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 On the theoretical side, the earlier empirical methods have now been replaced by sophisticated band structure calculations.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.     

用于预测疏松材料冲击压缩特性的热力学模型

 在一定的假设条件下，从基本的热力学关系出发，导出了一个新的物态方程表达式。利用这一新形式特态方程所建立的热力学模型，可预测疏松材料的冲击压缩行为。以低、中、高冲击阻抗的铝、铜和钨为示例，将本模型的理论计算曲线与实验冲击压缩数据比较，表明本模型的在宽广的压力范围内具有良好的普活性；对不同初妈密度，疏松材料的冲击压缩行为均显示出较为满意的理论经历测能力；与现有的其它疏松材料物态方程模型相比，本模型在理论上和实际应用中均具有较大的优越性。     

激光加载下铝材料的冲击温度测量

利用神光Ⅱ装置上搭建的用于激光冲击波实验的温度诊断系统（该系统包括高时空分辨的扫描高温计和谱时分辨的扫描高温计）,以强激光加载铝材料冲击温度的测量,获得了铝材料冲击高温辐射发光谱的高时空分辨信号图像,结合灰体辐射理论模型,计算得到了冲击波速度19.06 km/s时铝材料的冲击温度达2.95 eV,该温度与SESAME库中冲击温度接近。研究结果表明采用该测温系统能够有效诊断金属材料的冲击温度,为后续进一步获取金属材料冲击温度数据奠定了基础。     

稠密氦气物态方程研究

用二级氢气炮作为冲击压缩加载工具和多通道瞬态辐射高温计作为主要测量系统,测量了冲击压缩氦气等离子体的光辐亮度历史（初始温度293K,初始压力为1.2MPa）。根据实测记录信号波形的有关特征量,计算得到了氦等离子体的Hugoniot物态方程（含冲击温度）。结果发现：实测Hugoniot物态方程可用Saha方程加Debye-Huckel修正物理模型解释。     

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。     

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     

超越平均原子模型模拟高温高密等离子体离子布居

从实际应用的角度出发，常采用平均原子(AA)模型进行简化处理.为了能更精确计算高温高密等离子体的离子布居，提出了一套超越AA模型的方法.该方法能够较好地处理局域热动平衡(LTE)等离子体离子布居，也可有效地处理非局域热动平衡(n-LTE)等离子体离子布居. 关键词： 平均原子(AA)模型 离子布居 非局域热动平衡(n-LTE)     

A physically-based Mie–Grüneisen equation of state to determine hot spot temperature distributions

A physically-based form of the Mie–Grüneisen equation of state (EOS) is derived for calculating 1d planar shock temperatures, as well as hot spot temperature distributions from heterogeneous impact simulations. This form utilises a multi-term Einstein oscillator model for specific heat, and is completely algebraic in terms of temperature, volume, an integrating factor, and the cold curve energy. Moreover, any empirical relation for the reference pressure and energy may be substituted into the equations via the use of a generalised reference function. The complete EOS is then applied to calculations of the Hugoniot temperature and simulation of hydrodynamic pore collapse using data for the secondary explosive, hexanitrostilbene (HNS). From these results, it is shown that the choice of EOS is even more significant for determining hot spot temperature distributions than planar shock states. The complete EOS is also compared to an alternative derivation assuming that specific heat is a function of temperature alone, i.e. c_v(T). Temperature discrepancies on the order of 100–600 K were observed corresponding to the shock pressures required to initiate HNS (near 10 GPa). Overall, the results of this work will improve confidence in temperature predictions. By adopting this EOS, future work may be able to assign physical meaning to other thermally sensitive constitutive model parameters necessary to predict the shock initiation and detonation of heterogeneous explosives.     

凝聚态物质状态方程的一个数值模型

建立了凝聚态物质的一个三项式状态方程：以Faussurier平均原子模型为基础计算电子热压和电子热能;以Cowan模型为基础计算离子热压和离子热能;用基于实验数据的半经验拟合公式计算物质的冷压和冷能。用实验数据检验了用平均原子模型计算的平均电离度。将状态方程与Hugoniot关系式相结合,计算了Be和Al的冲击绝热曲线,结果充分地展现出电子在高温、高密度条件下的壳层结构效应。     

Finite-temperature thermophysical properties of fcc-Ca

At an extreme environment, such as high-temperature and high-pressure, harmonic theory has obvious limitations, where the anharmonic effects are influential in determining bulk properties of the materials. In this regard, necessity for incorporating anharmonicity through vibrational contribution and thermally excited electrons to the total free energy at finite temperatures is illustrated taking an example of divalent fcc-Ca. In this regard, we have employed a coupling scheme of combining recently proposed mean-field potential (MFP) with the local pseudopotential to obtain vibrational contribution to the total free energy. To access the applicability of the present coupling scheme, we have calculated temperature variation of several thermodynamical properties. Static EOS, shock Hugoniot and temperature along principal Hugoniot are also estimated. Results are satisfactorily compared with the other theoretical and experimental data and the use of local pseudopotential in conjunction with the MFP approach is justified.     

