Progress on Equation of State of Hydrogen and Deuterium
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摘要: 针对近二十多年的氢氘物态方程理论研究工作进行了综述分析，结合本课题组改进的自由能模型、直接量子蒙特卡洛和量子分子动力学方法的模拟结果，对多个研究小组采用不同方法获得的氢氘宽区物态方程数据进行了定量评估分析。结果表明：在当前理论框架下，仅基于第一原理数值模拟得到的氢氘物态方程能够描述的热力学相空间有限；多模型集成的H-REOS.3数据库在105 K以下温度与数值模拟结果的相对差别较大，且数据稀少，二者均不能满足工程应用需求。建议采用基于半经验模型的宽区域物态方程研究方法，即结合高精度的实验研究、数值模拟和解析模型，构建满足工程应用需求的氢氘宽区实用物态方程。Abstract: This paper reviews the research on the equation of state (EOS) for hydrogen and deuterium in the last twenty years.A quantitative analysis of the wide-range EOS for hydrogen and deuterium is given by combining the modified chemical free energy model and the modern computational techniques such as Quantum Molecular Dynamic (QMD) and Quantum Monte Carlo (QMC).It is demonstrated that the wide-range EOS obtained from ab initio calculations only covers a limited region of density-temperature space, and the H-REOS.3 database, which is obtained by integrating different models, exhibits disagreement with the modern computational results below the temperature of 105 K and its data points distribution is not dense enough.EOS of deuterium is not transformed from the H-REOS.3.Therefore, both the ab initio calculation and the H-REOS.3 are not sufficient for the engineering application, and it is necessary to construct a wide range EOS database for hydrogen and its isotopes, which combines the high-precision experiments, the modern computational techniques, and the analytical or semi-analytical models.
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图 1 QMD模拟氘物态方程的压强相对偏差
(下标i分别指代Gali2000、Desjarlais2003、Liu2004、Bonev2004、Danel2016、Lenosky2000, 以下类似)
Figure 1. Relative differences of pressure from QMD simulation for deuterium
(The subscript i represents Gali2000, Desjarlais2003, Liu2004, Bonev2004, Danel2016, Lenosky2000, respectively.Similarly hereinafter.)
图 2 QMD模拟氢物态方程的压强相对偏差
Figure 2. Relative differences of pressure from QMD simulation for hydrogen
图 3 不同泛函计算的氘物态方程压强相对差别
Figure 3. Relative differences of pressure from QMD simulation for deuterium in different exchange-correlation analysis
图 4 PIMC模拟氘物态方程的压强相对偏差
Figure 4. Relative differences of pressure from PIMC simulation for deuterium
图 5 PIMC模拟氢物态方程的压强相对偏差
Figure 5. Relative differences of pressure from PIMC simulation for hydrogen
图 6 氢的MP2011与REOS物态方程的相对偏差
Figure 6. Relative differences of equation of state for hydrogen between MP2011 and REOS
表 1 氢氘物态方程的QMD模拟工作
Table 1. Works of QMD simulation for equation of state of hydrogen and deuterium
Isotope Time Firstauthor Ref. Method Code Organization Temperature/K Density/(g·cm-3) D 1997 T. J. Lenosky [135] TBMD LANL 3 000-31 250 0.58-1.47 D 2000 G. Galli [136] CPMD GP code LLNL 10 000 0.67，1.0 D 2000 S. Bagnier [137] BOMD VASP CEA The effect of the local-spin-density-approximation functional D 2000 T. J. Lenosky [138] BOMD VASP LLNL，LANL 2 000-31 500 0.506-0.851 D 2002 F. Gygi [139] CPMD GP code LLNL The compressibility is determined by shock-induced electronic excitations D 2003 M. P. Desjarlais [140] BOMD VASP SNL 3 800-50 105 0.553-1.756 D 2004 S. A. Bonev [141] CPMD GP code LLNL 20-19 860 0.171-0.779 D 2004 H. F.Liu [149] BOMD VASP IAPCM 1 000-10 000 0.506-1.0 D 2016 J. F. Danel [142] QMD，OFWMD ABINIT，VAAQP CEA 11 604-116 045 0.2-20 D 2016 V. V. Karasiev [143] QMD，OFMD PROFESS@Q-ESPRESSO，ABINIT Universityof Florida 2 000-250 000 0.2-10, No data list D 2017 M. D. Knudson [12] QMD VASP，Diff Exc SNL, WashingtonState University H 2001 L. A. Collins [146] BOMD VASP LANL，LLNL 5 000-30 000 0.334-0.525 H 2008 B. Holst [147] BOMD VASP Institut für Physik，SNL 500-20 000 0.5-5.0 H 2010 M. A. Morales [126] BOMD，QMC QBOX，CEIMC University of Illinois，University of L'Aquila 2 000-10 000 0.724-2.329 H 2011 L. Caillabet [148] QMD，CEIMC PIMC, QMD, CEIMC CEA -116 045 0.2-5 H 2013 C. Wang [151] QMD，OFMD ABINIT IAPCM 1.564×104-5.004441×107 9.82×10-3-1.347×103 
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表 2 氢氘物态方程的QMC数值模拟
Table 2. Works of QMC simulation for equation of state of hydrogen and deuterium
Isotope Time Firstauthor Ref. Method Organization Temperature/K Density/(g·cm-3) D 2000 B. Militzer [114] PIMC(VDM) University of Illinois at Urbana-Champaign 105-106 0.674，0.838 D 2004 V. Bezkrovniy [155] DPIMC Universität Greifswald, Domstrasse, Germany；Russian Academy of Science 15 625-1 000 000 0.674，0.838，1.097 D 2011 S. X. Hu [46] RPIMC University of Rochester，University of California 15 665-63 822 000 0.002-1 596 H 20012003 V. S. Filinov [117]
[116]DPIMC Russian Academy of Sciences 31 250-106 0.419 H 2001 B. Militzer [114] RPIMC LLNL，University of Illinois at Urbana-Champaign 5 000-250 000 9.833×10-4-0.153 H 2004 C. Pierleoni [121] CEIMC Universita' of L'Aquila, Via Vetoio, University of Illinois at Urbana-Champaign, Université Pierre et Marie Curie 300-10 000 5.267，2.697，1.561 H 2010 M. A. Morales [126] CEIMC University of Illinois at Urbana-Champaign, University of L'Aquila, Italy 2 000-10 000 0.724-2.329 H 2011 L. Caillabet [148] QMD，CEIMC CEA 116 045 0.2-5 H 2015 Q. L. Zhang [150] DPIMC IAPCM 116 045 0.98×10-3-1 346.1
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