Aggregate Elastic Moduli Research Articles

First-Principles Study of Structural, Elastic and Electronic Properties of OsSi

First-principles study of structural, elastic, and electronic properties of the B20 structure OsSi has been reported using the plane-wave pseudopotential density functional theory method. The calculated equilibrium lattice and elastic constants are in good agreement with the experimental data and other theoretical results. The dependence of the elastic constants, the aggregate elastic modulus, the deviation from the Cauchy relation, the elastic wave velocities in different directions and the elastic anisotropy on pressure have been obtained and discussed. This could be the first quantitative theoretical prediction of the elastic properties under high pressure of OsSi compound. Moreover, the electronic structure calculations show that OsSi is a degenerate semiconductor with the gap value of 0.68 eV, which is higher than the experimental value of 0.26 eV. The analysis of the PDOS reveals that hybridization between Os d and Si p states indicates a certain covalency of the Os-Si bonds.

First-principles calculations on elasticity of [formula omitted] under pressure

First-principles calculations of the crystal structure and the elastic properties of OsN 2 have been carried out with the plane-wave pseudopotential density functional theory method. The calculated values are in very good agreement with experimental data as well as with some of the existing model calculations. The dependence of the elastic constants c i j , the aggregate elastic moduli ( B , G , E ) , Poisson’s ratio, and the elastic anisotropy on pressure has been investigated. Moreover, the variation of the Debye temperature and the compressional and shear elastic wave velocities with pressure P up to 60 GPa at 0 K have been investigated for the first time.

Elasticity and thermodynamic properties of α-Ta 4AlC 3 under pressure

First-principles calculations of the crystal structure and the elastic properties of α-Ta 4AlC 3 have been carried out with the plane-wave pseudopotential density functional theory method. The calculated values are in very good agreement with experimental data as well as with some of the existing model calculations. The pressure dependence of the elastic constants c ij , the aggregate elastic moduli ( B, G, E), the Poisson's ratio, and the elastic anisotropy has been investigated. Using the quasi-harmonic Debye model considering the phonon effects, the temperature and pressure dependencies of isothermal bulk modulus, and the thermal expansions, and Grüneisen parameters, as well as Debye temperatures are investigated systematically in the ranges of 0–60 GPa and 0–1500 K as well as compared to available data.

First‐principles calculations on elasticity and the thermodynamic properties of TaC under pressure

AbstractFirst‐principles calculations on the elastic and the thermodynamic properties of TaC have been carried out with the plane‐wave pseudopotential density functional method. The calculated values are in very good agreement with experimental data as well as with some of the existing model calculations. The dependence of the elastic constants cij, the aggregate elastic moduli (B, G, E), and the elastic anisotropy on pressure have been investigated. Moreover, the variation of the Poisson ratio and Debye temperature with pressure have been investigated for the first time. Through the quasi‐harmonic Debye model, the thermodynamic properties were also obtained successfully. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Elasticity and thermodynamic properties of RuB2 under pressure

Abstract First-principles calculations of the crystal structure and the elastic properties of RuB 2 have been carried out with the plane-wave pseudopotential density functional theory method. The calculated values are in very good agreement with experimental data as well as with some of the existing model calculations. The elastic constants c ij , the aggregate elastic moduli ( B , G , E ), Poisson's ratio, and the elastic anisotropy with pressure have been investigated. Through the quasi-harmonic Debye model considering the phonon effects, the isothermal bulk modulus, the thermal expansions, Gruneisen parameters, and Debye temperatures depending on the temperature and pressure are obtained in the whole pressure range from 0 to 60 GPa and temperature range from 0 to 1100 K as well as compared to available data.

Structure and elastic properties of boron suboxide at 240 GPa

Structure and elastic properties of boron suboxide at high pressure have been investigated using generalized gradient approximation within the plane-wave pseudopotential density functional theory. The elastic constants are calculated using the finite strain method. The pressure dependences of lattice parameters, elastic constants, aggregate elastic moduli, and sound velocities of boron suboxide are predicted. It is found that the most stable structure of hcp boron suboxide at zero pressure corresponds to the ratio c/a of about 2.274 and the equilibrium lattice parameters a0 and c0 are about 5.331 and 12.124 Å, respectively. The high-pressure elastic constants indicate that boron suboxide is mechanically stable up to 368 GPa. The pressure dependence of the calculated normalized volume and the aggregate elastic moduli agree well with the recent experimental results. The sound velocities along different directions for the structure of boron suboxide are obtained. It shows that the velocities of the shear wave decrease as pressure increases but those of all the longitudinal waves increase with pressure. Moreover, the azimuthal anisotropy of the compression and shear aggregate wave velocities for different pressures are predicted. They change behavior with increasing pressure around 87 GPa because of an electronic topological transition. A refined analysis has been made to reveal the high pressure elastic anisotropy in boron suboxide.

