High-pressure and high-temperature bulk modulus of cubic fluorite-type MgF2 from quasi-harmonic Debye model

A detailed theoretical study of the isothermal and adiabatic bulk moduli of MgF₂ with a fluorite structure under high pressure and temperature has been carried out by means of first-principles density functional theory calculations combined with the quasi-harmonic Debye model in which the phononic effects are considered. Particular attention is paid to the prediction of the isothermal bulk modulus and its first and second pressure derivatives for the first time. The calculated ground state properties agree well with other theoretical values. At extended pressure and temperature ranges, the variation of the bulk modulus which plays a central role in the formulation of approximate equations of state has also been predicted. The properties of MgF₂ with a fluorite structure are summarized in the pressure range of 0–135 GPa and the temperature up to melting temperature 1500 K.     

Effects of pressure and temperature on the isothermal bulk modulus of CaO

Molecular dynamics (MD) simulations have been performed to investigate the effects of pressure and temperature on the isothermal bulk modulus of CaO using pair-wise interactions that include polarization effects through the shell model (SM). The dependence of isothermal bulk modulus B_T of CaO on the compression ratio V/V₀ and pressure P have been obtained from MD runs at T=300 K, and compared with the available experimental data and other theoretical results. A good agreement between theory and experiment is obtained. Meanwhile, B_T dependence on temperature T at zero pressure is investigated. At extended pressure and temperature ranges, SM-MD method has also been carried out for predicting the P-V-T equation of state and isothermal bulk modulus at different temperatures along the isotherms 0, 1000, 2000, 3000, and 4000 K, and at different pressures along the isobars 5, 15, 30, 40, and 50 GPa for CaO, respectively.     

An equation of state for alkali metals

Semi-empirical equations of state based on Lindemann's law have been developed to determine the pressure (P) dependence of the melting temperature (T_m) of Li, K, Rb and Cs. The basic inputs are Grüneisen parameter and the bulk modulus. T_m–P variations exhibit maximum melting temperature with concave downwards. The maximum in T_m for Cs is found to occur at pressure of 2.2 GPa whereas for Li, K and Rb it falls in the range of 7–9.5 GPa. The predicted values of T_m as a function of pressure, based on the present empirical relation, fit quite well with the available experimental data. The empirical relation can also be used to extrapolate T_m at higher pressure from the values available at lower pressures.     

C60 under pressure-bulk modulus and equation of state

C₆₀ has been investigated under pressure up to 13 GPa using angular dispersive X-ray scattering and a diamond anvil cell. The resolution of the experimental setup allows to examine the volume decrease dV/dp under pressure even for pressures of a tenth of a GPa. The obtained data of numerous experimental runs result in a bulk modulus of 13.4 GPa, which is much smaller than the value reported by Duclos et al. [1]. At 170 K and 70 K a bulk modulus of 14.2 GPa and 14.7 GPa was obtained, respectively. The pressure induced fcc-sc transition at 300 K was clearly visible at approx. 0.3 GPa with a jump in the lattice parameter of 0.05 Å. With increasing pressure we found an extreme change in dV/dp, which disables the usage of common equations of state (EOS), like the Murnaghan [2] or Birch [3] equation. Considering the small compressibility of the fullerence molecules we suggest a modified EOS to describe the experimental data.     

Melting and isothermal bulk modulus of the rocksalt phase of ZnO with molecular dynamics simulation

The Buckingham potential has been employed to simulate the melting of the rocksalt phase of ZnO over a wide pressure–temperature range and isothermal bulk modulus with shell model molecular dynamics method. The melting curve from molecular dynamics simulations is in good agreement with the results obtained from Lindemann melting equation in the pressure below 7 GPa. The calculated null compression bulk modulus is compared with the available experimental data and other theoretical results. At extended temperature ranges, the isothermal bulk modulus has also been predicted up to 3000 K.     

Pressure-dependent mechanical and thermodynamic properties of newly discovered cubic Na2He

Recently for the first time, a stable compound of He and Na (Na₂He) is predicted at high pressure. We explore the pressure-dependent elastic, mechanical and thermodynamic properties of this newly discovered Na₂He by using ab initio technique. The calculation presents good accordance between the theoretical and experimental lattice parameters. Though the most stable structure of Na₂He is found at 300?GPa, present study ensures the mechanical stability of this compound up to 500?GPa. The study of Cauchy pressure, Pugh's ratio, and Poisson's ratio implies the ductile manner of Na₂He up to 500?GPa. According to the value of Poisson's ratio the bonding force exists in Na₂He is central. The study of Zener anisotropy factor indicates that Na₂He is an anisotropic material but near at 300?GPa approximately isotropic nature of Na₂He is revealed. The study of the bulk modulus, shear modulus, Young's modulus and Vickers hardness implies that the hardness of Na₂He can be improved by applying external pressure. However, the Debye temperature, melting temperature and minimum thermal conductivity of Na₂He are also calculated and discussed at different pressures.     

