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第一性原理研究Li2NH的晶格动力学和热力学性质

赵玉娜 丛红璐 成爽 于娜 高涛 马俊刚

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第一性原理研究Li2NH的晶格动力学和热力学性质

赵玉娜, 丛红璐, 成爽, 于娜, 高涛, 马俊刚

First-principles study of lattice dynamical and thermodynamic properties of Li2NH

Zhao Yu-Na, Cong Hong-Lu, Cheng Shuang, Yu Na, Gao Tao, Ma Jun-Gang
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  • 采用第一性原理的赝势平面波方法系统地研究了Li2NH的电子结构、晶格动力学和热力学性质. 计算得到的晶格常数与先前的理论和实验结果符合得很好. 运用线性响应理论计算了整个布里渊区高对称方向上的声子色散曲线和相应的声子态密度, 发现Li2NH(Pnma)声子色散曲线没有虚频, 动力学性能相对最稳定, 计算结果和先前实验及理论数据符合得很好. 最后, 利用得到的声子态密度进一步预测了Li2NH的热力学性质, 包括晶格振动对Helmholtz自由能、内能、熵和热容的贡献, 计算结果在一定程度上可为Li-N-H储氢体系的应用提供理论指导.
    One of the key issues for scale applications of hydrogen energy is the availability of safe, efficient and ecnomicical hydrogen storage technologies. In the past few years, light metal hydrides have attracted considerable attention due to their high hydrogen capacity. With a hydrogen capacity up to ~6.5 wt%, Li2NH is regarded as one of the most promising hydrogen storage materials. Although the hydrogen physical and thermodynamic properties of Li2NH have been studied, the electronic structure, phonon vibration mode and thermodynamic properties of Li2NH have not yet been resolved. In this paper, by using the first principles based on the density functional theory (DFT), we investigate the electronic structure, lattice dynamical and thermodynamic properties of Li2NH in detail.Firstly, the structure of Li2NH is optimized and the lattice parameters and total energy of the crystals are calculated. As shown by the calculation results, the lattice parameters are in good agreement with previous theoretical and experimental results. Our lowest-energy structure of Li2NH has orthorhombic Pnma symmetry at T=0 K for all of the proposed structures. Secondly, the electronic band-structure studies reveal that Li2NH has a small band gap of about 2.0 eV. The analysis of total and partial density of states of Li2NH show that the bonding between the N and H has a covalent character. Thirdly, the lattice dynamical properties of Li2NH are investgated at the corresponding equilibrium states. These results show that only the phonon dispersion curves of Li2NH (Pnma) without negative frequencies are calculated along the high-symmetry points. The optical modes of phonon frequencies at Γ point are assigned as Raman and Infrared-active modes. Based on the calculated phonon density of states, the thermodynamic properties are computed, such as the Helmholtz free energy, internal energy, entropy and the constant-volume specific heat versus temperature. The calculation results may explore the applications in areas of hydrogen storage for Li-N-H, which is of great importance forusing hydrogen in the future.
      通信作者: 马俊刚, jgma@bjtuhbxy.cn
    • 基金项目: 国家自然科学基金应急管理项目(理论物理专项)(批准号:11547224)和河北省高等教育教学改革研究与实践项目(批准号:2018GJJG649)资助的课题.
      Corresponding author: Ma Jun-Gang, jgma@bjtuhbxy.cn
    • Funds: Project supported by the Emergency Management Program of the National Natural Science Foundation of China(Special Funds for Theoretical Physics)(Grant No. 11547224) and the Research and Practice of the Higher Education reform in Hebei Province, China (Grant No. 2018GJJG649).
    [1]

    Chen P, Xiong Z, Luo J, Lin J, Tan K L 2002 Nature 420 302Google Scholar

    [2]

    Ohoyama K, Nakamori Y, Orimo S, Yamada K 2005 J. Phys. Soc. Jpn. 74 483Google Scholar

    [3]

    Noritake T, Nozaki H, Aoki M, Towata S, Kitahara G, Nakamori Y, Orimo S 2005 J. Alloys Compd. 393 264Google Scholar

    [4]

    Herbst J F, Hector Jr L G 2005 Phys. Rev. B 72 125120Google Scholar

    [5]

