Equation of State for Shock Compressed Xenon in the Ionization Regime:ab Initio Study

Quantum molecular dynamic (QMD) simulations have been applied to study the thermophysical properties of liquid xenon under dynamic compressions. The equation of state (EOS) obtained from QMD calculations are corrected according to Saha equation, and contributions from atomic ionization, which are of predominance in determining the EOS at high temperature and pressure, are considered. For the pressures below 160 GPa, the necessity in accounting for the atomic ionization has been demonstrated by the Hugoniot curve, which shows excellent agreement with previous experimental measurements, and three levels of ionization have been proved to be sufficient at this stage.     

氘、氦及其混合物状态方程第一原理研究

利用量子分子动力学方法对氘、氦及其混合物的状态方程进行了研究. 计算了氦在密度0.32-5 g/cm³, 温度1000-50000 K范围内的状态方程, 并与化学模型的结果进行了比较; 同时计算了冲击Hugoniot曲线, 与气炮实验的结果符合得很好. 通过计算对分布函数及态密度, 探讨了氦在高温高压下发生金属-绝缘体转变的机理. 计算了氘在密度0.19-0.84 g/cm³, 温度20-50000 K范围内的状态方程; 并计算了理论Hugoniot状态, 由于没有考虑原子的零点运动, 在低温区, 理论结果比实验值小. 对氘氦混合物的状态方程进行了研究, 计算了温度和密度区间为100-50000 K, 0.19-0.84 g/cm³, 不同混合度下的293个状态点的状态方程. 对线性混合近似进行了考查, 结果表明线性混合近似是一个粗略的近似.     

Equation of state theories of condensed matter up to about 10 TPa

A knowledge of the equation of state (EOS) of matter is necessary to describe the dependence of its thermodynamic properties on its microscopic internal structure. EOS data are also vital for a variety of applications, particularly those that involve numerical simulation of dynamic processes. This has motivated intense research on EOS of materials, both in experimental and theoretical areas. Various laboratories in the world are involved in the development of techniques for the generation of increasingly higher pressures using high power lasers, electric and rail guns etc. The range of these controlled dynamic pressures is currently reaching about10 TPa. On the theoretical side, the earlier empirical methods have now been replaced by sophisticated band structure calculations. In this article, we review these first principle theoretical attempts to calculate EOS over a range of densities and temperatures, where a variety of physical phenomena such as band crossings, band closures, phase transitions, nuclear and electronic thermal excitations, core ionization, liquid disorder etc. are encountered. The emphasis in this review is on shock Hugoniot equation of state theories.     

Thermodynamic properties of the Lennard-Jones FCC solid: perturbation theory parameterisation and Monte Carlo simulation

This work is concerned with a valid representation of the solid-phase equation of state (EOS), the validity of which is evaluated by comparing to Monte Carlo (MC) simulation results. The proposed EOS has been developed by employing an optimal division of the Lannard-Jones (LJ) potential and an effective temperature- and density-dependent diameter into the framework of the simplified perturbation theory. Then, with the aim of extending to the chain systems, the conventional chain contribution (i.e. TPT1) is added to the proposed model (i.e. the atomic LJ system). Finally, the solid-state EOS based on Helmholtz free energy will be introduced for low temperature and high density conditions. To verify the accuracy of the proposed model, its performance is compared with the results of MC simulation. The comparison between the obtained results from the proposed model and the MC simulations shows that the EOS can satisfactorily predict the properties of the solid LJ system, both for the atomic system and for the chains.     

