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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.
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Keywords:
- boron nitride /
- electronic properties /
- elastic property /
- optical properties
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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 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
表 1 c-BN和h-BN 晶胞晶格常数的计算值和实验值[6,32−39]
Table 1. Calculated and experimental value of lattice constants for c-BN and h-BN cells[6,32−39]
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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[35,36,40−46]
Table 2. Elastic constants, Debye temperature and average sound velocity of c-BN and h-BN at 0 K and 0 GPa[35,36,40−46]
方法 C11/GPa C12/GPa C13/GPa C33/GPa C44/GPa ΘD/K Vm/m·s–1 B G E B/G υ c-BN 实验值 820[40] 190[40] 480[40] 389—407[40] 本文计值 824.43 186.37 479.76 1929.94 11590.90 399.06 407.38 911.85 0.98 0.12 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 925.98 212.04 2.26 29.83 5.95 424.94 2928.86 142.88 98.85 240.98 1.45 0.22 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]
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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/GPa C11/GPa C12/GPa C13/GPa C33/GPa C44/GPa B/GPa G/GPa υ c-BN 0 824.43 186.374 479.76 399.06 407.38 0.119 5 830.11 185.83 493.23 400.59 415.80 0.124 10 889.09 226.27 527.81 447.21 437.96 0.130 15 911.61 241.91 540.63 465.15 446.14 0.137 20 932.97 257.00 552.40 482.33 453.61 0.142 25 954.49 272.25 563.79 499.66 460.89 0.147 30 975.51 287.24 574.81 516.66 467.91 0.152 35 996.42 302.42 585.82 533.75 474.82 0.157 40 1017.22 596.23 317.36 550.65 481.48 0.161 45 1037.37 332.13 606.51 567.21 487.92 0.166 50 1057.25 346.87 616.50 583.66 494.15 0.170 h-BN 0 925.98 212.04 2.26 29.8 5.95 142.88 98.85 0.219 5 1031.35 249.81 5.35 63.99 8.14 176.61 112.09 0.228 10 1148.41 283.48 26.06 132.72 26.16 231.48 145.44 0.240 15 1200.62 306.01 39.36 160.84 34.24 256.67 158.80 0.244 20 1246.22 327.55 53.25 187.08 42.77 280.31 171.49 0.246 25 1287.16 348.45 67.73 211.76 51.53 302.83 183.49 0.248 30 1320.57 372.62 82.18 236.37 60.42 324.77 194.15 0.251 35 1353.78 393.22 96.91 259.96 69.28 345.92 204.72 0.253 40 1385.71 412.37 111.71 283.31 78.45 366.65 215.30 0.254 45 1414.63 431.89 126.68 306.37 87.53 386.99 225.13 0.256 50 1445.81 447.45 141.74 328.44 96.53 406.75 235.27 0.258
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[1] 许斌, 时永鹏, 吕美哲, 郭全海 2016 人工晶体学报 45 2198
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Google Scholar
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Google Scholar
[18] Weng Q H, Wang X B, Wang X, Bando Y, Golberg D 2016 Chem. Soc. Rev. 45 3989
Google Scholar
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Google Scholar
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Google Scholar
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