    Balogh M P, Jones C Y, Herbst J F, Hector Jr. L G, Kundrat M 2006 J. Alloys Compd. 420 326Google Scholar

    [6]

    Mueller T, Ceder G 2006 Phys. Rev. B 74 134104Google Scholar

    [7]

    Kojima Y, Kawai Y 2005 J. Alloys Compd. 395 236Google Scholar

    [8]

    Magyari-Köpe B, Ozoliņš V, Wolverton C 2006 Phys. Rev. B 73 220101(R)Google Scholar

    [9]

    Song Y, Guo Z X 2006 Phys. Rev. B 74 195120Google Scholar

    [10]

    Hector Jr L G, Herbst J F 2008 J. Phys. Condens. Matter 20 064229Google Scholar

    [11]

    Yang J, Lamsal J, Cai Q, Yelon W B, James W J 2008 MRS Proceedings 1098 1098 1098−HH03-06

    [12]

    Miceli G, Cucinotta C, Bernasconi M, Parrinello M 2010 J. Phys. Chem. C 114 15174Google Scholar

    [13]

    Miceli G, Ceriotti M, Angioletti-Uberti S, Bernasconi M, Parrinello M 2011 J. Phys. Chem. C 115 7076Google Scholar

    [14]

    Wolverton C, Siegel J D, Akbarazadeh R A, Ozolis V 2008 J. Phys. Condens. Matter 20 064228Google Scholar

    [15]

    陈玉红, 吕晓霞, 杜瑞, 董肖, 张材荣, 康龙, 罗永春 2013 稀有金属材料与工程 4 2

    Chen Y H, Lv X X, Du R, Dong X, Zhang C R, Kang L, Luo Y C 2013 Rare Metal Materials and Engineering 4 2

    [16]

    Rajeswarapalanichamy R, Santhosh M, Sudhapriyanga G, Kanagaprabha S, Iyakutti K 2015 Acta Metall. Sinica 28 550Google Scholar

    [17]

    Crivello J C, Gupta M, Černý R, Latroche M, Chandra D 2010 Phys. Rev. B 81 104113Google Scholar

    [18]

    Wang Q, ChenY G, Zheng X, Niu G, Wu C L, Tao M D T 2009 Physica B 404 3431Google Scholar

    [19]

    The ABINIT code is a common project of the Université Catholique de Louvain, and other contributors (URL http://www.abinit.org)

    [20]

    Troullier N, Martins J L 1991 Phys. Rev. B 43 1993Google Scholar

    [21]

    Monkhorst H J, Pack J D 1976 Phys. Rev. B 13 5188Google Scholar

    [22]

    Baroni S, Giannozzi P, Testa A 1987 Phys. Rev. Lett. 58 1861Google Scholar

    [23]

    Baroni S, de Gironcoli S, Dal Corso A, Giannozzi P 2001 Rev. Mod. Phys. 73 515Google Scholar

    [24]

    Lee C, Gonze X 1995 Phys. Rev. B 51 8610Google Scholar

    [25]

    Li W 2011 Ph. D. Dissertation (Zhejiang: Zhejiang University)

    [26]

    Aulbur W G, Jonsson L, Wilkins J W 2000 Solid States Phys. 54 1Google Scholar

    [27]

    Stampfl C, Van de Walle C G 1999 Phys. Rev. B 5 9

    [28]

    Gupta M, Gupta R P 2007 J. Alloys Compd. 319 446

    [29]

    Yao J H 2007 Ph. D. Dissertation (London: University of London) 0-239

    [30]

    陈玉红2008 博士学位论文(兰州: 兰州理工大学)

    Chen Y H 2008 Ph. D. Dissertation(Lanzhou: Lanzhou University of Technology)(in Chinese)

    [31]

    Born M, Huang K 1954 Dynamical Theory of Crystal Lattices (Oxford:Oxford University Press) p121

    [32]

    Maradudin A A, Montroll E W, Weiss C H, Ipatova I P 1971 Theory of Lattice Dynamics in the Harmonic Approximation (2nd Ed.) (New York: Academic Press)

  • 图 1  Li2NH的三种晶体结构图 (a) Li2NH ($F\bar 43m$); (b) Li2NH ($Fm\bar 3m$); (c) Li2NH ($Pnma$)

    Fig. 1.  Crystal structures of Li2NH: (a) Li2NH ($F\bar 43m$); (b) Li2NH ($Fm\bar 3m$); (c) Li2NH ($Pnma$).