Investigations of phase transition, elastic and thermodynamic properties of GaP by using the density functional theory

The phase transition of gallium phosphide (GaP) from zinc-blende (ZB) to a rocksalt (RS) structure is investigated by the plane-wave pseudopotential density functional theory (DFT). Lattice constant a₀, elastic constants c_ij, bulk modulus B₀ and the pressure derivative of bulk modulus B₀' are calculated. The results are in good agreement with numerous experimental and theoretical data. From the usual condition of equal enthalpies, the phase transition from the ZB to the RS structure occurs at 21.9 GPa, which is close to the experimental value of 22.0 GPa. The elastic properties of GaP with the ZB structure in a pressure range from 0 GPa to 21.9 GPa and those of the RS structure in a pressure range of pressures from 21.9 GPa to 40 GPa are obtained. According to the quasi-harmonic Debye model, in which the phononic effects are considered, the normalized volume V/V₀, the Debye temperature θ, the heat capacity C_v and the thermal expansion coefficient α are also discussed in a pressure range from 0 GPa to 40 GPa and a temperature range from 0 K to 1500 K.     

Structural,elastic, thermodynamic and electronic properties of LuX (X = N,Bi and Sb) compounds: first principles calculations

ABSTRACT

The structural, electronic, elastic and thermodynamic properties of LuX (X = N, Bi and Sb) based on rare earth into phases, Rocksalt (B1) and CsCl (B2) have been investigated using full-potential linearized muffin-tin orbital method (FP-LMTO) within density functional theory. Local density approximation (LDA) for exchange-correlation potential and local spin density approximation (LSDA) are employed. The structural parameters as lattice parameters a₀, bulk modulus B, its pressure derivate B’ and cut-off energy (E_c) within LDA and LSDA are presented. The elastic constants were derived from the stress–strain relation at 0 K. The thermodynamic properties for LuX using the quasi-harmonic Debye model are studied. The temperature and pressure variation of volume, bulk modulus, thermal expansion coefficient, heat capacities, Debye temperature and Gibbs free energy at different pressures (0–50 GPa) and temperatures (0–1600 K) are predicted. The calculated results are in accordance with other data.     

Equation of state of boron subarsenide B12As2 to 47 GPa

Compressibility of boron subarsenide B₁₂As₂ has been studied by synchrotron X-ray diffraction up to 47?GPa at room temperature in a diamond anvil cell using Ne pressure transmitting medium. A fit of experimental p–V data by Vinet equation of state yielded the bulk modulus of 150(4) GPa and its first pressure derivative of 6.4(3). No pressure-induced phase transitions have been observed.     

高压下TiC的弹性、电子结构及热力学性质的第一性原理计算

利用基于密度泛函理论的第一性原理平面波赝势方法 并结合准谐徳拜模型研究了NaCl结构的TiC在高压下的弹性性质、电子结构和热力学性质. 计算所得零温零压下的晶格常数、体弹模量及弹性常数与实验值符合得很好. 零温下弹性常数和弹性模量随压强增大而增大. 通过态密度和电荷密度的分析, Ti-C键随压强增大而增强. 运用准谐德拜模型, 成功计算了TiC在高温高压下的体弹模量、熵、热膨胀系数、徳拜温度、 Grüneisen参数和比热容. 结果表明压强对体弹模量、热膨胀系数和徳拜温度的影响大于温度对其的影响. 热容随着压强升高而减小, 在高温高压下, 热容接近Dulong-Petit极限.     

Study of temperature dependence of density, bulk modulus, shear modulus and thermal pressure for mantle minerals

The temperature dependence of different parameters i.e. density ρ(T), bulk modulus K_T(T), shear modulus G_T(T) and thermal pressure ΔP_th for mantle minerals i.e. X₂SiO₄ (X=Mg, Fe, Co, Mn) have been studied in high temperature range on the basis of semi-phenomenological isobaric equation of state. The calculated values of these parameters are showing good agreements with experimental value in case of each mantle minerals.     

