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大规模、量子精度的分子动力学模拟: 以极端条件液态铁为例

曾启昱 陈博 康冬冬 戴佳钰

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大规模、量子精度的分子动力学模拟: 以极端条件液态铁为例

曾启昱, 陈博, 康冬冬, 戴佳钰

Large scale and quantum accurate molecular dynamics simulation: Liquid iron under extreme condition

Zeng Qi-Yu, Chen Bo, Kang Dong-Dong, Dai Jia-Yu
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  • 液态铁作为类地行星内核的主要组成成分, 其在高温高压条件下的热力学、输运及动力学性质研究, 对理解行星演化有着重要意义. 极端条件物态物性在实验条件下产生困难且诊断手段有限, 而理论模拟在动力学、输运性质计算方面面临着规模、精度的双重要求, 极大限制了这方面的有效进展. 本文结合深度学习技术, 通过神经网络构造液态铁的高维相互作用势能面, 在保证第一性原理计算精度的前提下, 将计算规模从数百原子扩展到数十万原子体系. 研究了从常压到核幔边界条件下液态铁的动力学及输运性质, 并与X射线衍射、非弹性X射线散射实验对比, 二者的一致性指出, 深度学习技术与分子模拟的结合为我们高通量研究极端条件下真实体系的物态物性及动力学提供了有效手段.
    Liquid iron is the major component of planetary cores. Its structure and dynamics under high pressure and temperature is of great significance in studying geophysics and planetary science. However, for experimental techniques, it is still difficult to generate and probe such a state of matter under extreme conditions, while for theoretical method like molecular dynamics simulation, the reliable estimation of dynamic properties requires both large simulation size and ab initio accuracy, resulting in unaffordable computational costs for traditional method. Owing to the technical limitation, the understanding of such matters remains limited. In this work, combining molecular dynamics simulation, we establish a neural network potential energy surface model to study the static and dynamic properties of liquid iron at its extreme thermodynamic state close to core-mantle boundary. The implementation of deep neural network extends the simulation scales from one hundred atoms to millions of atoms within quantum accuracy. The estimated static and dynamic structure factor show good consistency with all available X-ray diffraction and inelastic X-ray scattering experimental observations, while the empirical potential based on embedding-atom-method fails to give a unified description of liquid iron across a wide range of thermodynamic conditions. We also demonstrate that the transport property like diffusion coefficient exhibits a strong size effect, which requires more than at least ten thousands of atoms to give a converged value. Our results show that the combination of deep learning technology and molecular modelling provides a way to describe matter realistically under extreme conditions.
      通信作者: 康冬冬, ddkang@nudt.edu.cn ; 戴佳钰, jydai@nudt.edu.cn
    • 基金项目: NSAF联合基金(批准号: U1830206)、国家自然科学基金(批准号: 11874424, 12104507)和湖南省科技创新领军人才项目(批准号: 2021RC4026)资助的课题.
      Corresponding author: Kang Dong-Dong, ddkang@nudt.edu.cn ; Dai Jia-Yu, jydai@nudt.edu.cn
    • Funds: Project supported by the NSAF Joint Fund (Grant No. U1830206), the National Natural Science Foundation of China (Grant Nos. 11874424, 12104507), and the Science and Technology Innovation Program of Hunan Province, China (Grant No. 2021RC4026).
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    Vočadlo L 2015 Treatise on Geophysics 2.06—Earth’s Core: Iron and Iron Alloys (Amsterdam: Elsevier) pp117–147

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    Dziewonski A M, Anderson D L 1981 Phys. Earth Planet. Inter. 25 297Google Scholar

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    Wagner F W, Sohl F, Hussmann H, Grott M, Rauer H 2011 Icarus 214 366Google Scholar

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    Dai J, Kang D, Zhao Z, Wu Y, Yuan J 2012 Phys. Rev. Lett. 109 175701Google Scholar

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    Dai J, Hou Y, Kang D, Sun H, Wu J, Yuan J 2013 New J. Phys. 15 045003Google Scholar

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    Li Q, Sun T, Zhang Y G, Xian J W, Vocadlo L 2021 J. Chem. Phys. 155 194505Google Scholar

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    González L E, González D J 2023 J. Geophys. Res. Solid Earth 128 e2022JB025119Google Scholar

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    Ramakrishna K, Lokamani M, Baczewski A, Vorberger J, Cangi A 2023 Phys. Rev. B 107 115131Google Scholar

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    Kang D, Zeng Q, Zhang S, Wang X, Dai J 2020 High Power Laser Part. Beams 32 092006Google Scholar