    图 2  Li2NH的能带结构

    Fig. 2.  Band structure of Li2NH.

    图 3  Li2NH的总态密度和分波态密度

    Fig. 3.  Total and partial density of states of Li2NH(states/eV)

    图 4  Li2NH($Pnma$)的声子色散曲线

    Fig. 4.  The phonon dispersion curves of Li2NH ($Pnma$).

    图 5  Li2NH($F\bar 43m$)的声子色散曲线

    Fig. 5.  The phonon dispersion curves of Li2NH ($F\bar 43m$).

    图 6  Li2NH($Fm\bar 3m$)的声子色散曲线

    Fig. 6.  The phonon dispersion curves of Li2NH ($Fm\bar 3m$)

    图 7  Li2NH($Pnma$)的声子态密度

    Fig. 7.  The phonon density of states of Li2NH ($Pnma$).

    图 8  Li2NH的热力学性质 (a)晶格振动对自由能的贡献ΔF; (b)内能ΔE随温度的变化; (c)熵S随温度的变化; (d)热容Cv随温度的变化 (▼表示Debye的T3定律)

    Fig. 8.  Thermodynamic properties for Li2NH: (a) The phonon contribution to the free energies ΔF of Li2NH; (b)the internal energies ΔE verus temperature; (c)the entropy S verus temperature; (d) the constant-volume specific heats Cv verus temperature(▼ meansT3 law of Debye)

    表 1  Li2NH晶体结构参数

    Table 1.  Lattice parameters of Li2NH.

    Space groupLattice parameter Etot/eV
    PresentExperimentalOther CalculatedPresent
    $F\bar 43m$a = 5.6249a = 5.0769[2]a = 5.159[17],5.223[17],5.074[17],5.649[16],5.1076[18],5.2968[9]–1920.4448
    $Pnma$a = 7.781
    b = 3.623
    c = 4.902
    a = 7.733[8],7.704[16],7.742[17],7.753[17],7.775[17]
    b = 3.60[8],3.75[16],3.604[17],3.609[17],3.618[17]
    c = 4.872[8],5.074[16],4.883[17],4.890[17],4.881[17]
    –2702.3588
    $Fm\bar 3m$a = 5.0696a = 5.0742[3]a = 5.047[3],5.045[16]–1913.6655
    下载: 导出CSV

    表 2  Li2NH($Pnma$)在布里渊区中心Γ点的光学模声子频率(单位:cm–1)

    Table 2.  Phonon frequencies (unit:cm–1) at the Γ point of Li2NH.

    B2uB1uB3gB2gB3uAuB1gAg
    123.6137.9160161.5168198.5222223.5
    310195.8380232.0289243.0359287
    408318432300350.5446435335
    644450660350.5385625654380
    550412620542
    630580668598
    312264031233132
    3134
    下载: 导出CSV

    表 3  Li2NH的热力学函数

    Table 3.  Thermodynamic functions for Li2NH.

    Temprature/KS/J·(mol-c·K)–1CV/J·(mol-c·K)–1ΔH(HH298)/KJ·mol–1
    298248.9273.80
    300250.2274.92.9
    500405.4327.155.1
    700519.0347.075.0
    900607.7358.586.5
    1100680.5366.694.2
    1300742.3372.8100.8
    1500796.0377.5105.5
    下载: 导出CSV
  • [1]

    Chen P, Xiong Z, Luo J, Lin J, Tan K L 2002 Nature 420 302Google Scholar

    [2]

    Ohoyama K, Nakamori Y, Orimo S, Yamada K 2005 J. Phys. Soc. Jpn. 74 483Google Scholar

    [3]

    Noritake T, Nozaki H, Aoki M, Towata S, Kitahara G, Nakamori Y, Orimo S 2005 J. Alloys Compd. 393 264Google Scholar

    [4]

    Herbst J F, Hector Jr L G 2005 Phys. Rev. B 72 125120Google Scholar

    [5]

