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高温高压下立方氮化硼和六方氮化硼的结构、力学、热力学、电学以及光学性质的第一性原理研究

吕常伟 王臣菊 顾建兵

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高温高压下立方氮化硼和六方氮化硼的结构、力学、热力学、电学以及光学性质的第一性原理研究

吕常伟, 王臣菊, 顾建兵

First-principles study of structural, elastic, thermodynamic, electronic and optical properties of cubic boron nitride and hexagonal boron nitride at high temperature and high pressure

Lü Chang-Wei, Wang Chen-Ju, Gu Jian-Bing
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  • 本文采用基于密度泛函理论的第一性原理平面波赝势和局域密度近似方法, 优化了立方和六方氮化硼的几何结构, 系统地研究了零温高压下立方和六方氮化硼的几何结构、力学、电学以及光学性质. 结构与力学性质研究表明: 立方氮化硼的结构更加稳定, 两种结构的氮化硼均表现出一定的脆性, 而六方氮化硼的热稳定性则相对较差; 电学性质研究表明: 立方氮化硼和六方氮化硼均为间接带隙半导体, 且立方氮化硼比六方氮化硼局域性更强; 光学性质结果显示: 立方氮化硼和六方氮化硼对入射光的通过性都很好, 在高能区立方氮化硼对入射光的表现更加敏感. 此外, 还研究了高温高压下立方氮化硼的热力学性质, 并得到其热膨胀系数、热容、德拜温度和格林艾森系数随温度和压力的变化关系. 本文的理论研究阐述了高压下立方氮化硼和六方氮化硼的相关性质, 为今后的实验研究提供了比较可靠的理论依据.
    On the basis of the density functional theory of the first-principles, we employ the plane wave pseudopotential method and local density approximation to optimize the geometrical structure of cubic boron nitride and hexagonal boron nitride; then we study their mechanical properties, electronic structures and optical properties at zero temperature and zero pressure, and the thermodynamic properties at different temperatures and different pressures. By means of geometry optimization, we systematically investigate the elastic constant, bulk modulus, shear modulus, hardness and phonon spectrum for each of cubic boron nitride and hexagonal boron nitride. The results show that both cubic boron nitride and hexagonal boron nitride are structurally stable and brittle materials. Besides, cubic boron nitride is more stable than hexagonal boron nitride and it can be used as a superhard material. However, the thermal stability of hexagonal boron nitride is poor. The research results of electrical properties show that both cubic boron nitride and hexagonal boron nitride are indirect bandgap semiconductors, and the localization of cubic boron nitride is stronger than hexagonal boron nitride. The optical studies show that both cubic boron nitride and hexagonal boron nitride have good passivity to incident light. The c-BN is more sensitive to the incident light in high energy region. Last but not least, the thermodynamic properties of cubic boron nitride at high temperature and high pressure are also investigated. The relationships of thermodynamic expansivity, heat capacity, Debye temperature and Grüneisen parameter of c-BN with temperature and pressure are obtained. And the heat capacity of cubic boron nitride is found to be close to the Dulong-Petit limit at high temperatures. In this paper the relevant properties of cubic boron nitride and hexagonal boron nitride under high pressure are described theoretically, and a relatively reliable theoretical basis is provided for relevant experimental research.
      通信作者: 顾建兵, jianbinggu08@163.com
    • 基金项目: 国家自然科学基金(批准号: 11747062, 11747110)、河南省教育厅科技攻关项目(批准号: 172102210072)和河南省高等院校重点科研项目(批准号: 17A140014)资助的课题.
      Corresponding author: Gu Jian-Bing, jianbinggu08@163.com
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11747062, 11747110), the Science and Technology Research Project of the Education Department of Henan Province, China (Grant No. 172102210072), and the Key Research Project of Higher Education Institutions of Henan Province, China (Grant No. 17A140014).
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  • 图 1  0 GPa和0 K下c-BN和h-BN的总能量与晶胞体积关系

    Fig. 1.  Relationship between total energy and cell volume of c-BN and h-BN at 0 GPa and 0 K

    图 2  0 K时, 压力对c-BN和h-BN的弹性常数的影响

    Fig. 2.  Effect of pressure on the elastic constants of c-BN and h-BN at 0 K

    图 3  0K和0GPa时c-BN和h-BN的声子谱和声子色散

    Fig. 3.  Phonon spectrum and density of phonon states of c-BN and h-BN at 0 K and 0 GPa

    图 4  温度(a)和压力(b)对c-BN标准元胞体积V/V0的影响

    Fig. 4.  The normalized primitive cell volume V/V0 versus temperature (a) and pressure for the c-BN