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    Behler J, Parrinello M 2007 Phys. Rev. Lett. 98 146401Google Scholar

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    Bartok A P, Payne M C, Kondor R, Csanyi G 2010 Phys. Rev. Lett. 104 136403Google Scholar

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    Thompson A P, Swiler L P, Trott C R, Foiles S M, Tucker G J 2015 J. Comput. Phys. 285 316Google Scholar

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    Zhang L, Han J, Wang H, Car R, E W 2018 Phys. Rev. Lett. 120 143001Google Scholar

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    Zhang L 2018 arXiv: 180509003 [physics.comp-ph

    [15]

    Zhang Y, Gao C, Liu Q, Zhang L, Wang H, Chen M 2020 Phys. Plasmas 27 122704Google Scholar

    [16]

    Chen X, Gao X, Zhao Y, Lin D, Chu W, Song H 2020 Comput. Phys. Commun. 250 107057Google Scholar

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    Zeng Q, Yu X, Yao Y, Gao T, Chen B, Zhang S, Kang D, Wang H, Dai J 2021 Phys. Rev. Research 3 033116Google Scholar

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    Chen B, Zeng Q, Wang H, Zhang S, Kang D, Lu D, Dai J 2021 arXiv: 200613136 [cond-mat.mtrl-sci

    [19]

    Chen B, Zeng Q, Yu X, Chen J, Zhang S, Kang D, Dai J 2022 arXiv: 220801830 [astro-ph.EP

    [20]

    Yang F, Zeng Q, Chen B, Kang D, Zhang S, Wu J, Yu X, Dai J 2022 Chin. Phys. Lett. 39 116301Google Scholar

    [21]

    Zeng Q, Chen B, Zhang S, Kang D, Wang H, Yu X, Dai J 2023 arXiv: 230813863 [physics.comp-ph

    [22]

    Hosokawa S, Inui M, Matsuda K, Ishikawa D, Baron A Q R 2008 Phys. Rev. B 77 174203Google Scholar

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    Kuwayama Y, Morard G, Nakajima Y, Hirose K, Baron A Q R, Kawaguchi S I, Tsuchiya T, Ishikawa D, Hirao N, Ohishi Y 2020 Phys. Rev. Lett. 124 165701Google Scholar

    [24]

    Inui M, Maruyama K, Kajihara Y, Nakada M 2009 Phys. Rev. B 80 180201(RGoogle Scholar

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    Kresse G, Furthmüller J 1996 Phys. Rev. B 54 16Google Scholar

    [26]

    Morard G, Boccato S, Rosa A D, Anzellini S, Miozzi F, Henry L, Garbarino G, Mezouar M, Harmand M, Guyot F, Boulard E, Kantor I, Irifune T, Torchio R 2018 Geophys. Res. Lett. 45 2018GL079950Google Scholar

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    Perdew J, Burke J, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865Google Scholar

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    Holzwarth N, Tackett A, Matthews G 2001 Comput. Phys. Commun. 135 3Google Scholar

    [29]

    Marqués M, González L E, González D J 2015 Phys. Rev. B 92 134203Google Scholar

    [30]

    Marqués M, González L E, González D J 2016 J. Phys. Condens. Matter 28 075101Google Scholar

    [31]

    Wang H, Zhang L, Han J, E W 2018 Comput. Phys. Commun. 228 178Google Scholar

    [32]

    Zeng J, Zhang D, Lu D, Mo P, Li Z, Chen Y, Rynik M, Huang L, Li Z, Shi S, Wang Y, Ye H, Tuo P, Yang J, Ding Y, Li Y, Tisi D, Zeng Q, Bao H, Xia Y, Huang J, Muraoka K, Wang Y, Chang J, Yuan F, Bore S L, Cai C, Lin Y, Wang B, Xu J, Zhu J X, Luo C, Zhang Y, Goodall R E A, Liang W, Singh A K, Yao S, Zhang J, Wentzcovitch R, Han J, Liu J, Jia W, York D M, E W, Car R, Zhang L, Wang H 2023 J. Chem. Phys. 159 054801Google Scholar

    [33]

    Sun Y, Zhang F, Mendelev M I, Wentzcovitch R M, Ho K M 2022 Proc. Natl. Acad. Sci. U.S.A. 119 e2113059119Google Scholar

  • 图 1  液态铁的训练集采样示意图, 紫色空心圆圈表示在该(p, T)条件下采样的液态结构, 黑色实线为Morard等[26]确定的相边界

    Fig. 1.  Atomic configurations sampling in P-T space, where the black solid line denotes the experimental measured phase boundaries by Morard et al[26]