部分电离稠密氦等离子体物态方程的自洽变分计算

稠密氦在高温高压下将会发生电离, 电离能会因为原子、离子以及电子之间的相互作用而降低. 考虑He，He⁺，He²⁺，e之间的相互作用, 通过粒子化学势平衡得到非理想的电离平衡方程，用自洽流体变分过程对方程求解, 进而对自由能求导获得体系的热力学状态参量. 模型计算结果与已有的实验和理论计算相一致. 用此模型预测密度10^-3—10^0.3 g/cm³和温度4—7 eV范围的物态方程, 获得了压力在500　GPa以内的理论数据. 计算表明粒子间的非理想相互作用引起的电离能降低是出现压致电离现象的主要原因，在高温高密度物态方程的计算中必须考虑粒子间非理想相互作用对电离能修正的影响. 关键词： 氦 物态方程 部分电离等离子体 自洽变分     

Two-colour coherent control of multiphoton ionization： a comparison between long-range and short-range potential model atoms

Using the numerical solution of the time-dependent Schr\"odinger equation of a one-dimensional model atom in a two-colour laser field, we have investigated the effects of the potential models on coherent control of atomic multiphoton ionization. It is found that the photoelectron spectra are obviously different for the long-range (Coulomb-like) and short-range (with no excited bound states) potential model atoms, which are produced by two-colour coherent control of atomic multiphoton ionization in a few laser cycles. Our results indicate that two-colour coherent control of atomic multiphoton ionization can be observed in simulations, depending on the choice of the model potentials.     

Modeling pressure-ionization of hydrogen in the context of astrophysics

Abstract

The recent development of techniques for laser-driven shock compression of hydrogen has opened the door to the experimental determination of its behavior under conditions characteristic of stellar and planetary interiors. The new data probe the equation of state (EOS) of dense hydrogen in the complex regime of pressure ionization. The structure and evolution of dense astrophysical bodies depend on whether the pressure ionization of hydrogen occurs continuously or through a “plasma phase transition” (PPT) between a molecular state and a plasma state. For the first time, the new experiments constrain predictions for the PPT. We show here that the EOS model developed by Saumon and Chabrier can successfully account for the data, and we propose an experiment that should provide a definitive test of the predicted PPT of hydrogen. The usefulness of the chemical picture for computing astrophysical EOS and in modeling pressure ionization is discussed.     

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.     

Nucleus-electron model for states changing from a liquid metal to a plasma and the Saha equation

We extend the quantal hypernetted-chain (QHNC) method, which has been proved to yield accurate results for liquid metals, to treat a partially ionized plasma. In a plasma, the electrons change from a quantum to a classical fluid gradually with increasing temperature; the QHNC method applied to the electron gas is in fact able to provide the electron-electron correlation at an arbitrary temperature. As an illustrating example of this approach, we investigate how liquid rubidium becomes a plasma by increasing the temperature from 0 to 30 eV at a fixed normal ion density 1.03x10(22)/cm(3). The electron-ion radial distribution function (RDF) in liquid Rb has distinct inner-core and outer-core parts. Even at a temperature of 1 eV, this clear distinction remains as a characteristic of a liquid metal. At a temperature of 3 eV, this distinction disappears, and rubidium becomes a plasma with the ionization 1.21. The temperature variations of bound levels in each ion and the average ionization are calculated in Rb plasmas at the same time. Using the density-functional theory, we also derive the Saha equation applicable even to a high-density plasma at low temperatures. The QHNC method provides a procedure to solve this Saha equation with ease by using a recursive formula; the charge population of differently ionized species are obtained in Rb plasmas at several temperatures. In this way, it is shown that, with the atomic number as the only input, the QHNC method produces the average ionization, the electron-ion and ion-ion RDF's, and the charge population that are consistent with the atomic structure of each ion for a partially ionized plasma.     

非理想性参数在0.9～2.1区的氩等离子体物态方程研究

采用平面冲击压缩方法产生密度和温度都均匀的氩等离子体,根据辐射高温计记录和飞片速度的测定,通过阻抗匹配方法确定了氩等离子体的Hugoniot物态方程,等离子体温度在1.5 eV～2.6 eV范围,压力在0.2～0.8 GPa之间.计算表明,Saha-Debye-Hückel模型不适用于描述该密度区域的氩等离子体.本文采用Gryaznov模型的计算结果,测量值和理论计算结果符合较好.     

