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.     

Temperature Dependence of Elastic Properties for Amorphous SiO2 by Molecular Dynamics Simulation

Large-scale and long-time molecular-dynamics simulations are used to investigate the temperature dependences of elastic properties for amorphous SiO2. The elastic moduli increase in a temperature range up to 1600 K and decrease thereafter. The anomalous behaviour in elasticity is explained by analysing the changes of atomic-scale structure with respect to increment of temperature. The mechanism originates predominantly from distortion of the SiO4 tetrahedra network in low-temperature ranges. At an elevated temperature range, thermal-induced Si-O bond stretching dominates the process and leads to normal temperature dependence of elastic properties.     

Split interstitials in computer models of single-crystal and amorphous copper

The effect of interstitial atoms in a dumbbell configuration on elastic moduli of single crystal copper has been investigated using molecular dynamics simulation. It has been shown that shear components of the dipole tensor and λ-tensor increase when the concentration of split interstitials exceeds 0.6–0.7%. This is associated with their interaction responsible for a significant change in the distribution of orientations of split interstitials and, hence, for a change in the type of the induced local symmetry breakings of the face-centered cubic structure. It has been found that, in the model of amorphous copper, there are “defects” (elastic dipoles) with properties similar to those of split interstitials in the single crystal. The deviatoric component of their λ-tensor is more than an order of magnitude greater than the dilatation component and is responsible for the decreased value of the shear modulus and thermal effects in noncrystalline metallic materials.     

High pressure phase transition and elastic properties of thorium chalcogenides

The structural and elastic properties of thorium chalcogenides at high pressure, have been investigated using a suitable inter-ionic potential. The calculated equation of state, phase transition pressures for B1-B2 transition and bulk moduli for ThX (X=S,Se,Te) compounds agree well with the experimental results. ThTe, which crystallizes in the CsCl structure, does not show any structural transition up to 48 GPa. The present analysis does not show any anomalous features in elastic properties arising from ‘f’ electrons.     

Elastic dipoles in the model of single-crystal and amorphous copper

The characteristic values of the elastic polarizability tensor components of point defects in crystalline and amorphous copper, which determine changes in the elasticity tensor components upon introduction of defects, have been found using the molecular dynamics method. A relation of the elastic polarizability tensor with the main parameter of the interstitialcy theory, i.e., shear susceptibility, has been established. An analysis of the elastic polarizability tensors of defects in crystalline and amorphous copper has demonstrated that, in a noncrystalline structure, there are specific atomic configurations that under deformation manifest themselves similarly to elastic dipoles (interstitial atoms in a dumbbell configuration) in single-crystal copper.     

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.     

Die elastischen Moduln von Eis-Einkristallen

The velocity of sound has been measured in ice with temperatures from the melting point to ?140°C, using two different supersonic pulse methods. The complete set of the five elastic moduli has been determined from the measurements for the above mentioned temperature range. To explain various results for piezoelectricity, density and elastic moduli a model of an aging process is discussed.     

Thermal expansion of the C15 Laves-phase materials TaV2 and TaV2H x

The thermal expansion of the C15 Laves-phase material TaV₂H _x was measured over the temperature range of 130–350?K for x?=?0, 0.34 and 0.53. A primary objective of the study was to see if the anomalous temperature dependence of elastic constants found in an earlier study is due to, or associated with, unusual thermal expansion. The expansion was typical of transition metals, and quite close to theoretical results for related Laves-phase materials. Grüneisen parameters were determined from the measurements, and these were also typical of transition metals, and close to calculated values for related materials. Both the thermal expansion and the Grüneisen parameters of TaV₂ decreased somewhat with the addition of hydrogen. No anomalous behavior of the expansion was found that might account for the highly anomalous temperature dependence of elastic moduli reported earlier. This absence is consistent with the attribution of the elastic constant behavior to an electronic structure effect.     

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.     

A first-principles study on the structural and elastic properties and the equation of state of wurtzite-type cadmium selenide under pressure

A first-principles investigation on the crystal structural and elastic properties and the equation of state of wurtzite-type cadmium selenide (w-CdSe) has been conducted using the plane-wave pseudo-potential density functional theory and the quasi-harmonic Debye model. The elastic constants, the aggregate elastic moduli, the elastic anisotropy, and Poisson's ratio under pressure have been investigated. Our calculated equilibrium lattice constants, the elastic constants, and the aggregate elastic moduli at zero pressure are in good agreement with the experimental data and other theoretical results. The variations in the compressional and shear elastic wave velocities with pressure at zero temperature up to pressure 2.7 GPa have been studied; the computed Debye temperature at zero pressure and zero temperature is in reasonable agreement with the result of Bonello et al., In addition, the equation of state of w-CdSe in the pressure range of 0–2.7 GPa and up to a temperature of 900 K has also been obtained.     

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.     

Dislocation field theory in 2D: Application to graphene

A two-dimensional (2D) dislocation continuum theory is being introduced. The present theory adds elastic rotation, dislocation density, and background stress to the classical energy density of elasticity. This theory contains four material moduli. Two characteristic length scales are defined in terms of the four material moduli. Non-singular solutions of the stresses and elastic distortions of an edge dislocation are calculated. It has been pointed out that the elastic strain agrees well with experimental data found recently for an edge dislocation in graphene.     