    图 2  液态铁的能量、受力与压强在训练集上的预测偏差 (a) $ \sigma_{E}=7.36\; {\rm meV/atom}$; (b) $ \sigma_{f} = 0.36\; {\rm eV/\AA}$; (c) $ \sigma_{p} = 0.41\; {\rm GPa}$

    Fig. 2.  DP-predicted energy per atom, force, and pressures versus the true KS-DFT calculations in the testing dataset: (a) $ \sigma_{E}= $$ 7.36\; {\rm meV/atom} $; (b) $ \sigma_{f}=0.36\; {\rm eV/\AA} $; (c) $ \sigma_{p}=0.41\; {\rm GPa} $

    图 3  液态铁的静态结构因子 (a) p = 0 GPa, T = 1873 K; (b) p = 21 GPa, T = 2600 K; (c) p = 40 GPa, T = 3000 K; (d) p = 53 GPa, T = 3300 K; (e) p = 74 GPa, T = 3600 K; (f) p = 106 GPa, T = 4250 K; 彩色点为DPMD计算结果, 灰色点为Inui等[24](常压)和Kuwayama等[23] (高温高压)的实验测量结果, 灰色虚线为基于EAM势的CMD计算结果

    Fig. 3.  Static structure factor of liquid iron: (a) p = 0 GPa, T = 1873 K; (b) p = 21 GPa, T = 2600 K; (c) p = 40 GPa, T = 3000 K; (d) p = 53 GPa, T = 3300 K; (e) p = 74 GPa, T = 3600 K; (f) p = 106 GPa, T = 4250 K. Colored circles indicate the results from DPMD simulation, the gray square denotes the experimental measurements by Inui et al.[24] and Kuwayaka et al.[23], the gray dashed line denotes the results from CMD simulation with EAM potential

    图 4  (a)常压和(b)核幔边界条件下液态铁的动态结构因子, 彩色实线为DPMD计算结果, 黑色圆圈为Hosokawa等[22]的非弹性X射线散射实验测量结果, 黑色虚线为基于Sun等[33]开发的EAM势计算的结果

    Fig. 4.  Dynamic structure factor of liquid iron under (a) ambient pressure condition and (b) core-mantle boundary condition. Colored lines indicate the results from DPMD simulation, the black circles denote the experimental measurements by Hosokawa et al.[22], the black dashed lines denote the CMD simulation with EAM potential developed by Sun et al[33]

    图 5  液态铁的扩散系数 (a) p = 0 GPa, T = 1873 K; (b) p = 96 GPa, T = 3800 K; 彩色点为DPMD计算结果, 实线为线性关系的拟合结果, 黑色三角为González等[7]的AIMD计算结果

    Fig. 5.  Self-dissufion coefficient of liquid iron: (a) p = 0 GPa, T = 1873 K; (b) p = 96 GPa, T = 3800 K. Colored circles denote the results from DPMD simulation, colored solid lines denote the fitting curve for removal of size effect, and the balck triangle denotes the previous AIMD calcualtion by González et al[7]

  • [1]

    Vočadlo L 2015 Treatise on Geophysics 2.06—Earth’s Core: Iron and Iron Alloys (Amsterdam: Elsevier) pp117–147

    [2]

    Dziewonski A M, Anderson D L 1981 Phys. Earth Planet. Inter. 25 297Google Scholar

    [3]

    Wagner F W, Sohl F, Hussmann H, Grott M, Rauer H 2011 Icarus 214 366Google Scholar

    [4]

    Dai J, Kang D, Zhao Z, Wu Y, Yuan J 2012 Phys. Rev. Lett. 109 175701Google Scholar

    [5]

    Dai J, Hou Y, Kang D, Sun H, Wu J, Yuan J 2013 New J. Phys. 15 045003Google Scholar

    [6]

    Li Q, Sun T, Zhang Y G, Xian J W, Vocadlo L 2021 J. Chem. Phys. 155 194505Google Scholar

    [7]

    González L E, González D J 2023 J. Geophys. Res. Solid Earth 128 e2022JB025119Google Scholar

    [8]

    Ramakrishna K, Lokamani M, Baczewski A, Vorberger J, Cangi A 2023 Phys. Rev. B 107 115131Google Scholar

    [9]

    Kang D, Zeng Q, Zhang S, Wang X, Dai J 2020 High Power Laser Part. Beams 32 092006Google Scholar

    [10]

