应用于金属固体的四参数通用状态方程

提出一种能精确考虑固体结合能的四参数通用状态方程, 并且在高压和膨胀区域都具有正确的行为, 不会出现物理上不正确的振荡现象. 新方程可以将Vinet方程和普遍化Lennard-Jones (GLJ) 方程作为特例包括于其中. 将新方程与文献中的典型方程应用于32种金属固体, 结果表明新方程在给出正确结合能数据的同时, 能够很好的拟合实验压缩数据. 结果还表明, 多数金属的相互作用具有短程相互作用的性质, 但是结合能较大相互作用的强度较强.     

Five-parameter equation of solids considering thermal effect which correctly incorporates cohesive energy

A five-parameter equation of state (EOS) is proposed, which correctly incorporates the cohesive energy data without physically incorrect oscillations in both extreme high pressure and expansion regions. Based on a modified Einstein model, the thermal effect is included in the proposed EOS complying with the zero-pressure condition. With this thermal EOS applied to five solids (Ar, Al, Au, Cu and Li), some important thermodynamic properties as isotherm, isochore, thermal expansion coefficient, volume modulus, heat capacity and Hugoniot are calculated for each selected solid with good agreement with experimental data, which confirms the validity of the present work     

应用于碱卤化物固体的通用状态方程

提出一种能精确考虑固体结合能的通用状态方程,并且在高压和膨胀区域都具有正确的行为,不会出现物理上不正确的振荡现象.将新方程与文献中的典型方程应用于15种碱金属卤化物和一种碱土金属氧化物,结果表明新方程在给出正确结合能数据的同时,能够很好地拟合实验压缩数据.由Vinet方程和Morse方程定出的参数随数据范围变化很明显,新方程定出的参数随数据范围变化不明显.新方程的通用性优于Vinet方程和Morse方程. 关键词： 固体 通用状态方程 结合能 碱金属卤化物     

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.     

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.     

Thermal effect and equation of state in solids

In the present paper, an attempt has been made to include the thermal effect into an isothermal equation of state using the Debye approximation representing volume as a function of pressure. The calculations are done in case of NaCl, CsCl, Mo, and W. The present calculations are in good agreement with the reported results.     

Explicit Gibbs free energy equation of state for solids

Semi-empirical equations of state (EOS) are used for interpolation and extrapolation of experimental data and/or electronic structure calculations. For calculation of phase equilibria, it is preferable to use an explicit Gibbs free energy EOS, that is, to express the Gibbs free energy directly as a function of the pressure and temperature. Existing explicit Gibbs free energy EOS formulations often give unphysical predictions at high pressures. The origins of these problems are internal inconsistencies and uncontrolled extrapolations. A set of conditions is put forward, that should be fulfilled by semi-empirical EOS formulations in order to constrain them to known physical behaviour, e.g., to the Thomas-Fermi and quasi-harmonic models at high pressures. A new alternative integration path is devised that eliminates the need for the problematic extrapolation of the heat capacity to high temperatures at low pressures. Based on these developments, a new explicit Gibbs free energy EOS is formulated which is suitable for computational applications. The new EOS may be fitted to represent the thermophysical properties of solids with a reasonably small number of adjustable parameters. A sample application for MgO is presented.     

