Equation of state for solids with 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 Mie-Grüneisen-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 extreme compression and expansion region. We developed a Padé approximation-based analytic Debye quasiharmonic model with high accuracy which improves the performance of EOS in 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 Grüneisen 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.     

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.     

一个等温状态方程（Ⅴ）——不同温度的高压状态方程

 本文以NaCl为例，证实了在我们的状态方程体系中，不同温度的状态方程可以认为是在p_x坐标系中不同起点开始的同一状态方程。于是，可由室温状态方程和常压热膨胀的测量数据估计高温状态方程。     

盐石结构MgO的状态方程的第一原理计算

利用平面波密度泛函理论研究了盐石结构MgO的状态方程,所得到的结果与实验值和其他作者的计算值符合很好.同时,还研究了热膨胀系数随温度和压强的变化关系.结果显示:在高压下,温度对盐石结构MgO热膨胀系数的影响很小.     

V(P.T)-Measurements on polycarbonate and their analytical description in the glassy state

Abstract

We present an analytical equation of state (EOS) for solids using the bulk Grüneisenparameter γ. This EOS is applied to experimental V(p. T)-data of polycarbonate below the glass temperature, measured in a piston-cylinder apparatus up to 300 MPa. Bulk modulus K, the product K · α (α = thermal expansion coefficient) and the Grüneisenparameter γ are determined directly from the data as well as from a fit of the equation of state V(p.T) to the data. The fit with our EOS is better than the one with the empirical Tait-equation which is often used for polymeric materials.     

贵金属金的状态方程

 提出了一个热压强的计算公式，从而获得金的状态方程。并结合实验数据与文献中常用的其它两个状态方程进行了比较。结果发现，修正后的状态方程与实验数据吻合很好，略优于其它两个状态方程。     

Modelling phase equilibria of pure ionic liquids from a new equation of state

A perturbed hard-trimer (PHT) equation of state (EOS) has been employed to model densities and some derived thermodynamic properties of 39 ionic liquids (ILs) considering a trimer expression obtained from the statistical associating fluid theory as the reference physical model. The van der Waals dispersion forces were applied as perturbation term. The proposed model was tested using ILs containing imidazolium, pyrrolidinium, pyridinium, phosphonium and piperidinium cations. Two parameters appeared in the PHT EOS which are temperature-dependent, reflecting the dispersive energy parameters among trimers, ε and the hard-core diameter, σ, were determined based on the molecular scaling parameters. The performance of the proposed PHT EOS has been evaluated by predicting the volumetric and first and second derivatives thermodynamic properties in the pressure and temperature ranges within 0.1–200 MPa and 273–472.6 K, respectively. From 6331 data points examined, the average absolute deviation (AAD) of the correlated (at 0.1 MPa) and predicted (at high pressures) densities from the experimental ones was found to be 0.18 %. Furthermore, the isothermal compressibilities and thermal expansion coefficients as well as the heat capacities were estimated through the PHT EOS with uncertainties of the order of ±11.09, ±11.76 and ±3.34 %, respectively. Further, the vapour pressures of ILs are also predicted by the proposed model. The trend of the predicted vapour pressure is in accord with those reported in literature.

     

Thermodynamic properties of MgO under high pressure from first-principles calculations

The equations of state (EOS) and other thermodynamic properties of the rocksalt (RS) structure MgO are investigated by ab initio plane-wave pseudopotential density functional theory method. The obtained results are consistent with the experimental data and those calculated by others. Through the quasi-harmonic Debye model, in which the phononic effects are considered, the dependences of relative volume V/V₀ on pressure P, cell volume V on temperature T, and Debye temperature Θ and specific heat C_V on pressure P are successfully obtained. The variation of the thermal expansion with temperature and pressure is investigated, which shows the temperature has hardly any effect on the thermal expansion at higher pressure.     

Equations of State for Regular Solids

Equations of State (EOS) for solids under strong compression and wide ranges in temperature are most commonly represented by "parametric" EOS forms using temperature dependent parameters for the volume V 0 , the bulk modulus K 0 , and its pressure derivative K_{0}^{\prime} for the given ambient (or zero) pressure. Therefore, various common "parametric" EOS forms are compared at first with the recently proposed [1,2] A dapted P olynomical expansion AP2, and in the second part with the Mie-Grüneisen approach, which uses one of the common EOS forms for the pressure of the static lattice or for the zero temperature isotherm, p ZT ( V ), and a detailed modelling of the additional thermal pressure, p th ( V , T ), in the form p(V,T) = p_{\rm ZT}(V) + p_{\rm th}(V,T) . Thereby, it is shown, that "intrinsic" anharmonicity effects have to be taken into account and between the two schemes differences of the order of a few percent in pressure are noticed for regular solids, like Cu, Ag, and Au. These differences are discussed with respect to the present uncertainties in a practical pressure scale for wide ranges in pressure (up to several TPa) and in temperature (up to 1500 K and above).     