    Balogh M P, Jones C Y, Herbst J F, Hector Jr. L G, Kundrat M 2006 J. Alloys Compd. 420 326Google Scholar

    [6]

    Mueller T, Ceder G 2006 Phys. Rev. B 74 134104Google Scholar

    [7]

    Kojima Y, Kawai Y 2005 J. Alloys Compd. 395 236Google Scholar

    [8]

    Magyari-Köpe B, Ozoliņš V, Wolverton C 2006 Phys. Rev. B 73 220101(R)Google Scholar

    [9]

    Song Y, Guo Z X 2006 Phys. Rev. B 74 195120Google Scholar

    [10]

    Hector Jr L G, Herbst J F 2008 J. Phys. Condens. Matter 20 064229Google Scholar

    [11]

    Yang J, Lamsal J, Cai Q, Yelon W B, James W J 2008 MRS Proceedings 1098 1098 1098−HH03-06

    [12]

    Miceli G, Cucinotta C, Bernasconi M, Parrinello M 2010 J. Phys. Chem. C 114 15174Google Scholar

    [13]

    Miceli G, Ceriotti M, Angioletti-Uberti S, Bernasconi M, Parrinello M 2011 J. Phys. Chem. C 115 7076Google Scholar

    [14]

    Wolverton C, Siegel J D, Akbarazadeh R A, Ozolis V 2008 J. Phys. Condens. Matter 20 064228Google Scholar

    [15]

    陈玉红, 吕晓霞, 杜瑞, 董肖, 张材荣, 康龙, 罗永春 2013 稀有金属材料与工程 4 2

    Chen Y H, Lv X X, Du R, Dong X, Zhang C R, Kang L, Luo Y C 2013 Rare Metal Materials and Engineering 4 2

    [16]

    Rajeswarapalanichamy R, Santhosh M, Sudhapriyanga G, Kanagaprabha S, Iyakutti K 2015 Acta Metall. Sinica 28 550Google Scholar

    [17]

    Crivello J C, Gupta M, Černý R, Latroche M, Chandra D 2010 Phys. Rev. B 81 104113Google Scholar

    [18]

    Wang Q, ChenY G, Zheng X, Niu G, Wu C L, Tao M D T 2009 Physica B 404 3431Google Scholar

    [19]

    The ABINIT code is a common project of the Université Catholique de Louvain, and other contributors (URL http://www.abinit.org)

    [20]

    Troullier N, Martins J L 1991 Phys. Rev. B 43 1993Google Scholar

    [21]

    Monkhorst H J, Pack J D 1976 Phys. Rev. B 13 5188Google Scholar

    [22]

    Baroni S, Giannozzi P, Testa A 1987 Phys. Rev. Lett. 58 1861Google Scholar

    [23]

    Baroni S, de Gironcoli S, Dal Corso A, Giannozzi P 2001 Rev. Mod. Phys. 73 515Google Scholar

    [24]

    Lee C, Gonze X 1995 Phys. Rev. B 51 8610Google Scholar

    [25]

    Li W 2011 Ph. D. Dissertation (Zhejiang: Zhejiang University)

    [26]

    Aulbur W G, Jonsson L, Wilkins J W 2000 Solid States Phys. 54 1Google Scholar

    [27]

    Stampfl C, Van de Walle C G 1999 Phys. Rev. B 5 9

    [28]

    Gupta M, Gupta R P 2007 J. Alloys Compd. 319 446

    [29]

    Yao J H 2007 Ph. D. Dissertation (London: University of London) 0-239

    [30]

    陈玉红2008 博士学位论文(兰州: 兰州理工大学)

    Chen Y H 2008 Ph. D. Dissertation(Lanzhou: Lanzhou University of Technology)(in Chinese)

    [31]

    Born M, Huang K 1954 Dynamical Theory of Crystal Lattices (Oxford:Oxford University Press) p121

    [32]

    Maradudin A A, Montroll E W, Weiss C H, Ipatova I P 1971 Theory of Lattice Dynamics in the Harmonic Approximation (2nd Ed.) (New York: Academic Press)

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出版历程
  • 收稿日期:  2019-01-24
  • 修回日期:  2019-04-26
  • 上网日期:  2019-07-01
  • 刊出日期:  2019-07-05

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