An isothermal equation of state for solids

An isothermal equation of state (EOS) for solids, recently suggested by the authors in the realistic form, V/V₀=f(P), with relative volume as the dependent and the pressure as the independent variable, was shown to have an advantage for some close-packed materials in that it allows B′_∞=(∂B_s/∂P)_s(P→∞) to be fitted, and this is where the usual standard equations fail. In the present study, our EOS is applied to a number of inorganic as well as organic solids, including alloys, glasses, rubbers and plastics; varying widely in their bonding and structural characteristics, as well as in their bulk modulus values. A very good agreement is observed between the data and fits. The results obtained are compared with those from two well-known equations, expressible in the realistic form, proposed by Murnaghan and Luban. Further, the results are also compared with those from the widely used two- and three-parameter EOSs, expressible in the unrealistic form only, P=f(V/V₀), proposed by Birch—and also with those from the EOS model of Keane in which B′_∞ is explicitly expressed as an equation of state parameter. The results obtained from our model compare well to these EOSs. Our EOS, in general, yields the smallest mean-squared deviations between data and fits. The values of B′_∞calculated from our EOS are compared with those from Keane's model. Further, we have studied the variation of B′_∞with temperature using the experimental isotherms of Mo and W at 10 different temperatures ranging from 100 to 1000 K, and observed that the values of B′_∞ yielded by our model and that of Keane vary, as expected, within a narrow range. Furthermore, our EOS is applied to study the stability of the fit parameters with variation in the pressure ranges with reference to the isothermal compression data on Mo and W—and also to study the variation of isothermal bulk modulus with pressure, with reference to the ultrasonic data on NaCl and noted a very good agreement with experiment. In addition, our model is applied, with B₀ and B′₀ constrained to the theoretical values, to the five theoretical isotherms of MgO at 300, 500, 1000, 1500 and 2000 K obtained on the basis of a first principles approach—a good agreement is observed with the predictions, and the values of B′_∞ inferred at different temperatures tend to converge to a constant value.     

A phenomenological equation of state for isospin asymmetric nuclear matter

A phenomenological momentum-independent(MID) model is constructed to describe the equation of state(EOS) for isospin asymmetric nuclear matter,especially the density dependence of the nuclear symmetry energy Esym(ρ).This model can reasonably describe the general properties of the EOS for symmetric nuclear matter and the symmetry energy predicted by both the sophisticated isospin and momentum dependent MDI model and the Skyrme-Hartree-Fock approach.We find that there exists a nicely linear correlation betwee...     

统一状态方程描述同位素气体

通过对分子动力学模拟公式和同位素相互作用势特点的分析,提出用一个统一的状态方程描述同位素气体的P-V-T特性.进而选用Benedict-Webb-Rubin方程作为统一的状态方程,利用H2气体的135组实验值确定其八个参数.这个方程的计算结果与H2和D2气体的实验值符合良好.T2气体目前尚未见到成套的P-V-T实验数据报道,不能直接与实验结果对比,但与T2气体的分子动力学模拟计算结果一致.     

液氘状态方程实验数据测量

在神光Ⅱ高功率激光装置上建立了液氘状态方程实验研究系统, 在80 min内实现控温范围12–300 K可调、控温精度±0.03 K、机械震动 ≤20 μm的实验控制精度; 通过镀膜窗口质量筛选和靶体清洁工作解决了低温下窗口材料残余反射率高的难题, 获得了信噪比较好的实验图像; 利用神光II第九路输出3ω (351 nm)、3 ns、1000 J的能力, 采用阻抗匹配方法, 配合任意反射面速度干涉仪诊断系统, 在国内首次获得液氘在约60 GPa压力下的冲击绝热线实验数据, 数据与国外同压力区间数据符合较好, 为下阶段约100 GPa压力范围液氘状态方程的实验研究奠定了基础.     

Total energy, equation of state and bulk modulus of AlP, AlAs and AlSb semiconductors

Recently proposed model potential which combines both linear and quadratic types of interactions is employed for the investigation of some properties like the total energy, equation of state and bulk modulus of AlP, AlAs and AlSb semiconductor compounds using higher-order perturbation theory. The model potential parameter is determined using zero pressure condition. The ratio of the covalent bonding termE _cov to the secondorder termE ₂ is 6.77% to 11.85% which shows that contribution from higher order terms are important for zinc-blende-type crystals. The calculated numerical results of the total energy, energy band gap at Jones-zone face and bulk modulus of these compounds are in good agreement with the experimental data and found much better than other such theoretical findings. We have also studied pressure-volume relations of these compounds. The present study is carried out using six different screening functions along with latest screening function proposed by Sarkaret al. It is found from the present study that effect of exchange and correlation is clearly distinguishable.     