多体相互作用对高压固氦状态方程的影响

采用量子化学自洽场方法及原子团簇理论对固氦晶格原子势能进行多体展开，定量确定了最近邻原子间距R在0.26—0.175nm之间，短程的两体到五体相互作用对晶体结合能及压缩特性的贡献，并对不同间距下多体展开式的截断位置进行了讨论. 结果表明：当最近邻原子间距R在0.26—0.175 nm之间取值，在具有hcp相结构的晶格中，氦原子势能的多体展开式是一收敛的交错型级数，该级数中两体项、四体项为正值，而三体项、五体项为负值. 当R在0.26—0.23 nm之间取值时, 仅保留级数中两体和三体项就能很好地描述晶格原子势能；当R在0.23—0.20 nm之间取值，多体展式需要展开到四体相互作用项；当R在0.20—0.175 nm之间取值必须再加入五体项贡献. 考虑到五体相互作用后，理论计算已能圆满地解释目前固氦等温压缩数据，其最大压力达 60GPa. 关键词： 固氦 状态方程 多体相互作用     

Improved equation of state for ionic liquids using surface tension

The major objective of this work was the development of a reliable model to describe volumetric properties of ionic liquids (ILs). In this regard, we have applied the Ihm–Song–Mason equation of state (EOS) to some phosphonium- and imidazolium-based ILs. Three temperature-dependent parameters in the equation of state have been scaled based on the surface tension and the liquid density at room temperature. In order to improve the predictive power of the mentioned EOS for ILs, we have proposed using a simple modification. We have taken 1,228 experimental points to show the reliability of the improved EOS. The comparison of predicted densities with literature data over a broad range of temperature, 293–472 K, and pressures up to 200 MPa led to encouraging results. The average absolute deviation of calculated densities from literature values was found to be 0.75%.     

Ionization and excitation of some atomic targets and metal oxides by electron impact

We have calculated total inelastic and total ionization cross-sections for collisions of electrons on atomic targets oxygen (O), aluminium (Al) and copper (Cu) and metal oxides AlO and Al₂O, at impact energies from near excitation threshold to 2000 eV. A complex (optical) energy-dependent interaction potential is used to derive total inelastic cross-sections resulting from ionization as well as excitation processes. The inelastic cross-sections are bifurcated into discrete and continuum contributions and total ionization cross-sections have been deduced therefrom. Our calculation also provides information, hitherto sparse, on the excitation processes in the atomic targets O, Al, Cu and metal oxides AlO, Al₂O. Adequate comparisons are made with other theoretical and experimental data.     

激光支持等离子体流场的2维动态数值模拟

 采用高温气体（等离子体）电离度的一种近似计算方法,以及具有五阶精度的广义Godunov差分格式-加权本质无振荡格式,给出了高温气体状态方程的简便描述,并考虑激光与等离子体的相互作用和能量耦合模拟了强激光与固体靶相互作用时激光支持靶面等离子体流场的动态物理过程,并同理论模型结果进行了比较。结果表明：不考虑2维膨胀效应的理论模型结果比2维数值计算结果偏大,但两者只有接近一倍的差距,并无数量级的差别。考虑了膨胀效应的2维数值计算结果是可信的。     

广义Morse流体解析状态方程及对氮的应用

 根据Ross变分微扰理论以及硬球流体Percus-Yevick（PY） 径向分布函数表达式,建立了广义Morse势流体的解析状态方程。与模拟结果的比较一方面证实了广义Morse 势模型的合理性;另一方面表明了解析Ross变分微扰理论的精度相当或略好于非解析的Weeks-Chandler-Anderson （mWCA）理论,而优于复杂的优化超网络链积分方程理论（RHNC）。该解析状态方程被应用于拟合处于环境温度和压强小于1 GPa情形流体氮的实验数据,所得到的势能参数被用于预测高温高密度情形氮流体的压强,预测结果证实,该解析状态方程可以很好地适用于较宽的压强和温度范围。     

Secondary-ion emission from silicon bombarded with atomic and molecular noble-gas ions

The emission of Si⁺ from a clean silicon surface has been studied for bombardment with various atomic and molecular noble gas ions at energies between 1.5 and 30 keV. It was found that the degree of ionization of Si⁺ depends strongly (l?inearly) on the projectile energy but only weakly on the projectile mass. These results suggest that the degree of ionization is heavily affected by the (dynamic) perturbation of the bulk properties of the bombarded area which increases with increasing nuclear energy deposition.     