Network rigidity in GeSe2 glass at high pressure

Acoustic measurements using synchrotron radiation have been performed on glassy GeSe2 up to pressures of 9.6 GPa. A minimum observed in the shear-wave velocity, associated anomalous behavior in Poisson's ratio, and discontinuities in elastic moduli at 4 GPa are indicative of a gradual structural transition in the glass. This is attributed to a network rigidity minimum originating from a competition between two densification mechanisms. At pressures up to 3 GPa, a conversion from edge- to corner-sharing tetrahedra results in a more flexible network. This is contrasted by a gradual increase in coordination number with pressure, which leads to an overall stiffening of the glass.     

The pressure and temperature derivatives of the elastic moduli of lithium hydride

The pressure and temperature derivatives of the elastic moduli of single crystal LiH have been determined at room temperature, by the ultrasonic pulse echo method. From the pressure data, the mode Grüneisen parameters as well as the low and high temperature limiting values of the Grüneisen constant were computed; the latter were only slightly different. An equation of state has been constructed for LiH, and found to be in agreement with the experimental data. Based on a non-central force model, the values of the elastic moduli and their pressure derivatives have been calculated theoretically, and the latter values compared with the experimental data.     

Effects of pressure on structural,electronic, and mechanical properties of α,β,and γ uranium

The first-principles methods have been employed to calculate the structural, electronic, and mechanical properties of the α, β, and γ phases of uranium under pressure up to 100 GPa. The electronic structure has been viewed in forms of density of states and band structure. The mechanical stability of metal U in the α, β, and γ phases have been examined.The independent elastic constants, polycrystalline elastic moduli, as well as Poisson's ratio have been obtained. Upon compression, the elastic constants, elastic moduli, elastic wave velocities, and Debye temperature of α phase are enhanced pronouncedly. The value of B/G illustrates that α and γ phases are brittle in ground state.     

Complete elastic tensor through the first-order transformation in U2Rh3Si5

The complete elastic tensor of U(2)Rh(3)Si(5) has been determined over the temperature range of 5-300 K, including the dramatic first-order transition to an antiferromagnetic state at 25.5 K. Sharp upward steps in the elastic moduli as the temperature is decreased through the transition reveal the first-order nature of the phase change. In the antiferromagnetic state the temperature dependence of the elastic moduli scales with the square of the ordered moment on the uranium ion, demonstrating strong spin-lattice coupling. The temperature dependence of the moduli well above the transition indicates coupling of the ultrasonic waves to the crystal electric field levels of the uranium ion where the lowest state is a singlet. The elastic constant data suggest that the first-order phase change is magnetically driven by a bootstrap mechanism involving the ground state singlet and a magnetically active crystal electric field level.     

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.     

Strongly anisotropic elastic moduli of nematic elastomers: Analytical expressions and nonlinear temperature dependence

Exact formulae for the elastic moduli of the nematic elastomers are obtained by the implicit function method based on somewhat general energy functions. The formulae indicate that both the moduli parallel and perpendicular to the director of the nematic elastomers are smaller than the modulus of the classical elastomers because of the mechanical-nematic coupling. Moreover, the moduli are generally anisotropic due to the biaxiality induced by stretching the nematic elastomers perpendicular to the director. Then we get the explicit analytical expressions of the parallel and perpendicular moduli by making use of the Landau-de Gennes free energy and the neo-classical elastic energy. Very different from the classical elastomers, they are both strongly nonlinear functions of the temperature in the nematic phase. Furthermore, their ratio, the degree of anisotropy, changes with the temperature as well. The results agree qualitatively with some experiments. Better quantitative agreement is obtained by some modifications of the constitutive relation of the elastic energy.     

Ultrasonic studies on polystyrene/styrene butadiene rubber polymer blends filled with glass fiber and talc

The compatibility of solid blends: PS/SBR, PS/SBR filled with glass fiber and PS/SBR filled with talc were studied using ultrasonic pulse echo technique. Measurements were carried out at room temperature (298 K) and a frequency of 3 MHz. The ultrasonic velocity for the compressional wave and that for shear wave have been measured to obtain the elastic moduli data by knowing of density. The variation of ultrasonic wave velocities and elastic moduli with weight percent of the blend was found to be linear in PS/SBR blend, indicating some degree of compatibility but the drawback of elastic moduli indicate incompatibility of the system blend, while it deviates from linearity in blends of PS/SBR filled with glass fiber and talc but the increase in elastic moduli indicates that there is an increase in degree of compatibility between PS and SBR due to adding of glass fiber or talc. The ultrasonic absorptions for longitudinal wave in the temperature range from 298 to 423 K in the studied system were measured using ultrasonic pulse echo technique. Typical results showing the temperature dependence of the ultrasonic absorption at frequencies of 1, 2, 3 and 5 MHz are illustrated for all samples of the different compositions. The study of compositional and temperature dependence of the ultrasonic absorption in the present studied blends reveals the same behavior of the compatibility degree of the blends. Density data of the blends confirmed the ultrasonic results. Also the correlation between hardness and elastic moduli for the present blend systems has been studied.     

Size dependence of the thin-shell model for carbon nanotubes

There has been much debate on the choice for the representative wall thickness for the thin-shell model, although this model has demonstrated remarkable success in capturing many types of behavior of single-walled carbon nanotubes (SWNTs), in determining the buckling strains under compression, torsion, and bending, in particular. This analysis, using the Tersoff-Brenner potential and ab initio calculations, shows that the elasticity of the model thin shell evolves from isotropic to square symmetric with the decreasing tube diameter, leading to significant diameter dependence for all the elastic moduli and the representative wall thickness. Furthermore, the elastic moduli of multiwalled carbon nanotubes of diameters up to 10 nm are also size dependent.