experimental values. The results of electron density are compared with the theoretical and experimental data from the literature. From energetic point of view, it is found that with increase of Si content the structural stability of TiCuGe_1?xSi_x compounds increases apparently. The single-crystal elastic constants are obtained by computing stress–strain function according to Hooke's law, and then the bulk modulus B, shear modulus G, Young's modulus E and Poisson's ratio ν of polycrystalline aggregates are derived. The calculated results show that among the TiCuGe_1?xSi_x alloys, TiCuGe_0.75Si_0.25 exhibited the largest stiffness, while TiCuGe_0.25Si_0.75 showed the best ductility. Finally, the electronic density of states (DOSs) are further studied and discussed.     

Structural,elastic and mechanical properties of orthorhombic SrHfO3 under pressure from first-principles calculations

Structural, elastic and mechanical properties of orthorhombic SrHfO₃ under pressure have been investigated using the plane-wave ultrasoft pseudopotential technique based on the first-principles density functional theory. The calculated equilibrium lattice parameters and elastic constants of orthorhombic SrHfO₃ at zero pressure are in good agreement with the available experimental and calculational values. The lattice parameters, total enthalpy, elastic constants and mechanical stability of orthorhombic SrHfO₃ as a function of pressure were studied. With the increasing pressure, the lattice parameters and volume of orthorhombic SrHfO₃ decrease whereas the total enthalpy increases. Orthorhombic SrHfO₃ is mechanically stable with low pressure (<52.9 GPa) whereas that is mechanically instable with high pressure (>52.9 GPa). The bulk modulus, shear modulus, Young's modulus and mechanical anisotropy of orthorhombic SrHfO₃ as a function of pressure were analyzed. It is found that orthorhombic SrHfO₃ under pressure has larger bulk modulus, better ductility and less mechanical anisotropy than orthorhombic SrHfO₃ at 0 GPa.     

Size effect on nanomechanical properties of ZnO cones using in situ transmission electron microscopy

Nanoscale fracture and strain-induced structure variation of ZnO nanocones are determined using in situ transmission electron microscopy compression experiments. For the single-crystalline nanocones with diameters of 100–300 nm, the Young's modulus is in the range of 7.7–48 GPa and the ultimate tensile strength is in the range of 2.4–4.3%. The Young's modulus and tensile strength increase with decreasing diameter. Here, we report the nanogenerator of ZnO nanocones can be used mechanical energy to output 90 nW/mm².     

Pressure‐induced incompressibility and point singularity of mechanical properties of TaC in NiAs‐type structure

The structural and elastic properties of TaC in NiAs‐type structure under high pressure have been investigated using first principles calculations based on density functional theory. Results indicate that the incompressibility along the c‐axis of TaC exceeds that of diamond under higher pressure. Particularly, an interesting point singularity exists in its mechanical properties as the pressure increases from 20 GPa to 40 GPa. The minimal shear modulus, Young's modulus, Debye temperature, and maximum Poisson ratio of TaC are simultaneously obtained at 28 GPa. The calculations of hardness indicate that the NiAs‐type TaC crystal possesses excellent mechanical properties. (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Investigations on structural,elastic, thermodynamic and electronic properties of TiN,Ti2N and Ti3N2 under high pressure by first-principles