Isothermal compressibility and bulk modulus for methanol under the effect of pressure and temperatures

It has been demonstrated that the spinodal model produces very well the isothermal compressibility of liquid methanol for a wide range of pressures and temperatures. We have used the pseudospinodal model further to determine pressure derivatives, first-order as well as second-order of isothermal compressibility and bulk modulus for liquid methanol in the range of pressures (0–100 MPa) and temperatures (208.17 K–298.16 K). The results have been found to present close agreement with the available experimental data. We have also calculated the values of densities as a function of pressure and temperature for methanol using the Stacey equation of state.     

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.     

Thermo-elastic property of Ca(OH)2 portlandite

An equation of state (EoS) for Ca(OH)₂ portlandite has been obtained through measurements of pressure and temperature dependence of volume by means of in-situ X-ray observation. The bulk modulus and its pressure derivative at zero pressure calculated using third-order Birch-Murnaghan's equation of state is 33.1 GPa and 4.2 at 300 K, respectively. The unit cell parameters and the volumes have been also determined at 573 K and 673 K. Temperature derivatives of the bulk modulus and its pressure derivative have been calculated to be ?0.022 GPa/K and 0.0072 K^?1, respectively. Thermal expansion coefficient of portlandite has been calculated from the EoS. The pressure dependence of entropy has been obtained from the present thermo-elastic parameters.     

High pressure γ-to-β phase transition in bulk and nanocrystalline In2Se3

Pressure-dependent phase transitions of In₂Se₃ bulk powders and nanowire samples were studied at room temperature using synchrotron X-ray diffraction and a diamond anvil cell. γ-In₂Se₃, metastable under ambient conditions, transforms into to the stable high pressure β phase between 2.8 and 3.2?GPa in bulk powder samples and at slightly higher pressures, between 3.2 and 3.7?GPa, in nanowire samples. While the γ phase bulk modulus is similar to that of the β phase, the decrease due to pressure in the unit cell parameter ratio, c/a, is less than half the decrease seen in the β phase. First-principles calculations show that γ-In₂Se₃ has a higher energy and unit-cell volume than β-In₂Se₃, consistent with the experimental observations.     

Structural,elastic, electronic and thermal properties of M2SbP (M = Ti,Zr and Hf)

The structural, elastic, electronic and thermal properties of M₂SbP (M = Ti, Zr and Hf) were studied by means of a pseudo-potential plane-wave method based on the density functional theory within both the local density approximation and the generalised gradient approximation. The optimised zero-pressure geometrical parameters, i.e. the two unit cell lengths (a, c) and the internal coordinate (z), were in good agreement with available experimental and theoretical data. The effect of high pressure, up to 20 GPa, on the lattice constants shows that the contractions along the a-axis were higher than along c-axis. The anisotropic independent elastic constants were calculated using the static finite strain technique. Numerical estimations of the bulk modulus, shear modulus, Young's modulus, Poisson's ratio, average sound velocity and Debye temperature for ideal polycrystalline M₂SbP aggregates were performed in the framework of the Voigt–Reuss–Hill approximation. The calculated band structures show that all studied materials are electrical conductors. Analysis of the atomic site projected densities showed that the bonding is of covalent–ionic nature with the presence of metallic character. The density of states at the Fermi level is dictated by the transition metal d–d bands; the Sb element has little effect. Thermal effects on some macroscopic properties of M₂SbP were predicted using the quasi-harmonic Debye model, in which the lattice vibrations are taken into account. The variations of the volume expansion coefficient, heat capacity and Debye temperature with pressure and temperature in the ranges 0–50 GPa and 0–2000 K were obtained successfully.     

First-principles study of structural,elastic, lattice dynamical and thermodynamical properties of GdX (X = Bi,Sb)

The results are presented of first-principles calculations of the structural, elastic and lattice dynamical properties of GdX (X = Bi, Sb). In particular, the lattice parameters, bulk modulus, phonon dispersion curves, elastic constants and their related quantities, such as Young's modulus, Shear modulus, Zener anisotropy factor, Poisson's ratio, Kleinman parameter, and longitudinal, transverse and average sound velocities, were calculated and compared with available experimental and other theoretical data. The temperature and pressure variations of the volume, bulk modulus, thermal expansion coefficient, heat capacities, Grüneisen parameter and Debye temperatures were predicted in wide pressure (0?50 GPa) and temperature ranges (0–500 K). The plane-wave pseudopotential approach to the density-functional theory within the GGA approximation implemented in VASP (Vienna ab initio simulation package) was used in all computations.     