    图 5  c-BN比热容CV与压力(a)和温度(b)之间的关系

    Fig. 5.  The heat capacity CV versus temperature and pressure for the c-BN

    图 6  c-BN的热力学膨胀系数α与压力(a)和温度(b)的关系

    Fig. 6.  The thermodynamic expansivity α versus pressure (a) and temperature (b) for the c-BN

    图 7  c-BN的徳拜温度ΘD与压力(a)和温度(b)的关系

    Fig. 7.  The Debye temperature ΘD versus pressure (a) and temperature (b) for the c-BN

    图 8  c-BN的格林艾森系数γ与压力(a)和温度(b)的关系

    Fig. 8.  The Grüneisen parameter γ versus pressure (a) temperature and (b) for the c-BN

    图 9  0 GPa和0 K下c-BN (a)和h-BN (b)的能带结构

    Fig. 9.  Band structures for c-BN (a) and h-BN (b) at 0 GPa and 0 K

    图 10  0 GPa和0 K下c-BN和h-BN的态密度

    Fig. 10.  Density of states for c-BN and h-BN at 0 GPa and 0 K

    图 11  0 K和0 GPa时c-BN和h-BN的复介电函数

    Fig. 11.  Complex dielectric functions of c-BN and h-BN at 0 K and 0 GPa

    图 12  0 K和0 GPa时c-BN和h-BN的吸收系数

    Fig. 12.  Absorption coefficients of c-BN and h-BN at 0 K and 0 GPa

    图 13  0 K和0 GPa时c-BN和h-BN的反射率

    Fig. 13.  Reflectivity of c-BN and h-BN at 0 K and 0 GPa

    图 14  0 K和0 GPa时c-BN和h-BN的折射率和消光系数

    Fig. 14.  Refractive index and extinction coefficient of c-BN and h-BN at 0 K and 0 GPa

    图 15  0 K和0 GPa时c-BN和h-BN的损失函数

    Fig. 15.  Loss function of c-BN and h-BN at 0 K and 0 GPa

    图 16  0 K和0 GPa时c-BN和h-BN的光电导率

    Fig. 16.  Conductivity of c-BN and h-BN at 0 K and 0 GPa

    表 1  c-BN和h-BN 晶胞晶格常数的计算值和实验值[6,3239]

    Table 1.  Calculated and experimental value of lattice constants for c-BN and h-BN cells[6,3239]

    结构晶格常数/Åac
    c-BN实验值3.615
    本文计算值3.576
    其他计算值3.583[6], 3.627[32], 3.589[33], 3.581[34], 3.576[35], 3.583[36]
    h-BN实验值2.504[37]6.661[37]
    本文计算值2.4856.610
    其他计算值2.485[32], 2.489[33], 2.489[36]2.496[38], 2.489[39]6.491[32], 6.561[33], 6.501[36], 6.490[38], 6.501[39]
    下载: 导出CSV

    表 2  0 K和0 GPa时, c-BN和h-BN的弹性常数Cij、德拜温度ΘD和平均声速Vm[35,36,4046]

    Table 2.  Elastic constants, Debye temperature and average sound velocity of c-BN and h-BN at 0 K and 0 GPa[35,36,4046]

    方法C11/GPaC12/GPaC13/GPaC33/GPaC44/GPaΘD/KVm/m·s–1BGEB/Gυ
    c-BN实验值820[40]190[40]480[40]389—407[40]
    本文计值824.43186.37479.761929.9411590.90399.06407.38911.850.980.12
    其他计算823[35]185[35]479[35]1765[35]10783[35]407[35]910[35]0.975[35]0.12[35]
    824[36]193[36]476[36]403[36]404[36]0.998[36]0.12[36]
    820[41]194[41]477[41]375.923[41]409[41]854.81[41]0.97[41]0.12[41]
    815[42]194[42]494[42]1790[42]381[42]398[42]0.957[42]
    820[43]194[43]477[43]
    h-BN实验值811[40]169[40]0[40]32[40]7[40]26—335
    811[44]169[44]0[44]27[44]8[44]
    本文计值925.98212.042.2629.835.95424.942928.86142.8898.85240.981.450.22
    其他计算927[36]223[36]1[36]32[36]7[36]145[36]100[36]1.45[36]0.22[36]
    930[42]218[42]1[42]29[42]7[42]158[42]104[42]1.519[42]
    141[45]98[45]239[45]1.44[45]0.22[45]
    923.48[46]212.23[46]2.56[46]28.08[46]4.06[46]
    下载: 导出CSV