极端条件下锆的动力学稳定性研究

过渡金属Zr具有优良的物理、化学及力学性能, 具有广泛的应用价值. 主要通过新近发展的自洽晶格动力学方法, 充分考虑声子间的相互作用, 成功获得了β-Zr的高温高压声子色散曲线, 预测了β-Zr在相图中能够稳定存在的区域, 进一步比较α-Zr, ω-Zr和β-Zr的自由能, 获得了α-β 及ω-β 相变的相边界, 构建了Zr的参考相图. 同时, 也获得了β-Zr的高温状态方程及热膨胀系数, 能够为构建Zr的全区物态方程提供有益的参考.     

Modified equation of state for pure and hard sphere mixtures in mean ionic activity coefficient calculations by mean spherical approximation model

A hard sphere equation of state (EOS) based on tetrakaidecahedron cell geometry (instead of spherical shape) and highly optimized molecular dynamic simulation data is proposed. The EOS is extended to hard sphere mixture and its performance for compressibility factor calculation at different diameter size of hard sphere mixtures by using various mixing rule is compared with Monte Carlo simulation data. The results indicated that for all mixing rules, the proposed EOS has minimum error comparing with computer simulation data. Also the residual prosperities are derived by using the proposed EOS. The residual properties are used in mean spherical approximation model (MSA) to evaluate the mean ionic activity coefficient of aqueous electrolyte solutions. The results are compared with those obtained by similar hard sphere equations of state and it is shown that the proposed EOS has a better performance in predicting the mean ionic activity coefficient.     

Five-parameter equation of state for solids correctly incorporating cohesive energy data

A five-parameter equation of state (EOS) is proposed to correctly incorporate the cohesive energy data in it without physically incorrect oscillations.The proposed EOS is applied to 10 selected metals.It is shown that the calculated compression curves are in good accordance with the experimental data.The values of the bulk modulus and its derivative with respect to pressure extracted from the proposed EOS remain almost unchanged while the data range used is varied.     

Mean-field vs. Monte Carlo equation of state for the expansion of a Fermi superfluid in the BCS-BEC crossover

The equation of state (EOS) of a Fermi superfluid is investigated in the BCS-BEC crossover at zero temperature. We discuss the EOS based on Monte Carlo (MC) data and asymptotic expansions and the EOS derived from the extended BCS (EBCS) mean-field theory. Then we introduce a time-dependent density functional, based on the bulk EOS and Landau’s superfluid hydrodynamics with a von Weizsäcker-type correction, to study the free expansion of the Fermi superfluid. We calculate the aspect ratio and the released energy of the expanding Fermi cloud showing that MC EOS and EBCS EOS are both compatible with the available experimental data of ⁶Li atoms. We find that the released energy satisfies and approximate analytical formula that is quite accurate in the BEC regime. For an anisotropic droplet, our numerical simulations show an initially faster reversal of anisotropy in the BCS regime, later suppressed by the BEC fluid.     

沿等压路径求解疏松材料Hugoniot关系的微分方程组及其求解

 根据固体材料的三项式物态方程和Grüneisen物态方程,导出了沿等压路径求解疏松材料冲击温度和压缩体积随初始密度变化的微分方程组。从体积的微分方程出发,在假定Wu-Jing参量为常数的前提下,导出了冲击压缩体积和体积-焓物态方程的Wu-Jing表达式。采用数值差分方法求解微分方程组,计算了疏松铜的冲击压缩特性,并与文献中部分实验数据进行了比较,特别强调了热电子对冲击压缩体积、冲击温度和Wu-Jing参数的贡献。还讨论了Grüneisen物态方程与Wu-Jing物态方程的内在联系及后者的适用范围。     

A modified equation of state for Xe at high pressures by molecular dynamics simulation

The exact equation of state （EOS） for the fission gas Xe is necessary for the accurate prediction of the fission gas behavior in uranium dioxide nuclear fuel, However, the comparison with the experimental data indicates that the applicable pressure ranges of existing EOS for Xe published in the literature cannot cover the overpressure of the rim fission gas bubble at the typical UO2 fuel pellet rim structure. Based on the interatomic potential of Xe, the pressure-volume-temperature data are calculated by the molecular dynamics （MD） simulation. The results indicate that the data of MD simulation with Ross and McMahan＇s potential [M. Ross and A. K. McMahan 1980 Phys. Rev. B 21 1658] are in good agreement with the experimental data. A preferable EOS for Xe is proposed based on the MD simulation. The comparison with the MD simulation data shows that the proposed EOS can be applied at pressures up to 550 MPa and 3 GPa and temperatures 900 K and 1373 K respectively. The applicable pressure range of this EOS is wider than those of the other existing EOS for Xe published in the literature.     

