自动校准的多相状态方程建模方法及其在锡中的应用

孙毅 向士凯 耿华运 甘元超 吴凤超 王玉锋 陈涵 李俊 高俊杰 杨靖 戴诚达

孙毅, 向士凯, 耿华运, 甘元超, 吴凤超, 王玉锋, 陈涵, 李俊, 高俊杰, 杨靖, 戴诚达. 自动校准的多相状态方程建模方法及其在锡中的应用[J]. 高压物理学报, 2023, 37(2): 021301. doi: 10.11858/gywlxb.20220709
引用本文: 孙毅, 向士凯, 耿华运, 甘元超, 吴凤超, 王玉锋, 陈涵, 李俊, 高俊杰, 杨靖, 戴诚达. 自动校准的多相状态方程建模方法及其在锡中的应用[J]. 高压物理学报, 2023, 37(2): 021301. doi: 10.11858/gywlxb.20220709
SUN Yi, XIANG Shikai, GENG Huayun, GAN Yuanchao, WU Fengchao, WANG Yufeng, CHEN Han, LI Jun, GAO Junjie, YANG Jing, DAI Chengda. Automated Calibrated Modeling Method of Multiphase Equations of States: Applied to Tin[J]. Chinese Journal of High Pressure Physics, 2023, 37(2): 021301. doi: 10.11858/gywlxb.20220709
Citation: SUN Yi, XIANG Shikai, GENG Huayun, GAN Yuanchao, WU Fengchao, WANG Yufeng, CHEN Han, LI Jun, GAO Junjie, YANG Jing, DAI Chengda. Automated Calibrated Modeling Method of Multiphase Equations of States: Applied to Tin[J]. Chinese Journal of High Pressure Physics, 2023, 37(2): 021301. doi: 10.11858/gywlxb.20220709

自动校准的多相状态方程建模方法及其在锡中的应用

doi: 10.11858/gywlxb.20220709
基金项目: 国家重点研发计划(2021YFB3802300);国家自然科学基金(11902308);中国工程物理研究院创新发展基金(CX2019002)
详细信息
    作者简介:

    孙 毅(1982–),男,助理研究员,主要从事材料物性理论建模与计算模拟研究.E-mail:ssunyyi00@163.com

  • 中图分类号: O521.2

Automated Calibrated Modeling Method of Multiphase Equations of States: Applied to Tin

  • 摘要: 状态方程与描述能量、动量、质量守恒的偏微分方程一起,构成了可求解材料动态压缩行为的完备流体力学方程组。动态压缩下,相变会导致材料内能、密度、强度等物理性质的不连续变化,需要构建多相状态方程模型才能精确描述这些变化。通过多相状态方程模型的自动组装,采用计算机智能优化算法自动校准状态方程模型参数,发展了自动化的多相状态方程建模程序AEOS(automated equation of state)。利用AEOS,构建了锡的3套状态方程模型,3套模型的计算结果与相关实验结果基本一致,验证了AEOS程序的适用性。将构建的状态方程模型应用于一维流体力学模拟,发现锡冲击到17 GPa再等熵卸载到常压的压力-温度路径会经过β相-体心四方相-液相三相点,并且可以很好地解释在15.4 GPa的冲击压力下锡的微喷颗粒呈现固-液混合态的实验现象。AEOS的良好表现证明其在大型数字化科研平台以及高通量材料物性计算中将具有广泛的应用前景。

     

  • 图  AEOS建模程序的基本功能组成和建模流程示意图

    Figure  1.  Basic functional components of the AEOS program and a schematic diagram of the modeling process

    图  压力-温度相图中的压力-温度网格以及纯相区、相边界、三相点的指标化方法示意图

    Figure  2.  Pressure-temperature meshes in the p-T phase diagram and the schematic diagram of the digital representation method of the pure phase regions, the phase boundaries and the three-phase points

    图  由AEOS模型1计算的锡的高压物性理论结果与实验结果对比

    Figure  3.  Comparison of the high-pressure compression properties of tin between the experimental results and the theoretical results calculated by AEOS model 1

    图  AEOS模型2和模型3计算的锡的冲击雨贡纽p-V0/V关系及其与实验结果[21]的比较

    Figure  4.  p-V0/V Hugoniot relationship of tin calculated by AEOS models 2 and 3 compared with the experimental results[21]