First-principles calculations on the elastic and thermodynamic properties of NbN

<正>The elastic and thermodynamic properties of NbN at high pressures and high temperatures are investigated by the plane-wave pseudopotential density functional theory（DFT）.The generalized gradient approximation（GGA） with the Perdew-Burke-Ernzerhof（PBE） method is used to describe the exchange-correlation energy in the present work.The calculated equilibrium lattice constant a₀,bulk modulus B₀,and the pressure derivative of bulk modulus B₀’ of NbN with rocksalt structure are in good agreement with numerous experimental and theoretical data.The elastic properties over a range of pressures from 0 to 80.4 GPa are obtained.Isotropic wave velocities and anisotropic elasticity of NbN are studied in detail.It is indicated that NbN is highly anisotropic in both longitudinal and shear-wave velocities. According to the quasi-harmonic Debye model,in which the phononic effect is considered,the relations of（V-V₀）/V₀ to the temperature and the pressure,and the relations of the heat capacity C_V and the thermal expansion coefficientαto temperature are discussed in a pressure range from 0 to 80.4 GPa and a temperature range from 0 to 2500 K.At low temperature,C_V is proportional to T³ and tends to the Dulong-Petit limit at higher temperature.We predict that the thermal expansion coefficientαof NbN is about 4.20×10^-6/K at 300 K and 0 GPa.     

First-principles study of structural,elastic, electronic and thermodynamic properties of topological insulator Bi2Se3 under pressure

The structural, elastic, electronic and thermodynamic properties of the rhombohedral topological insulator Bi₂Se₃ are investigated by the generalized gradient approximation (GGA) with the Wu–Cohen (WC) exchange-correlation functional. The calculated lattice constants agree well with the available experimental and other theoretical data. Our GGA calculations indicate that Bi₂Se₃ is a 3D topological insulator with a band gap of 0.287 eV, which are well consistent with the experimental value of 0.3 eV. The pressure dependence of the elastic constants C_ij, bulk modulus B, shear modulus G, Young’s modulus E, and Poisson’s ratio σ of Bi₂Se₃ are also obtained successfully. The bulk modulus obtained from elastic constants is 53.5 GPa, which agrees well with the experimental value of 53 GPa. We also investigate the shear sound velocity V_S, longitudinal sound velocity V_L, and Debye temperature Θ_E from our elastic constants, as well as the thermodynamic properties from quasi-harmonic Debye model. We obtain that the heat capacity C_v and the thermal expansion coefficient α at 0 GPa and 300 K are 120.78 J mol^?1 K^?1 and 4.70 × 10^?5 K^?1, respectively.     

The bulk effect of point defects on young's modulus in electron irradiated copper

Abstract

Pairs of copper samples—one for electrical resistivity, the other for Young's modulus measurements - were irradiated simultaneously at 120°K with 3 MeV electrons up to an integrated dose of 2 × 10²⁰ el/cm². The effect of dislocation pinning and the bulk effect of point defects on Young's modulus E could clearly be separated. The following relation between the bulk effect ΔE/E and the resistivity increase Δρ[Ωcm] was found: ΔE/E = ?25 × 10⁴ × Δρ. Besides strong annealing in stages II and III (180–300°K) and some annealing between 300–500°K, stage V annealing (500–600°K) also was found. In stage III the resistivity annealed more than Young's modulus. whereas the converse occurred in stage V. These measurements are discussed in connection with the electron microsopical observation of point defect clusters after electron irradiation at 120°K and heating to room temperature.

Probenpaare, bestehend aus einer Widerstandsprobe und einer Probe zur Messung des Elastizitätsmoduls, wurden gleichzeitig bei 120°K mit 3 MeV-Elektronen bis zu einer Dosis von 2 × 10²⁰ el/cm² bestrahlt. Die direkte Reein-flussung des E-Moduls durch die im Gitter verteilten Punktdefekte (Volumeneffekt) konnte getrennt von der Beeinflussung durch Versetzungsverankerung gemessen werden. Es ergab sich dabei folgende Beziehung zwischen relativer Modulanderung ΔE/E und strahlungsinduziertem Widerstand Δρ[Ωcm]: ΔE/E = ?25 × 10⁴ × Δρ. Neben starker Erholung in den Stufen II und III (180–300 °K) und schwacher Erholung zwischen 300–500°K wurde auβerdem Stufe V (500–600°K) beobachtet. In Stufe III erholte sich der Widerstand starker als der E-Modul, wahrend in Stufe V das umgekehrte der Fall war. Die Messungen werden diskutiert in Zusammenhang mit der elektronenmikroskopischen Beobachtung von Punktdefektclustern nach Elektronenbestrahlung bei 120°K und anschlieβender Erwärmung auf Raumtemperatur.