Elastic Properties of <i>α</i>- and <i>β</i>-phases of Li<sub>3</sub>N

Investigations of elastic properties of Li3N in both α- and β-phases have been made by first-principles methods (HF-LCAO, DFT as implemented in CRYSTAL98 and in CASTEP). The theoretical equation of state of the α-phase (D46h structure) produced by our total-energy calculations is compared with the experimental EOS. Five independent elastic constants are calculated for the first time for both the phases. These are compared with the available four elastic constants of α-Li3N estimated from the slopes of the acoustic branches in the long wavelength region of the measured phonon dispersion curves. The aggregate elastic moduli (B, G, E), the Poisson’s ratio (ν) and the Debye temperature ΘD as a function of pressure are also calculated and the results discussed.Keywords: Li3N; α- and β-phases; Elastic properties; Debye temperature.©?2009 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved.DOI: 10.3329/jsr.v1i2.1763

Elastic moduli and strength of nanocrystalline cubicBC2Nfrom x-ray diffraction under nonhydrostatic compression

The stress behavior of nanocrystalline cubic boron carbon nitride $(c{\text{-BC}}_{2}\text{N})$ was investigated using radial and axial x-ray diffractions in the diamond-anvil cell under nonhydrostatic compression up to ~100 GPa. The radial x-ray diffraction (RXRD) data yield a bulk modulus ${K}_{0}=276\ifmmode\pm\else\textpm\fi{}20\text{ }\text{GPa}$ with a fixed pressure derivative ${K}_{0}^{\ensuremath{'}}=3.4$ at $\ensuremath{\psi}=54.7\ifmmode^\circ\else\textdegree\fi{}$, which corresponds to the hydrostatic compression curve. The bulk modulus obtained from axial x-ray diffraction (AXRD) gives a value of $420\ifmmode\pm\else\textpm\fi{}11\text{ }\text{GPa}$. A comparative study of the observed compression curves from radial and axial diffractions shows that the ruby-fluorescence pressure scale may reflect the maximum stress under nonhydrostatic compression. It was found that nanocrystalline $c{\text{-BC}}_{2}\text{N}$ sample could support a maximum differential stress of ~38 GPa when it started to yield at ~66 GPa under uniaxial compression. Moreover, the aggregate elastic moduli of the nanocrystalline $c{\text{-BC}}_{2}\text{N}$ have been determined from the RXRD data at high pressures.

Phase transition and elasticity of CdO under pressure

AbstractFirst‐principles calculations of the crystal structures, and phase transition, and elastic properties of cadmium oxide (CdO) have been carried out with the plane‐wave pseudopotential within the generalized gradient approximation in the frame of density functional theory method. The calculated values (for crystal structures) are in good agreement with experimental data as well as with some of the existing model calculations. For CsCl‐type CdO, the dependence of the elastic constants cij, the aggregate elastic modulus (B, G, E), and the elastic anisotropy on the pressure have been investigated. Moreover, the pressure dependences of the Poisson ratio, Debye temperature, and the compressional and shear elastic wave velocities have been investigated for the first time. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Sensitivity to grain discretization of the simulated crystal stress distributions in FCC polycrystals

An elastoviscoplastic finite element model of aluminum alloys is used to compare mechanical response among meshes formed with several different grain shapes. Tetrahedral elements are used to form grains of cubic, rhombic dodecahedral and truncated octahedral shape. The influence of the grain shape on the aggregate response is examined in terms of the stress variation and the aggregate elastic moduli. While elastic anisotropy in the bulk material is not found to be dependent on grain shape, consistent trends are observed in intragranular and intergranular stress distributions across these mesh definitions.

First-principles calculations on structure and elasticity of wurtzite-type indium nitride under pressure

First-principles calculations of the crystal structures, and elastic properties of wurtzite-type indium nitride (w-InN) have been carried out with the plane-wave pseudopotential density functional theory method. The calculated values (for crystal structures) are in very good agreement with experimental data as well as with some of the existing model calculations. The dependence of the elastic constants c ij , the aggregate elastic modulus ( B, G, E), and the elastic anisotropy on pressure have been investigated. Moreover, the variation of the Poisson ratio, Debye temperature, and the compressional and shear elastic wave velocities with pressure P up to 10 GPa at 0 K have been investigated for the first time.

