On mechanical stability of molybdenum

Investigations of the strength properties of materials under different loading conditions are of practical importance in many engineering applications. The knowledge of elastic moduli as a function of strain is required for determination of strength properties. In the present work, we have determined the elastic moduli of molybdenum through first principles study of the energy changes under three different loading conditions namely ‘uni-axial tensile deformation’ along [0 0 1] direction, ‘uni-axial tensile loading’ along [0 0 1] direction and ‘hydrostatic tensile loading’. The stability conditions for the system are expressed in terms of the elastic moduli and analyzed along the deformation paths corresponding to these three loading modes. The theoretical spall strength (σ_S), tensile strength (σ_T) along [0 0 1] direction and hydrostatic tensile strength (σ_H), are evaluated as a stress at the first onset of the instability for three loading conditions, respectively. The calculated equilibrium volume and elastic moduli are compared with that reported from experimental and other theoretical works.     

Elastic properties study of single crystal NH3 up to 26 GPa

Single crystal Brillouin and Raman scattering measurements on NH₃ in a diamond anvil cell have been performed under pressures up to 26 GPa at room temperature. The pressure dependencies of acoustic velocity, adiabatic elastic constants, and bulk moduli of ammonia from liquid to solid III and solid IV phase have been determined. All the nine elastic constants in orthorhombic structure phase IV were presented for the first time, each elastic constant grows monotonously with pressure and a crossover of the off‐diagonal moduli C₁₂ and C₁₃ was observed at around 12 GPa because of their different pressure derivative values. We also performed ab initio simulations to calculate the bulk elastic moduli for orthorhombic ammonia, the calculated bulk moduli agree well with experimental results. In Raman spectra the very weak bending modes ν₂ and ν₄ for orthorhombic ammonia are both observed at room temperature, a transition point near 12 GPa is also found from the pressure evolution of the Raman bands. Copyright © 2011 John Wiley & Sons, Ltd.     

Temperature dependence of elastic moduli for solid C60

The attenuation and velocity of ultrasonic waves (at a frequency of ～4 MHz) along the 〈111〉 and 〈100〉 directions in solid C₆₀ single-crystal samples are measured in the temperature range 100–300 K. The temperature dependences of the complete set of elastic constants for C₆₀ fullerite are determined from the experimental data. It is shown that the specific features in the behavior of the elastic moduli near the orientational phase transition temperature are associated with different contributions of the relaxation processes to the effective elastic moduli. The activation volume and deformation potentials for the ground and excited states of the C₆₀ low-temperature phase are evaluated from the results obtained in this work and the data available in the literature.     

Elastic moduli of single-crystal C60

The matrix of elastic constants of the fcc phase of solid C₆₀ has been determined experimentally from measurements of the the velocity of 5 MHz ultrasound in single-crystal samples with different crystallographic orientations. The following values were obtained for the elastic moduli: C ₁₁=14.9±0.9 GPa, C ₁₂=8.8±1.0 GPa, and C ₄₄=6.6±0.18 GPa. The results are compared with theoretical estimates of the elastic moduli and data obtained in previous measurements of the elastic characteristics of solid C₆₀. Fiz. Tverd. Tela (St. Petersburg) 40, 173–175 (January 1998)     

Structural investigation of glasses with doped some transition metal oxides under the influence of gamma irradiation

The ultrasonic velocity of the alkali-borosilicate with different transition metal oxides (TMO) has been studied using the pulse echo technique. The elastic moduli such as elastic constant and bulk modulus have been obtained from the experimental data. Changes in the structure with different gamma irradiation doses have been investigated by using FTIR spectroscopy and ultrasonic studies. The results show that structural changes in the BO₃ to BO₄ due to TMO and irradiation are obtained.     

Study of elastic properties of CeO2 by statistical moment method

The purpose of the present paper is to investigate the temperature and pressure dependences of the elastic properties of cerium dioxide using the statistical moment method (SMM). The equation of states of bulk CeO₂ is derived from the Helmholtz free energy, and the pressure dependences of the elastic moduli like the bulk modulus, B_T, shear modulus, G, Young’s modulus, E, and elastic constants (C11, C12, and C44) are presented taking into account the anharmonicity effects of the thermal lattice vibrations. In the present study, the influence of temperature and pressure on the elastic moduli and elastic constants of CeO₂ has also been studied, using three different interatomic potentials. We compare the results of the present calculations with those of the previous theoretical calculations as well as with the available experiments.     

Effect of hydrostatic pressure on the elastic properties of some rare earth-iron laves phase compounds

The pressure dependence of the Young's and shear moduli of RFe₂ (R = Sm, Gd, Tb, Dy, Ho and Er) has been determined at room temperature in the pressure range between 0 and 1 GPa The elastic moduli of GdFe₂, DyFe₂, HoFe₂ and ErFe₂ show a moderate increase with increasing hydrostatic pressure However, the elastic moduli of SmFe₂ and TbFe₂ exhibit an initially drastic increase followed by a high, and linear, pressure dependence From the pressure and temperature derivatives of the elastic moduli of these RFe₂ Laves phase compounds the equations of state and the Gruneisen parameters have been derived The variation of the elastic properties with hydrostatic pressure is compared with the effect of magnetic fields The anomalous behavior of SmFe₂ and TbFe₂ is discussed.     

