氢状态方程的路径积分蒙特卡罗研究

doi:10.19596/j.cnki.1001-246x.7855

计算物理 ›› 2019, Vol. 36 ›› Issue (4): 379-385.DOI: 10.19596/j.cnki.1001-246x.7855

所属专题：高压物态方程研究

• • 下一篇

氢状态方程的路径积分蒙特卡罗研究

张其黎, 刘海风, 李琼, 宋红州, 张弓木

北京应用物理与计算数学研究所, 北京 100094

收稿日期:2018-03-12 修回日期:2018-03-23 出版日期:2019-07-25 发布日期:2019-07-25
作者简介:张其黎(1972-),男,博士,副研究员,从事材料物性数值模拟研究,E-mail:zhang_qili@iapcm.ac.cn
基金资助:
科学挑战专题资助（TZ2016001），国家自然科学基金（11604018）及国家重点研发计划重点专项（2017YFA0403200）资助项目

Path Integral Monte Carlo Calculations of Equation of State of Hydrogen

ZHANG Qili, LIU Haifeng, LI Qiong, SONG Hongzhou, ZHANG Gongmu

Institute of Applied Physics and Computational Mathematics, Beijing 100094, China

Received:2018-03-12 Revised:2018-03-23 Online:2019-07-25 Published:2019-07-25

摘要/Abstract

摘要： 采用直接路径积分蒙特卡罗（DPIMC）方法计算氢在温稠密区的状态方程参数.在大部分区域压强与RPIMC的偏差在10%以内，温度较低时，有部分偏差超过20%.指出了RPIMC两个压强数据点的错误.在离解和电离区，DPIMC压强位于TF和TFC模型之间，在离解区与RPIMC的偏差达到15%，在电离区两者一致.在低密度区，DPIMC的内能与RPIMC的内能接近，小于QMD和IG模型，在高密度区，DPIMC的压强位于TFC和IG模型之间，内能则略小于IG模型.

关键词: DPIMC方法, 氢, 状态方程, 温稠密

Abstract: We computed equations of state of hydrogen in warm dense matter regime by using DPIMC method. In large part of the regime, pressure difference between DPIMC and RPIMC is less than 10%. In low temperature regime, some difference beyond 20%. We pointed out two clerical errors in pressure of RPIMC. In dissociation and ionization regime, pressures of DPIMC lie between results of TF and TFC model. In dissociation regime, the largest pressure difference between DPIMC and RPIMC is 15%. In ionization regime, pressures of DPIMC are agree with RPIMC. In low density regime, internal energies of DPIMC are close to those of RPIMC, less than those of QMD and those of IG model. In high density regime, pressures of DPIMC lie between results of TFC and IG model, internal energies of DPIMC less than those of IG model.

Key words: DPIMC method, hydrogen, equation of state, warm dense matter

中图分类号:

张其黎, 刘海风, 李琼, 宋红州, 张弓木. 氢状态方程的路径积分蒙特卡罗研究[J]. 计算物理, 2019, 36(4): 379-385.

ZHANG Qili, LIU Haifeng, LI Qiong, SONG Hongzhou, ZHANG Gongmu. Path Integral Monte Carlo Calculations of Equation of State of Hydrogen[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2019, 36(4): 379-385.