The lattice parameters, cell volume, elastic constants, bulk modulus, shear modulus, Young's modulus and Poisson's ratio are calculated at zero pressure, and their values are in excellent agreement with the available data, for TiN, Ti₂N and Ti₃N₂. By using the elastic stability criteria, it is shown that the three structures are all stable. The brittle/ductile behaviors are assessed in the pressures from 0 GPa to 50 GPa. Our calculations present that the performances for TiN, Ti₂N and Ti₃N₂ become from brittle to ductile with pressure rise. The Debye temperature rises as pressure increase. With increasing N content, the enhancement of covalent interactions and decline of metallicity lead to the increase of the micro-hardness. Their constant volume heat capacities increase rapidly in the lower temperature, at a given pressure. At higher temperature, the heat capacities are close to the Dulong–Petit limit, and the heat capacities of TiN and Ti₂N are larger than that of c-BN. The thermal expansion coefficients of titanium nitrides are slightly larger than that of c-BN. The band structure and the total Density of States (DOS) are calculated at 0 GPa and 50 GPa. The results show that TiN and Ti₂N present metallic character. Ti₃N₂ present semiconducting character. The band structures have some discrepancies between 0 GPa and 50 GPa. The extent of energy dispersion increases slightly at 50 GPa, which means that the itinerant character of electrons becomes stronger at 50 GPa. The main bonding peaks of TiN, Ti₂N and Ti₃N₂ locate in the range from −10 to 10 eV, which originate from the contribution of valance electron numbers of Ti s, Ti p, Ti d, N s and N p orbits. We can also find that the pressure makes that the total DOS decrease at the Fermi level for Ti₂N. The bonding behavior of N–Ti compounds is a combination of covalent and ionic nature. As N content increases, valence band broadens, valence electron concentration increases, and covalent interactions become stronger. This is reflected in shortening of Ti–N bonds.     

First-principles study on electronic structure and elastic properties of Fe16N2

We have performed first-principles study on structural stability, elastic properties and electronic structure of Fe₁₆N₂ by applying LSDA+U method. The calculated values of formation energy and reaction enthalpy for decomposition reaction indicate that Fe₁₆N₂ is a thermodynamically stable phase at the ground state. The six independent elastic constants are derived and the bulk modulus, Young's modulus, shear modulus, and Poisson's ratio are determined as 180 GPa, 199 GPa, 76 GPa and 0.32, respectively. The elastic constants meet all the mechanical stability criteria. The ductility of Fe₁₆N₂ is predicted by Pugh's criterion. The strong bonding between Fe and N atoms results in high values of elastic constants C₁₁ and C₃₃, and contributes to the strengthening of the Fe₁₆N₂ structural stability. The total and partial densities of states (DOS) suggest the existence of hybridization between N-p and Fe-d bands. The position of the Fermi level in DOS curve implies that Fe₁₆N₂ is a metastable phase.     

Composition-related structural,thermal and mechanical properties of Ba1−xSrxTiO3 ceramics (0 ≤ x ≤ 0.4)

The Ba_1?xSr_xTiO₃ (BST) ceramics were prepared by conventional ceramic method. The crystalline structure and morphology were studied by X-ray diffraction and scanning electron microscopy, respectively. Experimental results show that increase of sintering temperature leads to an uncontrolled precipitating of the phase with a lower content of Ti. The dielectric constant and specific heat as a function of composition and temperature were investigated. The increasing concentration of Sr ions leads to a shift of the Curie point below room temperature. To determine the elastic constants (the Young's modulus E, the shear modulus G and the Poisson's ratio v) of BST, a method of measurement of the longitudinal (ν_L) and transverse (ν_T) ultrasonic wave velocities for this type of material was developed. The structural, dielectric and mechanical properties of BST ceramics were discussed in terms of microstructure and chemical composition     

Elastic and thermal properties of Sr1−xYxCoO3

The elastic and thermal properties of Sr_1?xY_xCoO₃ (0 ≤ x ≤ 0.5) have been investigated, probably for the first time, by using modified rigid ion model. We present the elastic constants (C_11, C_12, C₄₄) and other elastic properties like bulk modulus (B), Young's modulus (Y), shear modulus (G), Poisson's ratio (σ), Lame's parameter (μ, λ), transverse, longitudinal and average wave velocity (υ_t, υ_l and υ_m) and anisotropy parameter (A). Besides, we have reported the thermodynamic properties molecular force constant (f), Reststrahlen frequency (υ), cohesive energy (φ), Debye temperature (θ_D) and Gruneisen parameter (γ). We have also computed the variation of specific heat (C) and volume thermal expansion coefficient (α). The computed results on the elastic and thermodynamic properties are the first report on them. This model is capable of explaining the Cauchy's discrepancy, elastic and thermal properties successfully.     

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.     

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)