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.     

Optical and acoustic properties of TeO2/WO3 glasses with small amount of additive ZrO2

The optical and acoustic properties of tellurite glasses in the system TeO₂/ZrO₂/WO₃ have been investigated. The refractive index at different wavelengths and the optical spectra of the glasses have been measured. From the refractive index and absorption edge studies for prepared glasses, the optical parameter viz; optical band gap (E_opt), Urbach energy, (ΔE), dispersion energy, E_d, and the average oscillator energy, E₀, have been calculated. Sound velocities were measured by pulse echo technique. From these velocities and densities values, various elastic moduli were calculated. The variations in the refractive index, optical energy gap and elastic moduli with WO₃ content have been discussed in terms of the glass structure. Quantitatively, we used the bond compression model for analyzing the room temperature elastic moduli data. By calculating the number of bonds per unit volume, the average stretching force constant, and the average ring size we can extract valuable information about the structure of the present glasses.     

Elastic moduli of nc-TiN/a-Si3N4 nanocomposites: Compressible, yet superhard

Earlier measurements of elastic moduli of nc-TiN/a-Si₃N₄ nanocomposites of different composition and hardness by means of vibrating reed and surface Brillouing scattering, that yield Young’s and shear modulus, as well as the Poisson’s ratio, have been confirmed by high-pressure X-ray diffraction measurements, that yield bulk modulus. It is found that elastic moduli of all measured samples are essentially the same within relatively small error of measurements, and only slightly lower than that of pure TiN. The nanocomposites are superhard thanks to their unique nanostructure with strengthened SiN_x interface.     

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.     

Investigations of radiation shielding using Monte Carlo method and elastic properties of PbO-SiO2-B2O3-Na2O glasses

Several physical parameters such as the packing density (PD), oxygen molar volume (OMV), oxygen packing density (OPD) and the elastic moduli of the quaternary glass system xPbO-(30-x)SiO₂-46.67B₂O₃-23.33Na₂O (x = 0, 5, 10 and 15 mol%) have been evaluated. The elastic moduli were computed according to Makishima-Mackenzie model and Rocherulle model. The values of these moduli have been compared to their experimental values. Moreover, different shielding parameters such as mass attenuation coefficients (MAC), half value layer (HVL), mean free path (MFP), effective atomic numbers (EAN), effective electron densities (EED) and buildup factors have been evaluated using the WinXcom program in the energy range 0.015–15 MeV for the quaternary studied glass system. The MAC values have been compared with MCNPX (version 2.6.0) Monte Carlo code. Besides, mass stopping power (MSP) for proton, alpha and electron as well as the removal cross section for fast neutron (∑_R) have been calculated. The results observed that the composition has the highest value of PbO (15 mol %) showed excellent nuclear radiation shielding and elastic properties.     

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.     

Ultrasonic study of solid-phase amorphization and polyamorphism in an H2O-D2O (1: 1) solid solution

The elastic moduli and volume of H₂O-D₂O (1: 1) isotopically mixed ice (solid solution) have been studied at the solid-phase amorphization of normal 1h ice under compression at a temperature of 77 K and at the transition from high-density amorphous ice to low-density amorphous ice with subsequent successive crystallization to cubic (1c) and hexagonal (1h) ice at isobaric (0.05 GPa) heating. Comparison of the results with the respective data for H₂O and D₂O ices indicates that the observed concentration (in the isotopic composition) dependences of the elastic moduli and their derivatives for different phases of ice at isotopic hydrogen substitution in the H₂O, H₂O-D₂O (1: 1), and D₂O chain can be both monotonic and significantly nonmonotonic.     

Low temperature elastic behaviour of As-Sb-Se and Ge-Sb-Se glasses

The ternary glasses of arsenic and germanium with antimony and selenium can be prepared in large sizes for optical purposes. The elastic behaviour of eight compositions of each glass has been studied down to 4.2 K using a 10 MHz ultrasonic pulse echo interferometer. The glasses have a normal elastic behaviour, with the velocities gradually increasing as the temperature is lowered. An anharmonic solid model of Lakkad satisfactorily explains the temperature variations. The elastic moduli of Ge _x Sb₁₀Se_90?x glasses increase linearly as the Ge content is increased up to 25 at. % and beyond this the increase is nonlinear. (AsSb)₄₀Se₆₀ glasses show a linear increase in elastic moduli with increasing Sb content. The elastic moduli of As _x Sb₁₅Se_85?x glasses exhibit a drastic change near the stoichiometric composition As₂₅Sb₁₅Se₆₀. These behaviours have been qualitatively explained on the basis of the structural changes in glasses.     