参考文献

[1] MCCRORY R L, et al. Progress in direct-drive inertial confinement fusion[J]. Phys Plasmas, 2008, 15:055503.
[2] MEYERHOFER D D. High-performance inertial confinement fusion target implosions on OMEGA[J]. Nucl Fusion, 2011, 51:053010.
[3] LINDL J D. Development of the indirect-drive approach to inertial confinement fusion and the target physics basis for ignition and gain[J]. Phys Plasmas, 1995, 2:3933.
[4] HUBBARB W B. Interiors of the giant planets[J]. Science, 1981, 214:145.
[5] STEVENSON D J. Interiors of the giant planets[J]. Annu Rev Earth Planet Sci, 1982, 10:257.
[6] ZHAO Y, ZHANG G, ZHANG Q, et al. Equation of state of detonation products for HMX explosive[J]. Chinese Journal of Computational Physics, 2017, 34(2):155-159.
[7] FOULKES W M C, MITAS L, NEEDS R J, et al. Quantum Monte Carlo simulations of solids[J]. Rev Mod Phys, 2001, 73:33.
[8] CEPERLEY D M. Path integrals in the theory of condensed helium[J]. Rev Mod Phys, 1995, 65:279.
[9] 李名锐, 周刚, 李志康, 等. 液氘单次冲击压缩的QMC模拟研究[J].高压物理学报,2015,29(1):1-8.
[10] KITAMURA H, TSUNEYUKI SH, TADASHI O, et al. Quantum distribution of protons in solid molecular hydrogen at megabar pressure[J]. Nature, 2000, 404:259-262.
[11] JOHNSON K A, ASHCROFT N W. Structure and bandgap closure in dense hydrogen[J]. Nature, 2000, 403:632-635.
[12] WANG Y, PERDEW J P. Correlation hole of the spin-polarized electron gas, with exact small-wave-vector and high-density scaling[J]. Phys Rev B, 1991, 44:13298.
[13] LENOSKY T J, BICKHAM S R, KRESS J D. Density-functional calculations of the Hugoniot of shocked liquid deuterium[J]. Phys Rev B, 2000, 61:1.
[14] DESJARLAIS M P. Density-functional calculations of the liquid deuterium Hugoniot, reshock, and reverberation timing[J]. Phys Rev B, 2003, 68:064204.
[15] 张其黎, 张弓木, 赵艳红, 等. 氘、氦及其混合物状态方程第一原理研究[J]. 物理学报, 2015, 64:094702.
[16] KNUDSON M D, DESJARLAIS M P, BECKER A, et al. Direct observation of an abrupt insulator-to-metal transition in dense liquid deuterium[J]. Science, 2015, 348(6242):1455.
[17] MILITZER B, CEPERLEY D M. Path integral Monte Carlo calculation of the deuterium hugoniot[J]. Phys Rev Lett, 2000, 85:1890-1893.
[18] TUBMAN N M, LIBERATORE E, PIERLEONI C, et al. Molecular-atomic transition along the deutrium Hugoniot curve with coupled electron-ion Monte Carlo simulations[J]. Phys Rev Lett, 2015, 115:45301.
[19] FILINOV V S, FORTOV V E, BONITZ M. Fermionic path integral Monte Carlo results for the uniform electron gas at finite temperature[J]. arXiv:1407.3600v1[cond-mat.str-el], 2014.
[20] LI Q, LIU H F, ZHANG G M, et al. The thermodynamical instability induced by pressure ionization in fluid helium[J]. Phys Plasmas, 2016, 23:112709.
[21] WANG C, ZHANG P. Wide range equation of state for fluid hydrogen from density function theory[J]. Phys Plasmas, 2013, 20:092703.
[22] HU S X, MILITZER B, GONCHAROV V N. First-principles equation-of-state table of deuterium for inertial confinement fusion applications[J]. Phys Rev B, 2011, 84:224109.
[23] PIERLEONI C, CEPERLEY D M, HOLZMANN M. Coupled electron-ion Monte Carlo calculations of dense metallic hydrogen[J]. Phys Rev Lett, 2004, 93(14):146402.
[24] MORALES M A, PIERLEONI C, CEPERLEY D M. Equation of state of metallic hydrogen from coupled electron-ion Monte Carlo simulations[J]. Phys Rev E, 2010, 81:021202.
[25] KNUDSON M D,DESJARLAIS M P. High-precision shock wave measurements of deuterium:Evaluation of exchange-correlation functionals at the molecular-to-atomic transition[J]. Phys Rev Lett, 2017, 118:035501.
[26] KERLEY G I. A theoretical equation of state for deuterium[R]. Technical Report No. LA-4776, Los Alamos Scientific Laboratory, 1972.
[27] KERLEY G I. Equation of state for hydrogen and deuterium[R]. Technical Report No. SAND2003-3613, Sandia National Laboratories, 2003.
[28] BECKER A, LORENZEN W, FORTNEY J J, et al. Ab initio equations of state for hydrogen (H-REOS.3) and helium (He-REOS.3) and their implications for the interior of brown dwarfs[J]. The AstroPhy J Supp Ser, 2014, 215:21.
[29] LIU H F, SONG H F, ZHANG Q L, et al. Validation for equation of state in wide regime:Copper as prototype[J]. Matter and Radiation at Extremes, 2016, 1:123-131.
[30] FILINOV V S, FORTOV V E, BONITZ M. Pair distribution functions of dense partially ionized hydrogen[J]. Phys Lett A, 2000, 274:228-235.
[31] FILINOV V S, BONITZ M, EBELING W. Thermodynamics of hot dense H-plasmas:Path integral Monte Carlo simulations and analytical approximations[J]. Plasmas Phys Control Fusion, 2001, 43:743-759.

