-
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 athttps://www.doi.org/10.57760/sciencedb.j00213.00166 .-
Keywords:
- wide-range equation of state /
- lead /
- multiphase /
- warm-dense matter
-
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 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.
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.
ρ0 2ρ0 3ρ0 4ρ0 5ρ0 T = 0.05 MK 1.00000 1.00000 1.00000 1.00000 1.00000 T = 0.1 MK 1.00000 1.00000 1.00000 1.00000 1.00000 T = 0.2 MK 0.99973 0.99977 0.99981 0.99984 0.99988 T = 0.3 MK 0.99492 0.99576 0.99640 0.99701 0.99746 T = 0.4 MK 0.97704 0.98074 0.98364 0.98612 0.98821 T = 0.5 MK 0.94243 0.95155 0.95881 0.96504 0.96917
下载: 导出CSV
-
[1] 徐锡申, 张万箱 1986 实用物态方程理论导引(北京: 科学出版社)第1页, 第191页
Xu X S, Zhang W X 1986 Introduction to Practical Equation of States (Beijing: Scientific Press) p1, p191
[2] Holzapfel W B, Hartwig M, Sievers W 2001 J. Phys. Chem. Ref. Data 30 515
Google Scholar
[3] Lyon S P, Johnson J D 1992 Los Alamos Technical Report No. LA-UR-92-3407
[4] More R M, Warren K H, Young D A, Zimmerman G B 1988 Phys. Fluids 31 3059
Google Scholar
[5] Liu H F, Song H F, Zhang Q L, Zhang G M, Zhao Y H 2016 Matter Radiat. Extrem. 1 123
Google Scholar
[6] Zhao Y H, Wang L F, Zhang Q L, Zhang L, Song H Z, Gao X Y, Sun B, Liu H F, Song H F 2025 Chin. Phys. B 34 036401
Google Scholar
[7] 汤文辉, 徐彬彬, 冉宪文, 徐志宏 2017 物理学报 66 030505
Google Scholar
Tang W H, Xu B B, Ran X W, Xu Z H 2017 Acta Phys. Sin. 66 030505
Google Scholar
[8] Graziani F, Desjarlais M P, Redmer R, Trickey S B (Eds.) 2014 Frontiers and Challenges in Warm Dense Matter (Cham: Springer International Publishing) p123
[9] 刘千锐 2023 博士学位论文(北京: 北京大学)
Liu Q R 2023 Ph. D. Dissertation (Beijing: Peking University
[10] Hohenberg P, Kohn W 1964 Phys. Rev. B 136 B864
Google Scholar
[11] Kohn W, Sham L J 1965 Phys. Rev. A 140 A1133
Google Scholar
[12] Martin R M 2004 Electronic Structure: Basic Theory and Practical Methods (Cambridge: Cambridge University Press) p119
[13] Cytter Y, Rabani E, Neuhauser D, Baer R 2018 Phys. Rev. B 97 115207
Google Scholar
[14] Militzer B, González-Cataldo F, Zhang S, Driver K P, Soubiran F 2021 Phys. Rev. E 103 013203
Google Scholar
[15] Zhang S, Wang H W, Kang W, Zhang P, He X T 2016 Phys. Plasmas 23 042707
Google Scholar
[16] Blanchet A, Clérouin J, Torrent M, Soubiran F 2022 Comput. Phys. Commun. 271 108215
Google Scholar
[17] White A J, Collins L A 2020 Phys. Rev. Lett. 125 055002
Google Scholar
[18] Liu Q R, Chen M H 2022 Phys. Rev. B 106 125132
Google Scholar
[19] Wilson B G, Johnson D D, Alam A 2011 High Energy Density Phys. 7 61
Google Scholar
[20] Starrett C E 2018 Phys. Rev. E 97 053205
Google Scholar
[21] Walsh J M, Rice M H, Mcqueen R G, Yarger F L 1957 Phys. Rev. 108 196
Google Scholar
[22] Al'tshuler L V, Krupnikov K K, Brazhnik M I 1958 Zh. Eksp. Teor. Fiz. 34 886 (in Russian
[23] Al'tshuler L V, Kormer S B, Bakanova A A, Trunin R F 1960 Zh. Eksp. Teor. Fiz. 38 790 (in Russian
[24] McQueen R G, Marsh S P 1960 J. Appl. Phys. 31 1253