Single-crystal elastic properties of (Mg0.987, Fe0.013)O to 9 GPa

The single-crystal elastic moduli of (Mg 0.987 ,Fe 0.013 )O were measured by Brillouin spectroscopy in a diamond-anvil cell at high pressures to 9 GPa at room temperature. The ambient-pressure single-crystal elastic moduli are (1) C 11 = 291.2(3.0) GPa; (2) C 12 = 96.1(2.0) GPa; and (3) C 44 = 151.9(2.0) GPa. From the single-crystal moduli, the aggregate elastic moduli are calculated to be adiabatic bulk modulus K S0 = 161.1(3.0) GPa, the Voigt bound of the shear modulus is G V = 130.0(2.0), and the Reuss bound G R = 124.2(2.0) GPa, giving a Voigt-Reuss-Hill average G = 127.1(2.0) GPa. We find that the addition of 1.3 mol% of Fe has a surprisingly large effect on the aggregate shear modulus, decreasing the room-pressure value by 2.4% as compared to Brillouin data for periclase (MgO) measured with the same technique. The adiabatic bulk modulus also decreases by 1.3%, although this decrease is within the mutual uncertainties of the measurements. Our results confirm significant non-linearity in single-crystal elastic moduli C 11 and C 44 and the aggregate shear modulus G of magnesiowustite in the Mg-rich end. The pressure derivative of the bulk modulus K S ′ = 4.2(2), as determined by a third-order finite-strain fit, is about 9% higher than the Brillouin results for the MgO end-member, whereas the pressure dependence of the shear modulus G ′ = 2.3(1) is found to be identical to that of periclase. The measurements demonstrate that even a small amount of Fe (1.3 mol%) has a measurable effect on the elastic properties of MgO-FeO solid solutions.

Dynamic modulus simulation of the asphalt concrete using the X-ray computed tomography images

The objective of this study is to predict the dynamic modulus of asphalt mixture using both two-dimensional (2D) and three-dimensional (3D) Distinct Element Method (DEM) generated from the X-ray computed tomography (X-ray CT) images. The 3D internal microstructure of the asphalt mixtures (i.e., spatial distribution of aggregate, sand mastic and air voids) was obtained using the X-ray CT. The X-ray CT images provided exact locations of aggregate, sand mastic and air voids to develop 2D and 3D models. An experimental program was developed with a uniaxial compression test to measure the dynamic modulus of sand mastic and asphalt mixtures at different temperatures and loading frequencies. In the DEM simulation, the mastic dynamic modulus and aggregate elastic modulus were used as input parameters to predict the asphalt mixture dynamic modulus. Three replicates of a 3D DEM and six replicates of a 2D DEM were used in the simulation. The strain response of the asphalt concrete under a compressive load was monitored, and the dynamic modulus was computed. The moduli of the 3D DEM and 2D DEM were then compared with both the experimental measurements results. It was revealed that the 3D discrete element models successfully predicted the asphalt mixture dynamic modulus over a range of temperatures and loading frequencies. It was found that 2D discrete element models under predicted the asphalt mixture dynamic modulus.

First-principles calculations on phase transition and elasticity of CdO under pressure

First-principles calculations of the crystal structures, and phase transition, and elastic properties of cadmium oxide (CdO) have been carried out with the plane-wave pseudopotential density functional theory method. The calculated values (for crystal structures) are in good agreement with experimental data as well as with some of the existing model calculations. The dependence of the elastic constants c i j , the aggregate elastic modulus ( B , G , E ), and the elastic anisotropy on pressure have been investigated. Moreover, the variation of the Poisson ratio, Debye temperature, and the compressional and shear elastic wave velocities with pressure P up to 119 GPa at 0 K have been investigated for the first time. We also find that NaCl-type CdO should be unstable at pressures higher than 119.07 GPa.

Elastic and Thermodynamic Properties of CdSe from First-Principles Calculations

The lattice parameters, bulk modulus, phase transition pressure, and temperature dependencies of the elastic constants cij of CdSe are investigated by using the Cambridge Serial Total Energy Package (CASTEP) program in the frame of Density Functional Theory (DFT). It is found that the phase transitions from the ZB structure to the RS structure and from WZ structure to RS structure are 2.2 GPa and 2.8 GPa, respectively. Our results agree well with the available experimental data and other theoretical results. The aggregate elastic modulus (B, G, E, A), the Poisson's ratio (υ), the Grüneisen parameter (γ), the Debye temperature ΘD on pressure and temperature are also successfully obtained.