氢状态方程的路径积分蒙特卡罗研究

Path Integral Monte Carlo Calculations of Equation of State of Hydrogen

RichHTML

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics

作者中心

审稿中心

期刊浏览

期刊介绍

[1]	王晓慧, 张平. 高压下FCC相金属氢结构稳定性和非谐效应的理论研究[J]. 计算物理, 2022, 39(2): 159-164.
[2]	牛霄, 倪国喜, 马文铧. 自适应多分辨率方法在反应多相流数值模拟中的应用[J]. 计算物理, 2020, 37(6): 639-652.
[3]	张乐, 孙博, 宋海峰. 钚氧化物中氢行为的第一性原理研究[J]. 计算物理, 2020, 37(5): 595-602.
[4]	任娟, 张宁超, 刘萍萍. 碳气凝胶储氢性能的理论研究[J]. 计算物理, 2019, 36(6): 749-756.
[5]	王子昂, 余彬, 杭皓天, 张斌, 刘洪. 化学反应机理对激波与可燃氢气泡相互作用影响的数值研究[J]. 计算物理, 2018, 35(4): 388-396.
[6]	孟续军, 王瑞利. 含温有界原子理论体系下电子状态方程不确定度的量化计算[J]. 计算物理, 2018, 35(2): 138-150.
[7]	麻洪吉, 张国英, 方戈亮. 元素替代对MgH₂储氢材料释氢影响机理的第一原理研究[J]. 计算物理, 2017, 34(6): 705-712.
[8]	许亮, 冯成亮, 刘铁钢. 虚拟流体方法的设计原则[J]. 计算物理, 2016, 33(6): 671-680.
[9]	杭旭登, 李双贵, 杨容, 袁光伟. 分片光滑物态方程的能量方程非线性迭代解法[J]. 计算物理, 2015, 32(5): 505-513.
[10]	唐维军, 蒋浪, 程军波. 多组份流动质量分数保极值原理算法[J]. 计算物理, 2014, 31(3): 292-306.
[11]	王青, 党文强, 杜瑞, 戴剑锋, 李维学. 掺杂元素Fe对LiAlH₄放氢性能影响的第-性原理研究[J]. 计算物理, 2012, 29(2): 297-302.
[12]	梁仙红, 李征, 何长江, 刘超. 多介质流体力学两步欧拉方法的模型封闭性方法[J]. 计算物理, 2010, 27(5): 658-664.
[13]	胡维军, 杨华, 孟现美, 孙平. NH₃(H₂O)₄稳定结构的理论研究[J]. 计算物理, 2010, 27(5): 765-770.
[14]	程锦荣, 方兴, 袁兴红, 王晓, 汪志. 锂掺杂单壁氮化硼纳米管阵列储氢的理论研究[J]. 计算物理, 2010, 27(3): 428-432.
[15]	惠萍. 用B-splines技术计算超强平行外磁场中氢分子离子的能级[J]. 计算物理, 2010, 27(3): 451-456.