    表 3  0 K时, 压力P对c-BN和h-BN的弹性常数Cij, B, G的影响

    Table 3.  Effect of pressure on the elastic constants of c-BN and h-BN at 0 K

    P/GPaC11/GPaC12/GPaC13/GPaC33/GPaC44/GPaB/GPaG/GPaυ
    c-BN0824.43186.374479.76399.06407.380.119
    5830.11185.83493.23400.59415.800.124
    10889.09226.27527.81447.21437.960.130
    15911.61241.91540.63465.15446.140.137
    20932.97257.00552.40482.33453.610.142
    25954.49272.25563.79499.66460.890.147
    30975.51287.24574.81516.66467.910.152
    35996.42302.42585.82533.75474.820.157
    401017.22596.23317.36550.65481.480.161
    451037.37332.13606.51567.21487.920.166
    501057.25346.87616.50583.66494.150.170
    h-BN0925.98212.042.2629.85.95142.8898.850.219
    51031.35249.815.3563.998.14176.61112.090.228
    101148.41283.4826.06132.7226.16231.48145.440.240
    151200.62306.0139.36160.8434.24256.67158.800.244
    201246.22327.5553.25187.0842.77280.31171.490.246
    251287.16348.4567.73211.7651.53302.83183.490.248
    301320.57372.6282.18236.3760.42324.77194.150.251
    351353.78393.2296.91259.9669.28345.92204.720.253
    401385.71412.37111.71283.3178.45366.65215.300.254
    451414.63431.89126.68306.3787.53386.99225.130.256
    501445.81447.45141.74328.4496.53406.75235.270.258
    下载: 导出CSV

    表 4  c-BN和h-BN的带隙宽度[33,5057]

    Table 4.  Bandgap of c-BN and h-BN[33,5057]

    c-BNh-BN
    Eg/eV实验本文计算其他计算实验本文计算其他计算
    5.38 [56]4.3914.11 [57]5.955 [58]4.0713.378—4.194 [59]
    4.81 [33]4.01 [33]
    4.24 [60]4.07 [62]
    4.67 [61] 4.95[63]
    下载: 导出CSV
  • [1]

    许斌, 时永鹏, 吕美哲, 郭全海 2016 人工晶体学报 45 2198Google Scholar

    Xu B, Shi Y P, Lv M Z, Guo Q H 2016 J. Synthetic Cryst. 45 2198Google Scholar

    [2]

    Pallas A, Larsson K 2014 Mol. Plant-Microbe Interact. 13 1034

    [3]

    Bello I, Chong Y M, Ye Q, Yang Y, He B, Kutsay O, Wang H E, Yan C, Jha S K, Zapien J A, Zhang W J 2012 Vacuum 86 575Google Scholar

    [4]

    Bello I, Chan C Y, Zhang W J, Chong Y M, Leung K M, Lee S T, Lifshitz Y 2005 Diamond Relat. Mater. 14 1154Google Scholar

    [5]

    殷红, 赵艳 2015 超硬材料工程 27 49Google Scholar

    Yin H, Zhao Y 2015 Superhard Mater. Eng. 27 49Google Scholar

    [6]

    Nose K, Yang H S, Yoshida T 2005 Diamond Relat. Mater. 14 1297Google Scholar

    [7]

    Ying J, Zhang X W, Yin Z G, Tan H R, Zhang S G, Fan Y M 2011 J. Appl. Phys. 109 312

    [8]

    Tian Y J, Xu B, Yu D L, Ma Y M, Wang Y B, Jiang Y B, Hu W T, Tang C C, Gao Y F, Luo K, Zhao Z S, Wang L M, Wen B, He J L, Liu Z Y 2013 Nature 493 385Google Scholar

    [9]

    Gong H R, Wang Q, Chen L, Xiong L 2017 J. Phys. Chem. Solids 104 276Google Scholar

    [10]

    Era K, Mishima O, Wada Y, Tanaka J, Yamaoka S 1988 Appl. Phys. Lett. 53 962Google Scholar

    [11]

    Duan X M, Yang Z H, Chen L, Tian Z, Cai D L,Wang Y J, Jia D C, Zhou Y 2016 J. Eur. Ceram. Soc. 36 3725Google Scholar

    [12]

    高世涛, 李斌, 李端, 张长瑞, 刘荣军, 王思青 2018 硅酸盐通报 37 1929

    Gao S T, Li B, Li D, Zhang C R, Liu R J, Wang S Q 2018 Bull. Chin. Ceramic Soc. 37 1929

    [13]

    Ouyang T, Chen Y P, Xie Y E, Yang K K, Bao Z G, Zhong J X 2010 Nanotechnology 21 245701Google Scholar

    [14]

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出版历程
  • 收稿日期:  2018-11-15
  • 修回日期:  2019-01-21
  • 上网日期:  2019-03-23
  • 刊出日期:  2019-04-05

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