Equation of state for solids considering cohesive energy and anharmonic effect and its application to MgO

A simple equation of state(EOS) in wide ranges of pressure and temperature is constructed within the MieGrneisen-Debye framework.Instead of the popular Birch-Murnaghan and Vinet EOS,we employ a five-parameter cold energy expression to represent the static EOS term,which can correctly produce cohesive energy without any spurious oscillations in the extreme compression and expansion regions.We developed a Pad’e approximation-based analytic Debye quasiharmonic model with high accuracy which improves the performance of EOS in the low temperature region.The anharmonic effect is taken into account by using a semi-empirical approach.Its reasonability is verified by the fact that the total thermal pressure tends to the lowest-order anharmonic expansion in the literature at low temperature,and tends to ideal-gas limitation at high temperature,which is physically correct.Besides,based on this approach,the anharmonic thermal pressure can be expressed in the Gru¨neisen form,which is convenient for applications.The proposed EOS is used to study the thermodynamic properties of MgO including static and shock compression conditions,and the results are very satisfactory as compared with the experimental data.     

160 GPa压力范围内重新标定的红宝石压标

 在同一理论框架内,基于冲击Hugoniot和热力学参数计算了Al、Cu、W、 Au、Pt、Ta、Ag、Mo、Ni、Co和Zn的300 K等温压缩线,并结合现有静高压实验数据,在160 GPa压力范围内重新标定了红宝石压标。所采用的两种红宝石压标形式的标定结果分别为A=1 923.4 GPa、B=9.75和m=1 889.0 GPa、n=5.48,两者具有非常好的自洽性,200 GPa压力范围内确定的压力偏差小于2.1 GPa。基于提出的红宝石压标,重新计算了3组Au等温压缩实验的加载压力。固定等温体模量为167 GPa,重算的实验数据拟合至Vinet物态方程所得等温体模量对压力的一阶偏导为5.95,与超声实验数据非常吻合。     

Thorium: Phase transformations and equation of state to 300 GPa

Abstract

Equation of state and phase transformations of thorium metal have been investigated to 300 GPa at 300 K in a diamond anvil cell using energy dispersive X-ray diffraction employing synchrotron source. Phase transformations in the 70–100 GPa range indicative of 5f-electron bonding are observed and thorium metal is isostructural with its 4f counterpart cerium at ultra high pressures. The measured static equation of state of thorium to 300GPa (volume fraction V/V _o = 0.40) at 300K is given. At high pressures, the sd to f electronic transfer has significant influence on the measured equation of state of thorium.     

Pressure-volume relations for Zn,Cd, Ga,In and TI at room temperature to 30 GPa and above

Abstract

The elemental metals Zn, Cd, Ga, In and TI are studied by energy dispersive X-ray diffraction under pressures up to 30 GPa and above. Room temperature equation of state (EOS) data are derived and compared with results of earlier static and dynamic measurements at lower and higher pressures, respectively.     

Equation of state of turbostratic boron nitride

Abstract

The lattice parameters of turbostratic boron nitride (tBN) have been measured to 6.1 GPa at room temperature using energy-dispersive powder diffraction with synchrotron radiation. A fit to the experimental p-V data using Birch-Murnaghan equation of state gives values of the tBN bulk modulus 17.5(8) GPa and its pressure derivative ll.4(5). These values point to significantly higher compressibility of turbostratic BN as compared to three-dimensionally ordered graphite-like hexagonal and rhombohedral boron nitride.     