The effects of magnetic moment collapse under high pressure,on physical properties in mono-borides TMB (TM = Mn,Fe): a first-principles

In this paper, spin polarization and pressure effects on the structure, magnetic and anisotropic elastic properties of the 3d transition-metal mono-borides TMB (TM = Mn, Fe) have been investigated by using generalized gradient approximation within the framework of density functional theory. It seems that manganese in MnB carries a higher magnetic moment (1.83 μ_B) than iron in FeB (1.12 μ_B). Applied pressure ranges from 0 to 150 GPa, these ferromagnetic compounds show at a certain pressure (143 GPa for MnB and 77 GPa for FeB) a pronounced abrupt collapse of the magnetic moment (first-order quantum phase transitions). Furthermore, elastic properties, including bulk, shear and Young moduli as well as the Poisson ratio are obtained by Voigt–Reuss–Hill approximation. By the elastic stability criteria, it is predicted that MnB and FeB are stable up to the selected pressures. In both cases, mechanical anisotropies are discussed by calculating different anisotropic indexes and factors. The three-dimensional surfaces and planar contours of Young, and bulk moduli of compounds are plotted, at several crystallographic planes ((100), (010) and (001)) to reveal their elastic anisotropy.     

Comparative first-principles calculations of electronic, optical and elastic anisotropy properties of CsXBr3 (X=Ca,Ge,Sn ) crystals

Detailed ab initio calculations of the structural, electronic, optical and elastic properties of CsCaBr₃, CsGeBr₃ and CsSnBr₃ crystals are presented in this paper. Based on the obtained results, CsCaBr₃ is characterized as a dielectric with an indirect band gap, whereas CsGeBr₃ and CsSnBr₃ are semiconductors with very narrow direct band gaps. The first theoretical estimations of the refractive indexes for all compounds are reported. Variations of the electron density difference distribution induced by changes of the second cation were analyzed and related to the type of chemical bonding between atoms. In addition, the complete set of elastic parameters (which includes the elastic constants, elastic compliance constants, bulk and Young’s moduli, elastic anisotropy) was obtained. Directional anisotropy of elastic properties was visualized; the directions in the crystal lattices, along which the maximal and minimal values of the Young’s moduli are realized, were identified.     

Structural,elastic, electronic properties and Fermi surface for superconducting Mo2GaC in comparison with V2GaC and Nb2GaC from first principles

First-principles calculations were performed to investigate structural, elastic and electronic properties of the first discovered superconducting nanolaminate Mo₂GaC in comparison with isostructural Ga-containing phases V₂GaC and Nb₂GaC. As a result, the optimized lattice parameters, independent elastic constants, bulk moduli, compressibility, shear moduli, Young’s moduli and Poisson’s ratio were evaluated. Besides, electronic bands, densities of states (DOS), total and site-projected l-decomposed DOS at the Fermi level, as well as the shapes of the Fermi surfaces for these Ga-containing nanolaminates were obtained and analyzed in comparison with the available theoretical and experimental data.     

On-line phase transition in La1− x Sr x MnO3 (0.28 ≤ x ≤ 0.36) perovskites through ultrasonic studies

La_{1? x} Sr _x MnO₃ perovskite manganite materials with different compositions (x?=?0.28, 0.31 and 0.36) have been prepared employing solid-state reaction technique. On-line evaluation of ultrasonic velocities and longitudinal attenuation of the above samples has been done over a wide range of temperatures using the transmission method. The observed anomalies in velocities, attenuation and elastic moduli reveal the occurrence of lattice softening and hardening near Curie temperature. The observed dramatic hardening in sound velocities and softening in attenuation are correlated with the phase transition, i.e. ferromagnetic to paramagnetic. The increase in magnitude of maximum velocity with change in Sr content at T _c indicates the existence of linear magnetostriction effect. The elastic moduli study elucidates the observations made from the above-mentioned studies. The variation in the ultrasonic velocities, longitudinal attenuation and its derived parameters help us to understand the competitions between ferromagnetism and paramagnetism.     

Effect of ZnF2 and WO3 on elastic properties of oxyfluoride tellurite ZnF2–WO3–TeO2glasses: Theoretical analysis

The elastic properties of oxyfluoride tellurite glasses in the ternary system ZnF₂-WO₃ -TeO₂ were analyzed and their changes when ZnF₂ was replaced with TeO₂ or WO₃ were predicted. The most significant structural and compositional parameters were evaluated on the basis of the well known models and approaches existing in the field and correlated with both elastic moduli and Poisson's ratio. It has been found that the molar volume, fractal bond connectivity, first-order stretching force constant of the Te–O and W–O covalent bonds and dissociation energy per unit volume of the constituent components play an important role in determining and predicting of elastic moduli. The semi-empirical formula of Abd El-Moneim and Alfifi, which correlates bulk modulus with the ratio between packing density and mean atomic volume, appears to be valid for the investigated oxyfluoride tellurite glasses. On the basis of Makishima-Mackenzie's theory, the agreement between the theoretically calculated and experimentally measured values is excellent for shear and Young's moduli and satisfactory for Poisson's ratio as well as bulk and longitudinal moduli. The slight divergence between the theoretical and experimental values was interpreted in terms of the basic structural units that constituting the glass network.