Equation of state and elastic properties of lithium: Isotope effects

The equations of state and elastic properties of the lithium isotopes Li⁶ and Li⁷ at high pressures are investigated at a temperature of 76 K by a pulsed ultrasonic method. Proofs of the existence of appreciable quantum contributions to the pressure and elastic moduli of lithium are given. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 1, 36–40 (10 January 1999)     

Periodic DFT calculation of the pressure-induced phase transition and thermodynamical properties of magnesium silicide polymorphs

The plane-wave pseudo-potential method within the framework of first-principles is used to investigate the structural and elastic properties of Mg₂Si in its low pressure phase (Fm-3m) and intermediate pressure phase (Pnma). The high-pressure lattice constants, the elastic constants, the elastic moduli and the anisotropy factors of the anti-cotunnite Mg₂Si are presented and discussed. The results show that our system is mechanically stable. The reversible phase transition from anti-fluorite to anti-cotunnite structure is successfully reproduced through the quasi-harmonic Debye model. The phase boundary can be described as P=4.06826−6.95×10⁻³T+5.08838×10⁻⁵T²−4.24073×10⁻⁸T³. To complete the fundamental characteristics of these compounds we have analysed the thermodynamic properties such as thermal expansion, bulk modulus, isochoric heat capacity and Debye temperature in a pressure range 0-21 GPa and a temperature range 0-1200 K. The obtained results tend to support the experimental data when available. Therefore, the present results indicate that the combination of first-principles and quasi-harmonic approximations is an efficient scheme to simulate the high-temperature behaviours of semiconductors like Mg₂Si.     

Relaxing local modes and the theory of low-frequency Raman scattering in glasses

Raman scattering in glasses is investigated theoretically. The experimental Raman spectra of glasses exhibit a low-frequency peak (at ～10 cm^?1) that, as a rule, is attributed to vibrational modes of nanometer-sized structural units (nanocrystallites). It is established that the elastic moduli of nanocrystallites must necessarily be dependent on their sizes due to the Laplace pressure effect. A theory of the low-frequency peak is constructed using a realistic size distribution function of nanocrystallites with allowance made for the Laplace pressure effect and the dissipation of vibrational energy. Within this theory, the shape of the low-frequency peak and its evolution with temperature can be analyzed quantitatively. The proposed approach offers a physical interpretation of the experimental data and provides insight into the relation of the characteristic nanocrystallite sizes to the elastic moduli and surface tension coefficients of materials.     

The bond force constants and elastic properties of boron nitride nanosheets and nanoribbons using a hierarchical modeling approach

A hierarchical approach bridging the atomistic and nanometric scales is used to compute the elastic properties of boron nitride nanosheets and nanoribbons, examining the effect of sheet size, aspect ratio and anisotropy. The approach consists in obtaining the bond force (force field) constants by dedicated computations based on density functional theory (DFT) and using such constants as input for larger scale structural models solved by finite element analysis (FEA). The bond force constants calculated by DFT are 616.9 N/m for stretching, 6.27×10⁻¹⁹ Nm/rad² for in-plane rotation and 1.32×10⁻¹⁹ Nm/rad² for dihedral rotation. Using these constants, the elastic properties of boron nitride nanosheets and nanoribbons predicted by FEA are almost independent of the sheet size, but strongly dependent on their aspect ratio. The sheet anisotropy increases with increased aspect ratio, with nanoribbons of aspect ratios of 10 exhibiting a ratio of elastic moduli along both in-plane directions of 1.7.     

A new belt-type apparatus for neutron-based rheological measurements at gigapascal pressures

We have developed a new solid-media apparatus for performing rheological investigations at multi-gigapascal pressures. The pressure cell consists of a simple belt design and fits in a modified 250 tonne Paris–Edinburgh press. Elastic strains are measured by neutron diffraction, on the ENGIN-X experimental station at ISIS. Stresses are estimated from the measured strains in combination with published values of the elastic moduli. As an exemplair of the method, we present data from initial deformation experiments on pyrope garnet at 1.5 GPa and 873 K. Data collection times are as short as 60 min and the elastic strain resolution is better than 10^?4. We anticipate, however, that by interrupted testing, strain rates as low as 10^?9/s, or lower, will be measurable.     