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.     

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.     

Ab initio simulations of the K-edge shift along the aluminum Hugoniot

We develop a first-principles approach to calculate the near-edge absorption spectrum of dense plasmas based on density functional electronic structure calculations and molecular dynamics simulations. We apply the method to the calculation of the K-edge shift along the aluminum shock compressed Hugoniot. We obtain a good agreement with measurements performed at moderate compression and find that the variation of the XANES spectra could be used as a signature for melting along the Hugoniot. We also show that the calculation of the K-edge shift along the Hugoniot formally requires a fully self-consistent calculation beyond the frozen-core approximation and provides an opportunity to test the accuracy of first principle simulation methods in the high-pressure high-temperature regime.     

从头算方法研究面心立方铝在高温高压下的热力学状态方程

用从头算方法优化计算了面心立方铝的电子结构和总能,得到了它在零温下的状态方程和弹性性质.将得到的总能与晶格体积拟合到Debye模型,获得了非平衡态下的Gibbs自由能与温度、压力之间的关系,在此基础上计算了相应的热状态方程,利用Burakovsky-Preston-Silbar （BPS） 熔化模型计算了铝的熔化曲线.所有的电子结构和总能计算都是基于局域密度近似（LDA）和广义梯度近似（GGA）的平均得到的.计算得到的铝在高温、高压下的状态方程与一些热力学性质和熔化曲线同冲击波和静高压实验数据在225 G 关键词： 铝 热力学状态方程 从头算 熔化曲线     

40GPa压力范围内铜和铝的准等熵压缩线

 基于自行研制的磁驱动准等熵压缩加载实验装置CQ-1.5,利用全光纤位移干涉仪（Doppler Pins System, DPS）、激光速度干涉计（Velocity Interferometer System for Any Reflectors, VISAR）两种测试手段,以及反积分数据处理方法,实验测量了40 GPa压力范围内T1铜、LY12硬铝和L1纯铝3种材料的准等熵压缩线,将实验准等熵压缩线与基于Grüneisen状态方程的理论等熵压缩线和冲击Hugoniot线进行了比较。结果表明,在该压力范围内,实验准等熵压缩线与理论等熵压缩线相一致,两者偏差小于3%;实验准等熵压缩线靠近冲击Hugoniot线,位于其下方,与国外文献发表的结果相同,进一步表明,实验测量结果正确可靠。     

电子束对LY12硬铝的损伤效应

对LY12硬铝受到电子束辐照时产生的热激波及材料的损伤破坏效应进行了理论计算,将计算值同实验结果进行比较,二者基本上是一致的。在研究中等能量沉积产生材料的破坏效应时,应适当考虑材料的熔化过程,所用的状态方程是GRAY三相状态方程,而在研究材料的损伤破坏时,我们修正了计及损伤效应的Bodner-Partom本构模型。     

Reflected shock experiments on the equation-of-state properties of liquid deuterium at 100-600 GPa (1-6 mbar)

New laser-driven shock experiments have been used to study the equation-of-state (EOS) properties of liquid deuterium. Reflected shocks are utilized to increase the shock pressure and to enhance the sensitivity to differences in compressibility. The results of these experiments differ substantially from the predictions of the Sesame EOS. EOS models showing large dissociation effects with much greater compressibility (up to a factor of 2) agree with the data. By use of independent techniques, this experiment offers the first confirmation of an earlier observation of enhanced compressibility in liquid deuterium.     

A model for shock waves in solids and evidence for a thermal catastrophe

Shock-wave experiments and computer simulations yield a linear relation between shock velocity and particle velocity. We show that a Mie-Grüneisen equation of state combined with the Hugoniot relations matches the computer results and the experiments and leads to an explanation of the generality of the linear velocity dependence. At high shock velocities the onset of a thermal catastrophe, which results in a maximum shock compression, is predicted from our model.     

A caloric equation of state of a condensed medium derived based on generalized Hugoniot curves

The caloric equation of state, which expresses the internal energy through the volume and pressure is required in analyzing and calculating shock-wave processes in reacting media. The present work develops a method for constructing such an equation for condensed media on the basis of generalized Hugoniot curves. Expressions approximating the dependence of the Grüneisen coefficient and pressure on the volume along the Hugoniot curve. Formulas for calculating detonation Hugoniot curves from the shock Hugoniot curve of the condensed reaction products. The expressions obtained can be applied to approximate calculations of shockwave processes (for example, gasless detonation) in reacting condensed media. If necessary, such calculations can be performed with the use of physical quantities from standard handbooks.