    Behler J, Parrinello M 2007 Phys. Rev. Lett. 98 146401Google Scholar

    [11]

    Bartok A P, Payne M C, Kondor R, Csanyi G 2010 Phys. Rev. Lett. 104 136403Google Scholar

    [12]

    Thompson A P, Swiler L P, Trott C R, Foiles S M, Tucker G J 2015 J. Comput. Phys. 285 316Google Scholar

    [13]

    Zhang L, Han J, Wang H, Car R, E W 2018 Phys. Rev. Lett. 120 143001Google Scholar

    [14]

    Zhang L 2018 arXiv: 180509003 [physics.comp-ph

    [15]

    Zhang Y, Gao C, Liu Q, Zhang L, Wang H, Chen M 2020 Phys. Plasmas 27 122704Google Scholar

    [16]

    Chen X, Gao X, Zhao Y, Lin D, Chu W, Song H 2020 Comput. Phys. Commun. 250 107057Google Scholar

    [17]

    Zeng Q, Yu X, Yao Y, Gao T, Chen B, Zhang S, Kang D, Wang H, Dai J 2021 Phys. Rev. Research 3 033116Google Scholar

    [18]

    Chen B, Zeng Q, Wang H, Zhang S, Kang D, Lu D, Dai J 2021 arXiv: 200613136 [cond-mat.mtrl-sci

    [19]

    Chen B, Zeng Q, Yu X, Chen J, Zhang S, Kang D, Dai J 2022 arXiv: 220801830 [astro-ph.EP

    [20]

    Yang F, Zeng Q, Chen B, Kang D, Zhang S, Wu J, Yu X, Dai J 2022 Chin. Phys. Lett. 39 116301Google Scholar

    [21]

    Zeng Q, Chen B, Zhang S, Kang D, Wang H, Yu X, Dai J 2023 arXiv: 230813863 [physics.comp-ph

    [22]

    Hosokawa S, Inui M, Matsuda K, Ishikawa D, Baron A Q R 2008 Phys. Rev. B 77 174203Google Scholar

    [23]

    Kuwayama Y, Morard G, Nakajima Y, Hirose K, Baron A Q R, Kawaguchi S I, Tsuchiya T, Ishikawa D, Hirao N, Ohishi Y 2020 Phys. Rev. Lett. 124 165701Google Scholar

    [24]

    Inui M, Maruyama K, Kajihara Y, Nakada M 2009 Phys. Rev. B 80 180201(RGoogle Scholar

    [25]

    Kresse G, Furthmüller J 1996 Phys. Rev. B 54 16Google Scholar

    [26]

    Morard G, Boccato S, Rosa A D, Anzellini S, Miozzi F, Henry L, Garbarino G, Mezouar M, Harmand M, Guyot F, Boulard E, Kantor I, Irifune T, Torchio R 2018 Geophys. Res. Lett. 45 2018GL079950Google Scholar

    [27]

    Perdew J, Burke J, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865Google Scholar

    [28]

    Holzwarth N, Tackett A, Matthews G 2001 Comput. Phys. Commun. 135 3Google Scholar

    [29]

    Marqués M, González L E, González D J 2015 Phys. Rev. B 92 134203Google Scholar

    [30]

    Marqués M, González L E, González D J 2016 J. Phys. Condens. Matter 28 075101Google Scholar

    [31]

    Wang H, Zhang L, Han J, E W 2018 Comput. Phys. Commun. 228 178Google Scholar

    [32]

    Zeng J, Zhang D, Lu D, Mo P, Li Z, Chen Y, Rynik M, Huang L, Li Z, Shi S, Wang Y, Ye H, Tuo P, Yang J, Ding Y, Li Y, Tisi D, Zeng Q, Bao H, Xia Y, Huang J, Muraoka K, Wang Y, Chang J, Yuan F, Bore S L, Cai C, Lin Y, Wang B, Xu J, Zhu J X, Luo C, Zhang Y, Goodall R E A, Liang W, Singh A K, Yao S, Zhang J, Wentzcovitch R, Han J, Liu J, Jia W, York D M, E W, Car R, Zhang L, Wang H 2023 J. Chem. Phys. 159 054801Google Scholar

    [33]

    Sun Y, Zhang F, Mendelev M I, Wentzcovitch R M, Ho K M 2022 Proc. Natl. Acad. Sci. U.S.A. 119 e2113059119Google Scholar

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出版历程
  • 收稿日期:  2023-08-02
  • 修回日期:  2023-09-09
  • 上网日期:  2023-09-18
  • 刊出日期:  2023-09-20

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