Elasticity and thermodynamic properties of RuB2 under pressure

First-principles calculations of the crystal structure and the elastic properties of RuB₂ 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, Grüneisen 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.     

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.     

Boron–Carbon Nanocomposites Fabricated at High Pressures and Temperatures

Interaction of amorphous boron and C₆₀ fullerite is analyzed at pressures of 2.0 and 7.7. GPa and temperatures of 600–1800°C. Effect of pressure and temperature on the material structure is studied, temperatures for synthesis of boron carbide and diamond are found, and the sequence of transformations of the carbon component is determined. Ultrasonic method is used to measure elastic moduli of the samples, and the dependences of the moduli on the structure are analyzed. It is demonstrated that the boron–carbon nanocomposite synthesized at relatively low pressure (2.0 GPa) and temperature (about 1000°C) exhibits high elastic parameters (bulk modulus, B ≈ 75.3–84.0 GPa; Young modulus, E ≈ 108–119 GPa; and shear modulus, G ≈ 43–47 GPa at a density of about 2.2 g/cm³). The results can be used for development of novel nanocomposite materials.     

Theoretical Study of Elastic Properties of Tungsten Disilicide

The plane-wave pseudopotential method using the generalized gradient approximation within the framework of density functional theory is applied to analyse the lattice parameters, elastic constants, bulk moduli, shear moduli and Young's moduli of WSi₂. The quasi-harmonic Debye model, using a set of total energy versus cell volume obtained with the plane-wave pseudopotential method, is applied to the study of the elastic properties and vibrational effects. The athermal elastic constants of WSi₂ are calculated as a function of pressure up to 35GPa. The relationship between bulk modulus and temperature up to 1200K is also obtained. Moreover, the Debye temperature is determined from the non-equilibrium Gibbs function. The calculated results are in good agreement with the experimental data.     

First-principles calculations of elastic and thermo-physical properties of Al, Mg and rare earth lanthanide elements

The elastic constants of the Al, Mg and rare earth (RE) lanthanide elements have been calculated at T=0 K by using the projector augmented-wave (PAW) method within the generalized gradient approximation (GGA). The bulk moduli, shear moduli, Young's moduli and Poisson's ratio of poly-crystalline solid are estimated from the calculated elastic constants of single crystal. Based on the quasi-harmonic Debye model, the Debye temperature, heat capacity, Grüneisen parameter and linear thermal expansion coefficient are also estimated. The present calculated results are in reasonable agreement with the available experimental data and other theoretical results. The present calculation of elastic constants for Ce also indicates that the PAW potential (named “Ce_3”), for which one f electron is kept frozen in the core and hence fix the valency of Ce to three (Ce_3) does not yield good results for the elastic constants.     

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.     

First principles study of structural,phonon, optical,elastic and electronic properties of Y3Al5O12

Structural, phonon, optical, elastic and electronic properties of Y₃Al₅O₁₂ have been investigated by means of the first principles method with the Cambridge Serial Total Energy Package (CASTEP) code based on the density functional theory. The calculated lattice parameters, valence charge density, bond length and single crystal elastic properties at zero pressure are in good agreement with the available experimental data. The close agreement with the experimental values provides a good confirmation of the reliability of the calculations. Optical, elastic and phonon properties of Y₃Al₅O₁₂ under pressures are performed. The results that are obtained show the changes of optical and elastic properties under the influence of applied pressure, and proving the dynamical stability of YAG are destructed when applied pressure up to 7 GPa. Moreover, polycrystalline elastic moduli are deduced according to the Reuss assumption. Those elastic constants provide important parameters that describe reliability of both physical model and engineering application at the atomistic level. The result of the density of states explains the nature of the electronic band structure.     

Pressure dependence of c-axis elastic parameters of oriented graphite

The elastic c-axis moduli C₃₃ and C₄₄ of compression-annealed pyrolytic graphite and their derivatives with hydrostatic pressure have been measured at room temperature over a pressure range from 1 to 7000 bars (700 MNm^?2) using an ultrasonic pulse-echo technique. The experiments were also made with material irradiated with fast neutrons. The pressure dependence of the c-axis compressibility of these materials was calculated from the experimental data, enabling pressure derivatives of the c-axis moduli to be also expressed as c-axis strain derivatives.     

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.     