固氪物态方程的关联量子化学计算

运用多体展开理论和量子化学方法—–超分子单、双(三重)激发微扰处理耦合簇CCSD(T)方法,首次系统地计算了面心立方固氪在较宽(从晶格平衡位置到体积压缩率超过3倍)区间的两体、三体和四体相互作用对结合能和物态方程的贡献大小,包括Hartree-Fock自洽场项和范德瓦耳斯长程关联作用项;并与实验数据进行比较.结果表明,在考虑到两体、三体、四体相互作用能后,多体展开理论以及CCSD(T)方法对平衡位置结合能测量数据0—130 GPa整个研究区间的实验物态方程数据都做出令人满意的描述.     

用Hugoniot数据计算高压状态方程

提出了利用Hugoniot数据、变形Morse势和Grüneisen模型来确定固体材料的高压状态方程的方法。该方法物理意义明确,表达式简洁。用此方法计算Au的高压状态方程,将所得的状态方程与Sesame数据库中Au的状态方程进行比较,发现在密度20~28 g/cm3内两者吻合较好,相对误差在0~10%的范围内,表明运用Hugoniot数据结合Grüneisen模型计算材料的状态方程是很适合的。     

用Hartree-Fock-Slater-Boltzmann-Saha模型研究等离子体细致组态原子结构及其状态方程

用平均原子自洽势计算等离子体的自由电子背景，通过在Hartree Fock Slater自洽场原子结构中引入背景修正计算离子组态结构，为Boltzmann Saha方程提供能级参数，再通过调节共同的背景电子实现Saha方程与Hartree Fock Slater方程的耦合，自洽求解等离子体细致组态原子结构，提高Saha方程的计算精度.以碳、铝等离子体作为算例，分析了本方法的适用范围. 关键词： 原子结构 Boltzman Saha方程 状态方程     

Thermal equation of state for lattice Boltzmann gases

The Galilean invariance and the induced thermo-hydrodynamics of the lattice Boltzmann Bhatnagar--Gross--Krook model are proposed together with their rigorous theoretical background. From the viewpoint of group invariance, recovering the Galilean invariance for the isothermal lattice Boltzmann Bhatnagar--Gross--Krook equation (LBGKE) induces a new natural thermal-dynamical system, which is compatible with the elementary statistical thermodynamics.     

The statistical theory of the condensed system equation of state at high pressures

Abstract

One of the main problems in the statistical physics of condensed systems is the problem of the adequate equation of state to describe the thermodynamical properties of the substance in the wide range of pressure values. Here it is being solved by means of thermodynamic perturbation theory and the integral equations of the statistical theory of dense gases and liquids.     

Empirical equations of state for solids

A comparison of three one-parameter empirical equations of state due to Lennard-Jones, Bardeen, and Birch using Bridgman's experimental compression data shows that they do not generally fit the data within experimental error. Heuristic arguments are used to derive a well known three-parameter equation of state which includes these equations as special cases. Several simple two-parameter equations of state, including the Murnaghan equation, can be obtained as special cases of the general form. All of these two-parameter equations are shown to fit Bridgman's data within experimental error with about equal success. It is also shown that the general three-parameter equation, and hence its special cases, is consistent with the observation of Grover, Getting, and Kennedy that the log of the bulk modulus of solids is a linear function of compression. Several of the two-parameter special cases are shown to give satisfactory extrapolations.     

Quintessence models with an oscillating equation of state and their potentials

In this paper, we investigate the quintessence models with an oscillating equation of state (EOS) and its potentials. From the constructed potentials, which have an EOS of $\omega_{\phi}=\omega_0+\omega_1\sin z$, we find that they are all the oscillating functions of the field $\phi$, and the oscillating amplitudes decrease (or increase) with $\phi$. From the evolutive equation of the field $\phi$, we find that this is caused by the expansion of the universe. This also makes it very difficult to build a model whose EOS oscillates forever. However one can build a model with EOS oscillating for a certain period of time. Then we discuss three quintessence models, which are the combinations of the invert power law functions and the oscillating functions of the field $\phi$. We find that they all follow the oscillating EOS.