(Fe0.03Ni0.97)8(Si0.79P0.21)3的等温状态方程研究

 采用固态高温烧结反应方法,成功合成出了陨硅镍铁石样品(Fe_0.03Ni_0.97)₈(Si_0.79P_0.21)₃。X射线衍射结果表明,合成样品的结构为R3'c,对应的晶胞参数为a=b=0.663 8(1) nm,c=3.789 2(2) nm,V=1.446 15(6) nm³。在室温下,对样品进行原位高压X射线衍射研究,实验最高压力达到21.3 GPa,随着压力的升高,晶胞体积逐渐减小,但并没有观察到结构相变。利用Birch-Murnaghan状态方程对体积与压力的关系进行拟合,获得常温常压下的体积V₀=1.441 4(24) nm³,体积模量K₀=220(7) GPa。晶轴与压力的关系利用Murnaghan状态方程拟合,获得a轴和c轴的模量分别为K_a=257(9)和K_c=165(4),c轴较a轴容易压缩。     

Equation of state of fluid helium at high temperatures and densities

Hugoniot curves and shock temperatures of gas helium with initial temperature 293 K and three initial pressures 0.6, 1.2, and 5.0 MPa were measured up to 15000 K using a two-stage light-gas gun and transient radiation pyrometer. It was found that the calculated Hugoniot EOS of gas helium at the same initial pressure using Saha equation with Debye-Hückel correction was in good agreement with the experimental data. The curve of the calculated shock wave velocity with the particle velocity of gas helium which is shocked from the initial pressure 5 MPa and temperature 293 K, i.e., theD ≈u relation,D=C ₀+λu (u<10 km/s, λ=1.32) in a low pressure region, is approximately parallel with the fittedD ≈u (λ=1.36) of liquid helium from the experimental data of Nellis et al. Our calculations show that the Hugoniot parameter λ is independent of the initial density p{in0}. TheD≈u curves of gas helium will transfer to another one and approach a limiting value of compression when their temperature elevates to about 18000 K and the ionization degree of the shocked gas helium reaches 10⁻³.     

Equation of state of fluid helium at high temperatures and densities

Helium, hydrogen, and their isotopes are the simplest monoatomic and diatomic molecules. It is relatively easy to describe their properties using the basic principles of quantum mechanics. In condensed matter physics, hydrogen and helium serve as the models for the condensed matter properties at extreme conditions so that both experi- mental and theoretical physicists pay much attention to the study of their properties[1], especially the insulator-metal transition of hydrogen[2]. The aim to st…     

Equation of state of LiCoO_2 under 30 GPa pressure

LiCoO_2 is one of the most important cathode materials for high energy density lithium ion batteries. The compressed behavior of LiCoO_2 under high pressure has been investigated using synchrotron radiation x-ray diffraction. It is found that LiCoO_2 maintains hexagonal symmetry up to the maximum pressure of 30.1 GPa without phase transition. The elastic modulus at ambient pressure is 159.5(2.2) GPa and its first derivative is 3.92(0.23). In addition, the high-pressure compression behavior of LiCoO_2 has been studied by first principles calculations. The derived bulk modulus of LiCoO_2 is 141.6 GPa.     

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.     

Equation of state for pure fluids at critical temperature

In this paper, we employ the concept of probability for creating a cavity with diameter d in fluid along with the perturbation and variation approach, and develop an equation of state (EOS) for a hard sphere (HS) and Lennard– Jones (LJ) fluids. A suitable axiomatic form for surface tension S(r) is assumed for the pure fluid, with r as a variable. The function S(r) has an arbitrary parameter m. S(r) = A + B(d/r)/[1 + m(d/r)]. We use the condition in terms of radial distribution function G(λd, η) containing the self-consistent parameter λ and the condition of continuity at r = d/2 to determine A and B. A different EOS can be obtained with a suitable choice of m and the EOS has a lower root-mean-square deviation than that of Barker–Henderson BH2 for LJ fluids.     

High pressure measurement of n-dodecane heat capacity up to 100 MPa. Calculation from equations of state

Abstract

Isobaric heat capacities of liquid n-dodecane were measured at temperatures from 313.15 to 373.15 K and at pressures up to 100 MPa using a calorimetric device based on a Calvet calorimeter (Setaram (280). These experimental data were used to perform a comparative study in order to choose, from among the great number of equations of state proposed in the literature, the most appropriate to calculate the isobaric heat capacity.     