    图  AEOS构建的锡的3个状态方程模型的计算结果及其与其他文献结果[25-29]的比较

    Figure  5.  The theoretical results of the three AEOS models for tin and their comparisons with the results of other literatures[25-29]

    表  1  锡的固-液两相状态方程模型1的校准参数

    Table  1.   Calibrated parameters of the solid-liquid two-phase EOS model 1 for tin

    V0/(cm3·g−1)C/(km·s−1)SγaNe
    0.13412.6121.4821.4704.0
    ΔSTm0/Kγ0mam
    1.16R836.92.200.035
    下载: 导出CSV

    表  2  锡的多相状态方程模型2的校准参数

    Table  2.   Calibrated parameters of the multiphase EOS model 2 for tin

    PhaseE0/(J·g−1)V0/(cm3·g−1)B0/GPaa1γaΔS
    β00.136956.751.391.850.780
    bct36.30.132959.780.702.663.571.23R
    Liquid−16.60.142545.061.891.561.753.22R
    下载: 导出CSV

    表  3  锡的多相状态方程模型3的校准参数

    Table  3.   Calibrated parameters of the multiphase EOS model 3 for tin

    PhaseE0/(J·g−1)V0/(cm3·g−1)B0/GPaa1γacV0/(J·g−1·K−1)ΔS
    β00.136956.70.751.541.640.2330
    bct32.50.133854.81.142.423.480.2541.18R
    Liquid−14.70.141348.01.751.531.740.3023.43R
    下载: 导出CSV
  • [1] OERTEL M, HEMPEL M, KLÄHN T, et al. Equations of state for supernovae and compact stars [J]. Reviews of Modern Physics, 2017, 89(1): 015007. doi: 10.1103/RevModPhys.89.015007
    [2] 龚自正, 谢鸿森, FEI Y W. 我国动高压物理应用于地球科学的研究进展 [J]. 高压物理学报, 2013, 27(2): 168–187. doi: 10.11858/gywlxb.2013.02.003

    GONG Z Z, XIE H S, FEI Y W. Reviews of recent advances of shock wave physics applied to earth science in China [J]. Chinese Journal of High Pressure Physics, 2013, 27(2): 168–187. doi: 10.11858/gywlxb.2013.02.003
    [3] GRIGORIEV B, ALEXANDROV I, GERASIMOV A. Application of multiparameter fundamental equations of state to predict the thermodynamic properties and phase equilibria of technological oil fractions [J]. Fuel, 2018, 215: 80–89. doi: 10.1016/j.fuel.2017.11.022
    [4] 王利生. 状态方程及其应用于石油与天然气相平衡计算的有关进展 [J]. 石油与天然气化工, 1996, 25(3): 137–142.

    WANG L S. The development concerning equations of state and their applications in phase equilibrium calculation for oil and natural gas [J]. Chemical Engineering of Oil and Gas, 1996, 25(3): 137–142.
    [5] 段振豪. 地质流体状态方程 [J]. 中国科学: 地球科学, 2010, 40(4): 393–413.
    [6] YOUNG D A. Phase diagrams of the elements [M]. Berkeley, USA: University of California Press, 1991.
    [7] DUVALL G E, GRAHAM R A. Phase transitions under shock-wave loading [J]. Reviews of Modern Physics, 1977, 49(3): 523–579. doi: 10.1103/RevModPhys.49.523
    [8] JOHNSON J N, HAYES D B, ASAY J R. Equations of state and shock-induced transformations in solid Ⅰ–solid Ⅱ–liquid bismuth [J]. Journal of Physics and Chemistry of Solids, 1974, 35(4): 501–515. doi: 10.1016/S0022-3697(74)80004-1
    [9] ZHU Q, ZHANG F, HUANG Y, et al. An all-round AI-chemist with a scientific mind [J]. National Science Review, 2022, 9(10): nwac190. doi: 10.1093/nsr/nwac190
    [10] DOROGOKUPETS P I, DYMSHITS A M, LITASOV K D, et al. Thermodynamics and equations of state of iron to 350 GPa and 6000 K [J]. Scientific Reports, 2017, 7: 41863. doi: 10.1038/srep41863
    [11] 孙毅, 耿华运, 吴强, 等. AEOS建模程序-V1.0: 2022SR0346940 [P]. 2022−03−15.
    [12] 向士凯, 孙毅, 耿华运, 等. ICON高维参数全局智能优化软件: 2022SR0441868 [P]. 2022−04−07.
    [13] CHISOLM E D. Evaluating thermodynamic quantities in mixed-phase regions of a single-component material: LA-UR-17-30700 [R]. Los Alamos: Los Alamos National Laboratories, 2017.
    [14] COX G A, CHRISTIE M A. Fitting of a multiphase equation of state with swarm intelligence [J]. Journal of Physics: Condensed Matter, 2015, 27(40): 405201. doi: 10.1088/0953-8984/27/40/405201
    [15] COX G. Generating a multiphase equation of state with swarm intelligence [J]. AIP Conference Proceedings, 2018, 1979(1): 040002. doi: 10.1063/1.5044780
    [16] VELIZHANIN K A, COE J D. Automated fitting of a semi-empirical multiphase equation of state for carbon [J]. AIP Conference Proceedings, 2020, 2272(1): 070051. doi: 10.1063/12.0000798
    [17] 谭华. 金属的冲击波温度测量(Ⅱ)——界面卸载近似 [J]. 高压物理学报, 1996, 10(3): 161–169. doi: 10.11858/gywlxb.1996.03.001