Elastic properties and spectroscopic studies of lithium lead borate glasses

Elastic properties of xLi₂O — 20PbO — (80-x)B₂O₃ glasses have been measured at a frequency of 10 MHz using X-cut and Y-cut quartz transducers. The trends in the variation of elastic moduli, Poisson’s ratio and Debye temperature have been studied. The elastic moduli namely longitudinal and young’s modulus show strong linear dependence while bulk and shear modulus vary marginally as a function of Li₂O concentration. The Poisson’s ratio is found to be almost constant and Debye temperature increases with the increase of Li₂O concentration. IR, MAS-NMR and glass transition temperature studies have been also carried out. Glass transition temperature is found to increase with increase of Li₂O concentration. IR and MAS-NMR spectra show characteristic features of borate network and systematic change as a function of Li₂O concentration. The variation in the elastic properties and structural features of IR and MAS-NMR indicate that Pb²⁺ ions are likely to occupy network forming positions in this glass system. Paper presented at the 2nd International Conference on Ionic Devices, Anna University, Chennai, India, Nov. 28–30, 2003.     

Structural, high pressure and elastic properties of transition metal monocarbides: A FP-LAPW study

The structural, elastic and thermal properties of four transition metal monocarbides ScC, YC (group III), VC and NbC (group V) have been investigated using full potential linearized augmented plane wave (FP-LAPW) method within generalized gradient approximation (GGA) both at ambient and high pressure. We predict a B₁ to B₂ structural phase transition at 127.8 and 80.4 GPa for ScC and YC along with the volume collapse percentage of 7.6 and 8.4%, respectively. No phase transition is observed in case of VC and NbC up to pressure 400 and 360 GPa, respectively. The ground state properties such as equilibrium lattice constant (a₀), bulk modulus (B) and its pressure derivative (B′) are determined and compared with available data. We have computed the elastic moduli and Debye temperature and report their variation as a function of pressure.     

Phase inversion in two-phase solid systems driven by an elastic modulus mismatch

We have used phase field simulations to study elastic stress-driven phase inversion in which an initial microstructure with a minority phase embedded in a majority phase evolves to one in which the latter becomes embedded in the former. Such phase inversion is possible if the majority phase is elastically stiffer than the minority phase. For a given set of parameters (volume fraction and elastic moduli of the phases), phase inversion occurs at a characteristic microstructural length-scale (? ^c ). Our results show that ? ^c is lower for systems with larger mismatch in elastic moduli, and (to a smaller extent) in those with greater elastic anisotropy.     

压力下Nd60Al10Fe20Co10块体金属玻璃的弹性行为

室温下在等静压最高达～0.5GPa的条件下，利用超声回波技术测量了超声波横波和纵波在Nd₆₀Al₁₀Fe₂₀Co₁₀块体金属玻璃中的传播时间来确定横波和纵波速度.测量时所采用的超声波频率为10MHz.利用所测量的数据，建立了超声波波速、样品的密度、弹性模量以及Debye温度等与所施加的压力之间的相互关系.并且推导出Murnaghan状态方程.另外，基于非晶态与晶态物理性能的相似性，对此块体非晶的压缩曲线、弹性常数和Debye温度等进行了理论计算，结果表明Nd₆₀Al₁₀Fe₂₀Co₁₀块体金属玻璃的弹性性能与其组成的元素有着密切的关系. 关键词： 块体金属玻璃 弹性性能 等静压     

Investigation of the effect of uniaxial pressure on antiferromagnetic resonance in KFe11O17 Crystals

The deformation dependence of the resonance field in KFe₁₁O₁₇ single crystals was investigated by the AFMR method. The measurements were performed at T=77 K and ν=47.52 GHz for two orientations of the external pressure. The experimental data are discussed in terms of a model of a very simple easy-plane antiferromagnet taking account of the elastic and magnetoelastic contributions to the thermodynamic potential. The magnetostriction, magnetoelastic, and elastic contants are calculated and the results are λ=1.94×10⁻⁵, B ₁=2.75×10⁸ erg/cm³, and C ₁₁−C ₁₂=1.42×10¹³ erg/cm³, respectively. The alues of these constants imply that the origin of the initial gap in the AFMR spectrum is not of magnetoelastic origin. Fiz. Tverd. Tela (St. Petersburg) 40, 513–515 (March 1998)