The Influence of the Renormalization Condition to the Equation of State of the Nuclear Matter

In the relativistic σ-ω model, the influences of the parameters b, c, d in the potential U(σ) = (1/2!)bo2 - -(1/3!)cσ3 (1/4!)dσ4 to the incompressibility, effective mass and binding energy of the nuclear matter are studied in detail.The calculation of equation of state of nuclear matter shows that the values of b, c, d depend on the renormalization condition, we also find that a soft equation of state of nuclear matter can be obtained in a suitable renormalization condition, and the experimental incompressibility coefficient can be reproduced. These results are also used to study the thermal properties of hot A-resonant nuclear matter.self-interaction of σ meson, renormalization, hot and dense hadronic matter ``     

P- V- T Data of hexagonal boron nitride h BN and determination of pressure and temperature using thermoelastic equations of state of multiple phases

Abstract

A synchrotron x-ray diffraction study on hexagonal boron-nitride (hBN) was conducted at simultaneous high pressures and temperatures. The pressure applied to the sample is pseudo-hydrostatic up to 9.0 GPa and the temperature was homogeneous in the range of 300 K to 1280 K. A modified Rietveld profile refinement has been applied to these diffraction spectra of low symmetry and multiple phases observed in the energy-dispersive mode. Thermoelastic parameters of hBN were derived by fitting a modified high temperature Birch-Murnaghan equation of state. The results are: bulk modulus K=17.6 GPa, pressure derivative K′=?K/?P=19.5, temperature derivative [kdot]=?K/?T=?0.69 × 10^?2 Gpa/K, volumetric thermal expansivity α=a+bT with values of a=4.38 × 10^?5K^?1 and b=1.75 × 10^?8K^?2, respectively. It is observed that the thermal expansion and compression along different crystal axes are significantly different. The crystal c-axis is much more expandable and compressible than the a-axis. This is attributed to the layered structure of the hBN. Because the thermoelastic equations of state of hBN and NaCl are quite different, the unit cell volumes of these two materials, derived from the same diffraction pattern, can be used to derive the experimental P-T conditions. The large intersection angle of isochoric lines of these phases in P-T space ensures a determination of P-T with satisfactory precision. The application and limitations of this method in obtaining experimental pressure and temperature using diffraction data and thermoelastic equations of state of multiple phases are discussed.     

Solidification of selenium melt under pressure up to 6.5 GPa

Abstract

High purity selenium samples were melted under high pressure (≤6.4 GPa) and quenched at various rates ranging from 2 K s^?1 to 500 K s^?1 and the recovered material was examined by X-ray diffraction and electron microscopy. In the entire range of pressure and cooling rate, the melt was found to solidify into a polycrystalline aggregate of the trigonal phase of selenium. The samples obtained by slow cooling of the melt at 6.4 GPa contain, in addition to crystalline phase, regions which appear to be amorphous.     

Pressure dependent study of semiconductors using semiempirical equations of state

Abstract

Variation of bulk modulus of Si, Ge and GaAs with pressure is studied using four semiempirical equations of state, two of which being proposed very recently. Hence an expression for bulk modulus for arbitrary pressure for the semiconductors similar to Cohen's formula for zero pressure is arrived at. The applicability of these equations of state for the high pressure phases of Si and Ge is tested using the recent experimental and theoretical pressure-volume data of these phases.     

Equation of state and interaction potential of helium under high temperatures and high densities

Based on the thermodynamics statistic method, the improved variational perturbation theory and the modified quantum mechanics correction model have been used to calculate the equation of state of liquid helium at pressure from 0.7 to 108 GPa. The calculation results are in good agreement with the experimental data. The EXP-6 potential (α = 13.1) can more accurately describe the interaction of helium atoms than other potentials in the scheme. Finally, a comparison is shown between our interatomic potentials and other potentials.