    TAN H. Shock temperature measurements for metals-release approximation at the interface [J]. Chinese Journal of High Pressure Physics, 1996, 10(3): 161–169. doi: 10.11858/gywlxb.1996.03.001
    [18] 莫建军, 孙承纬. 金属铝和铜等熵压缩线计算: GF-A0114670G [R]. 绵阳: 中国工程物理研究院流体物理研究所, 2007.
    [19] ROYCE E B. GRAY, a three-phase equation of state for metals: UCRL-51121 [R]. Livermore, USA: California University, 1971.
    [20] SALAMAT A, BRIGGS R, BOUVIER P, et al. High-pressure structural transformations of Sn up to 138 GPa: angle-dispersive synchrotron X-ray diffraction study [J]. Physical Review B, 2013, 88(10): 104104. doi: 10.1103/PhysRevB.88.104104
    [21] MARSH S P. LASL shock Hugoniot data [M]. Berkeley, USA: University of California Press, 1980.
    [22] HU J B, ZHOU X M, TAN H, et al. Successive phase transitions of tin under shock compression [J]. Applied Physics Letters, 2008, 92(11): 111905. doi: 10.1063/1.2898891
    [23] 李俊. 冲击测温研究2018年度总结 [R]. 绵阳: 中国工程物理研究院流体物理研究所, 2018.
    [24] COX G A. A multi-phase equation of state and strength model for tin [J]. AIP Conference Proceedings, 2006, 845(1): 208–211. doi: 10.1063/1.2263300
    [25] GREEFF C, CHISOLM E, GEORGE D, et al. SESAME 2161: an explicit multiphase equation of state for tin: LA-UR-05−9414 [R]. Los Alamos, USA: Los Alamos National Laboratories, 2005.
    [26] BRIGGS R, DAISENBERGER D, LORD O T, et al. High-pressure melting behavior of tin up to 105 GPa [J]. Physical Review B, 2017, 95(5): 054102. doi: 10.1103/PhysRevB.95.054102
    [27] REHN D A, GREEFF C W, BURAKOVSKY L, et al. Multiphase tin equation of state using density functional theory [J]. Physical Review B, 2021, 103(18): 184102. doi: 10.1103/PhysRevB.103.184102
    [28] KINGON A I, CLARK J B. A redetermination of the melting curve of tin to 3.7 GPa [J]. High Temperatures-High Pressures, 1980, 12: 75.
    [29] XU L, BI Y, LI X H, et al. Phase diagram of tin determined by sound velocity measurements on multi-anvil apparatus up to 5 GPa and 800 K [J]. Journal of Applied Physics, 2014, 115(16): 164903. doi: 10.1063/1.4872458
    [30] 杨靖. 国家自然科学基金青年基金项目(11902308)结题报告 [R]. 绵阳: 中国工程物理研究院流体物理研究所, 2023.
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出版历程
  • 收稿日期:  2022-12-20
  • 修回日期:  2023-02-25
  • 网络出版日期:  2023-04-13
  • 刊出日期:  2023-04-05

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