3D Microstructural Models for Asphalt Mixtures Using X-Ray Computed Tomography Images

In this paper, aggregate orientation, aggregate gradation, sand mastic (a very fine sand-asphalt mixture) distribution, and air void distribution in the asphalt mixture were analyzed and modeled by capturing images using the X-ray Computed Tomography (CT) techniques. The mixture properties were predicted from X-ray CT images of the aggregate, mastic, and air voids. Moreover, the asphalt mixture images were utilized in modeling using the distinct element method approach for both two-dimensional (2D) and three-dimensional (3D) approaches. Three replicates of 3D distinct element model and six replicates of 2D distinct element model were simulated. 2D images were visualized by vertical orientation so that real distribution of air void levels could be captured. The mastic dynamic modulus and aggregate elastic modulus were determined and used as input parameters in the distinct element modeling. The strain responses of the asphalt mastic and mixture models under compressive load were monitored, and the dynamic moduli computed. The experimental measurements were compared with the 2D and 3D predictions. The 3D distinct element models were able to predict the asphalt mixture dynamic modulus. The 3D model's prediction is much better than that of 2D models. This outcome is a significant breakthrough in the modeling of asphalt mixture from 2D approach to 3D.

Single-crystal elasticity of diaspore, AlOOH, to 12 GPa by Brillouin scattering

The high-pressure elasticity of diaspore (AlOOH) has been determined by Brillouin spectroscopy to 12 GPa in diamond anvil cells. Experiments were carried out using a 16:3:1 methanol–ethanol–water mixture as pressure medium, and ruby as pressure standard. Acoustic velocities were measured in three roughly orthogonal planes at ambient and eight elevated pressures. The nine individual elastic stiffness constants of the orthorhombic crystal were obtained by fitting the velocity data to Christoffel's equation. Aggregate elastic moduli and pressure derivatives were calculated from the C ij s by fits to Eulerian finite strain equations, yielding: K S 0 = 152 ( 1 ) GPa , G 0 = 117.2(5) GPa, ( ∂ K S / ∂ P ) T 0 = 3.7 ( 1 ) , ( ∂ G / ∂ P ) 0 = 1.5 ( 1 ) for the Voigt–Reuss–Hill average. All individual C ij s increase with pressure but C 23 and C 55 exhibit anomalously low pressure derivatives. From calculated linear compressibilities, the a-axis is the most compressible. The b-axis becomes the least compressible axis at high pressures. Over the examined pressure range, the azimuthal P-wave anisotropy decreased from 22% to 16%, while the azimuthal S-wave anisotropy increased from 15% to 21%. Both volume and axial compression curves calculated using our Brillouin results are in good agreement with the results from static compression studies. High-pressure sound velocities in diaspore exceed those of other hydrous minerals as well as many anhydrous phases relevant to Earth's upper mantle.

The phase transition, and elastic and thermodynamic properties of CaS derived fromfirst-principles calculations

First-principles calculations of the crystal structures, phase transition, and elasticproperties of B1–B2 phase calcium sulfide (CaS) have been carried out with the plane-wavepseudopotential density functional theory method. The calculated values (for crystal structuresand the phase transition) are in very good agreement with experimental data as well aswith some of the existing model calculations. The dependence of the elastic constantscij, the aggregate elastic modulus, the deviation from the Cauchy relation, and the elasticanisotropy on pressure have been investigated. The normalized elastic constantscij′ have been introduced to investigate the elasticity of CaS in detail. Moreover, the variation of thePoisson ratio, Debye temperature, and longitudinal and transverse elastic wave velocity with pressureP up to 70 GPa at 0 K have been investigated for the first time.

First-Principle Calculations of Elastic Properties of Wurtzite-Type Aluminum Nitride Under Pressure

The elastic properties of the wurtzite-type aluminum nitride (w-AlN) are investigated by ab initio plane-wave pseudopotential density functional theory method. The pressure dependences of the normalized primitive cell volume V/V0, the elastic constants cij, the aggregate elastic modulus (B, G, E), the Poisson's ratio (ν), and the Debye temperature θD are successfully obtained. From the elastic constants of the w-AlN under pressure, we find that the w-AlN should be unstable at higher pressure than 61.33 GPa.

Structural and elastic properties of MgS via first-principle calculations

The structural B1–B2 (B1 is the NaCl phase and B2 is the CsCl phase) phase transition of MgS and the elastic properties of the B1 and B2 phases of MgS are investigated by ab initio plane-wave pseudopotential density functional theory method. The dependences of the elastic constants c ij , the aggregate elastic modulus B S, G, and the Debye temperature Θ D on pressure are successfully discussed. From the usual condition of equal enthalpies, we find that the structure B1–B2 phase transition of MgS occurs at 255.5 GPa. Moreover, the dependences of the aggregate elastic modulus and the Debye temperature on the pressure P have been investigated for the first time.