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金属铅的宽区多相物态方程

方俊 赵艳红 高兴誉 张其黎 王越超 孙博 刘海风 宋海峰

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金属铅的宽区多相物态方程

方俊, 赵艳红, 高兴誉, 张其黎, 王越超, 孙博, 刘海风, 宋海峰

A wide-range multiphase equation of state for lead

FANG Jun, ZHAO Yanhong, GAO Xingyu, ZHANG Qili, WANG Yuechao, SUN Bo, LIU Haifeng, SONG Haifeng
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  • 本文从Helmholtz自由能出发构建了铅的宽区多相物态方程, 覆盖从常温到10 MK、从常压到107 GPa的温压范围, 计算了冲击雨贡纽线、300 K等温线、熔化线及温稠密过渡区热力学物性, 并与实验值、铅已有的宽区物态方程数据库SESAME-3200以及第一性原理模拟结果进行了对比分析. 一方面, 本文的模型能较好地再现各类实验数据; 另一方面, 在温稠密过渡区, 本文的模型获得了扩展的第一性原理分子动力学模拟结果的验证, 相比SESAME-3200更符合第一性原理的模拟结果. 本文数据集可在https://www.doi.org/10.57760/sciencedb.j00213.00166中访问获取.
    We present a multi-phase equation of state (EOS) for lead (Pb, Z = 82) in wide ranges of densities and temperatures: $ {11}{.34}\;{\text{g}}/{\text{c}}{{\text{m}}^3} < \rho < 80\; {\text{g}}/{\text{c}}{{\text{m}}^3}{,} $ $ 300\;{\mathrm{K}} < T < 10\;{\mathrm{MK}}. $ The EOS model is based on a standard decomposition of the Helmholtz free energy that is regarded as a function of the specific volume and the temperature into cold term, ion-thermal term, and electronic excitation term. The cold term models both the compression and the expansion states; the ion-thermal term introduces the Debye approximation and the melting entropy; the electronic excitation term employs the Thomas-Fermi-Kirzhnits (TFK) model. The thermodynamic properties of the warm-dense lead are calculated using the extended first-principles molecular dynamics (ext-FPMD) method, with the density reaching five times that of ambient density and the temperature of 0.4 MK. Our EOS model is used to predict the principle Hugoniot, the room-temperature isotherm, the melting curve, and the thermodynamic properties in the warm-dense region. A systematic comparison with the experimental data, the SESAME-3200 table, and the ext-FPMD calculations is made and shows that our EOS model is consistent with not only the various experimental data, but also the ext-FPMD calculations, indicating some superiority over the SESAME-3200 table in the warm-dense region. The datasets presented in this paper, including the tabular EOS consisting of internal energy and pressure at the different densities and temperatures, are openly available at https://www.doi.org/10.57760/sciencedb.j00213.00166.
  • 图 1  面心立方铅的冷压线(压强-体积)22个价电子的PAW势计算结果与WIEN2k全势结果的对比

    Fig. 1.  Cold pressure results of face-centered-cubic lead calculated by CESSP with the 22 electron PAW potential, compared with full-potential results from WIEN2k.

    图 2  冲击雨贡纽线(压强-压缩比)理论计算值, 以及与SESAME-3200和实验数据的对比

    Fig. 2.  Principle Hugoniot predicted by the theoretical model in this work, compared with the SESAME-3200 table and the experimental data.

    图 3  300 K等温压缩线(体积比-压强)理论计算值与SESAME-3200[3]和实验数据[31]的对比

    Fig. 3.  Room-temperature isotherm predicted by the theoretical model in this work, compared with the SESAME-3200 table[3] and the experimental data[31].

    图 4  熔化线及雨贡纽线(温度-压强)理论计算值与SESAME-3200和实验数据的对比

    Fig. 4.  Melting curve predicted by the theoretical model in this work, compared with the experimental data. The T-P Hugoniot curves from our model and the SESAME-3200 table are also given to illustrate the difference.

    图 5  温稠密过渡区物性(压强-压缩比)理论模型与SESAME-3200[3]和第一性原理ext-FPMD模拟的对比

    Fig. 5.  Thermodynamic properties of the warm-dense lead predicted by the theoretical model in this work, compared with the SESAME-3200 table[3] and the ext-FPMD calculations.

    表 1  Ext-FP方法与标准DFT方法下铅的计算结果比较

    Table 1.  Comparison of results from the ext-FP method and the DFT method.

    电子温度/MK Ext-FP方法 标准DFT方法
    Ncut P/GPa ΔP/% Nocc P/GPa
    0.1 40 134.654 –0.01 100 134.670
    0.2 60 414.783 –0.03 200 414.890
    0.3 80 791.144 –0.23 350 792.977
    下载: 导出CSV

    表 2  不同温度密度条件下最低价态(铅的5s态)的占据数

    Table 2.  Occupation numbers of the lowest energy valence state (5s state of lead) at the different temperatures and densities.

    ρ02ρ03ρ04ρ05ρ0
    T = 0.05 MK1.000001.000001.000001.000001.00000
    T = 0.1 MK1.000001.000001.000001.000001.00000
    T = 0.2 MK0.999730.999770.999810.999840.99988
    T = 0.3 MK0.994920.995760.996400.997010.99746
    T = 0.4 MK0.977040.980740.983640.986120.98821
    T = 0.5 MK0.942430.951550.958810.965040.96917
    下载: 导出CSV
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