Kaon production at subthreshold energies

We present a comprehensive investigation of subthreshold and threshold kaon production in the framework of the QMD model. The calculation shows that the kaon yield depends strongly on the nuclear equation of state (EOS) and subthreshold kaon experiments may therefore offer the up to now best possibility to determine this yet unknown property of nuclear matter. Whereas static equations of state are in quite good agreement with the data the more realistic momentum dependent EOS's underpredict the data by about a factor of three. Most kaons are produced in a two step process with an intermediate Δ, a process which is absent in NN collisions. Therefore the kaon yield is much higher than expected from the extrapolation of pp data. We discuss in detail the influence of the elementary kaon production cross section, the contribution of different production channels and the properties of the nuclear environment at the place where the kaon is produced. The decrease of the number of produced kaons per participant with decreasing participant number, which is also observed experimentally, has two sources: The nonmaxwellian momentum distribution for small participant numbers as well as a reduction of the ΔΔ channel. This finding is supported by the observed decrease of high momentum pions. We compare our results with other calculations and discuss in detail the theoretical and experimental uncertainties. They include the yet only vaguely known elementary kaon production cross section at the threshold, the lack of a quantum-mechanical treatment of the two step production process as well as the behaviour of the kaon (and therefore also of the kaon production threshold) in the nuclear environment.     

200 GPa压力范围内铝和铜的等熵压缩线计算

 将冲击Hugoniot线作为Grüneisen物态方程的参考线,以冲击的初始状态为参考状态,推导得到线性和二次曲线表示的冲击绝热线所对应的等熵压缩线方程,计算了200 GPa压力范围内铝和铜两种材料的等熵压缩线,并且计算了以Hugoniot关系为基础的Appy经验物态方程导出的等熵压缩线。计算结果表明,以Appy经验物态方程导出的等熵压缩线与以线性冲击绝热线导出的等熵压缩线接近,在200 GPa压力范围内两者相差不到1.5%。将计算得到的铝的等熵压缩线与美国Sandia实验室ICE实验Z864数据进行了比较,由线性Hugoniot得到的等熵压缩线与实验数据相差不到1%,由Appy经验物态方程得到的等熵线与实验数据几乎重合,说明在200 GPa压力范围内,以Appy物态方程和以线性Hugoniot为参考来计算的等熵压缩线有较高的精度。     

Molecular dynamic simulations and global equation of state of square-well fluids with the well-widths from λ = 1.1 to 2.1

We present the results of extensive new molecular dynamic (MD) simulations in the one-phase region for square well fluids with well widths λ?=?1.10, 1.15, 1.20, 1.25, 1.375, 1.50, 1.75, 1.90, 2.0, and 2.10. These data have been used in developing a crossover equation of state (CR EOS) for square-well fluids with well widths 1.1?≤?λ?≤?2.1. The CR EOS incorporates non-analytic scaling laws in the critical region, and in the limit of low densities yields the exact second and third virial coefficients. Also in the high-temperature region, it reproduces first-order perturbation theory results. The CR EOS was tested against our new MD simulations, and earlier MD and Monte-Carlo (MC) simulations reported by other authors as well. Excellent agreement between calculated values and simulation data for all SW fluids is observed. In combination with the density-functional theory, the CR EOS is also capable of reproducing surface tension simulations with high accuracy. Application of the CR EOS for solid–liquid equilibrium calculations in combination with the Lennard–Jones and Devonshire cell model for the solid phase, is also discussed.