Google Scholar
[25] Al'tshuler L V, Bakanova A A, Bushman A V, Dudoladov I P, Zubarev V N 1977 Zh. Eksp. Teor. Fiz. 73 1866 (in Russian
[26] Marsh S P (Ed. ) 1980 LASL Shock Hugoniot Data (Berkeley: Univ. California Press) p100
[27] Avrorin E N, Vodolaga B K, Voloshin N P, Kuropatenko V F, Kovalenko G V, Simonenko V A, Chernodolyuk B T 1986 Pis'ma Zh. Eksp. Teor. Fiz. 43 241 (in Russian
[28] Mitchell A C, Nellis W J, Moriarty J A, Heinle R A, Holmes N C, Tipton R E, Repp G W 1991 J. Appl. Phys. 69 2981
Google Scholar
[29] Trunin R F, Il'kaeva L A, Podurets M A, Popov L V, Pechenkin B V, Prokhorov L V, Sevast'yanov A G, Khrustalev V V 1994 Teplofiz. Vys. Temp. 32 692 (in Russian
[30] Trunin R F 1994 Usp. Fiz. Nauk 164 1215 (in Russian
[31] Mao H K, Wu Y, Shu J F 1990 Solid State Commun. 74 1027
Google Scholar
[32] Partouche-Sebban D , Pélissier J L 2005 J. Appl. Phys. 97 043521
[33] Dewaele A, Mezouar M, Guignot N, Loubeyre P 2007 Phys. Rev. B 76 144106
Google Scholar
[34] Smirnov N A 2020 J. Phys. : Condens. Matter 33 035402
[35] Zhang S, Morales M A 2020 AIP Conf. Proc. 2272 090004
[36] Yang X, Zeng X G, Chen H Y, Wang Y T, He L, Wang F 2019 J. Alloy. Comp. 808 151702
Google Scholar
[37] Strässle Th, Klotz S, Kunc K, Pomjakushin V, White J S 2014 Phys. Rev. B 90 014101
[38] Kozyrev N V, Gordeev V V 2022 Metals 12 16
[39] Schulte O, Holzapfel W B 1995 Phys. Rev. B 52 12636
Google Scholar
[40] Morita K, Sobolev V, Flad M 2007 J. Nucl. Mater. 362 227
Google Scholar
[41] Sobolev V P, Schuurmans P, Benamati G 2008 J. Nucl. Mater. 376 358
Google Scholar
[42] Song P, Cai L C 2010 Physica B 405 1509
Google Scholar
[43] Gao X Y, Mo Z Y, Fang J, Song H F, Wang H 2017 Comput. Phys. Commun. 211 54
Google Scholar
[44] Zhou Y Z, Wang H, Liu Y, Gao X Y, Song H F 2018 Phys. Rev. E 97 033305
Google Scholar
[45] Fang J, Gao X Y, Song H F 2019 Commun. Comput. Phys. 26 1196
Google Scholar
[46] Blanchet A, Torrent M, Clérouin J 2020 Phys. Plasmas 27 122706
Google Scholar
[47] Sjostrom T, Crockett S, Rudin S 2016 Phys. Rev. B 94 144101
Google Scholar
[48] Kadatskiy M A 2019 High Energy Density Phys. 33 100700
Google Scholar
[49] Liu X, Zhang X H, Gao C, Zhang S, Wang C, Li D F, Zhang P, Kang W, Zhang W Y, He X T 2021 Phys. Rev. B 103 174111
Google Scholar
[50] Schwarz K 2003 J. Solid State Chem. 176 319
Google Scholar
[51] Benedict L X, Driver K P, Hamel S, Militzer B, Qi T, Correa A A, Saul A, Schwegler E 2014 Phys. Rev. B 89 224109
Google Scholar
[52] Mattsson A E 2012 Sandia Technical Report No. SAND2012-7389
[53] Eliezer S, Ricci R A (Eds.) 1991 High Pressure Equations of State: Theory and Applications (Amsterdam: North Holland) p249
[54] Johnson J D 1991 Int. J. High Press. Res. 6 277
Google Scholar
[55] Benedict L X, Ogitsu T, Trave A, Wu C J, Sterne P A, Schwegler E 2009 Phys. Rev. B 79 064106
Google Scholar
[56] Wilson B, Sonnad V, Sterne P, Isaace W 2006 J. Quant. Spectrosc. Ra. 99 658
Google Scholar
下载:
计量
- 文章访问数: 275
- PDF下载量: 9
- 被引次数: 0