一种新的对比态混合物状态方程的建立

1引言在混合替代工质的研究中，要分析其热力学性质和循环性能，必须有能够准确描述混合制冷剂性质的状态方程。目前计算采用的各种混合状态方程都必需有混合物各组分间的二元交互作用系数Kij。Kij的值一般需要由回归二元混合工质的PVTx实验数据或相平衡数据而得到。实际的混合工质替代研究中，常常没有或缺少混合物的实验数据。对于二元混合物而言，其热力性质应与组成这种混合物的两种纯质的性质密切相关，有可能以纯质的物性来表达混合物的性能，而大多数纯质制冷剂都有用实验数据回归的精度很高的专用状态方程和蒸气压方程。所以，如…     

Thermodynamic properties of cubic boron nitride under high pressure from ab initio calculations

The equations of state (EOS) and other thermodynamic properties of cubic boron nitride (C-BN) have been studied by the first-principles method under high pressure. Under ambient conditions, our results are consistent with the available experimental data and those calculated by others. At the same time, the dependences of Young’s modulus and the shear modulus of C-BN on pressure P are successfully obtained. Moreover, the variation of the Poisson ratio, Debye temperature, specific heat, and thermal expansion coefficient with pressure P up to 200 GPa at 300 K have been investigated for the first time by means of a quasi-harmonic Debye model, in which phononic effects are considered.     

Elastic, thermal and structural properties of platinum

The thermal equation of state (EOS) for platinum has been calculated to 300 GPa and 3000 K using ab initio molecular dynamics employing the local density approximation (LDA) and the projector augmented-wave methods (PAW). Direct ab initio molecular dynamics avoids the simplifying assumptions inherent in empirical treatments of thermoelasticity. A third-order Birch-Murnaghan equation EOS fitted to the 300 K data yielded an isothermal bulk modulus of B_T0=290.8 GPa and a pressure derivative of B_T′=5.11, which are in better agreement with the measured values than those obtained by previous calculations. The high-temperature data were fitted to a thermal pressure EOS and a Mie-Grüneisen-Debye EOS. The resulting calculated thermal expansion coefficient, α₀, temperature derivative of the isothermal bulk modulus, (∂B_T/∂T)_V, and second temperature derivative of the pressure, (∂²P/∂T²)_V, were 1.94×10⁻⁵ K⁻¹, −0.0038 GPa K⁻¹, and 1.7×10⁻⁷ GPa² K⁻², respectively. A fit to the Mie-Grüneisen-Debye EOS yielded values for the Grüneisen parameter, γ₀, and its volume dependence parameter, q, of 2.18 and 1.75, respectively. An analysis of our data revealed a strong volume dependence of the thermal pressure of platinum. We also present a qualitative analysis of the effects of intrinsic anharmonicity from the calculated Grüneisen parameter at high temperatures.     

Effects of temperature on the structure of neutron stars at high temperature

In Newtonian physics, higher temperature leads to higher thermal pressure, which provides stronger support against the gravitational contraction of stars. However, in the temperature range of tens of MeV involved in the evolution of a proto-neutron star or a higher massive neutron star, the effects of temperature are richer. We showed that, for a high temperature neutron star (HTNS) constructed with a realistic equation of state (EOS), the HTNS may expand or contract during cooling, the central density may increase or decrease, the quasi-normal mode oscillation frequencies may increase or decrease, and in particular, (i) independent of the EOS, for a HTNS of a given mass, there exists a maximum temperature \(T_{max}\) that it could ever attend at birth (with the value of \(T_{max}\) different for different EOS), and (ii) for the Hempel EOS and the Shen EOS, there is a range of mass that the HTNS may gravitationally collapse after a period of radiative cooling; however, for the Lattimer–Swesty EOS and Banik EOS, no delayed collapse is possible. Our study, which describes the cooling of HTNSs with simple quasi-stationary TOV sequences, provides an understanding of the effects of the thermal energy/pressure at high temperature, and a demonstration that different EOSs can lead to qualitatively different evolution paths.