高压下立方BC<sub>3</sub>的力学和热力学性质

摘要: 采用基于密度泛函理论的第一性原理赝势方法，系统地研究了立方BC₃在常压和高压下的晶格常数和力学性质，包括弹性常数、弹性模量和力学各向异性。利用准简谐近似下的德拜模型研究了高温高压条件下的热力学性质。研究结果表明：常压下立方BC₃具有较大的弹性模量和力学各向异性；高压下，立方BC₃的晶格常数、弹性常数和弹性模量显著增加。热力学性质的计算结果表明，立方BC₃具有较高的德拜温度，其摩尔定容热容和摩尔定压热容在高温高压条件下呈现明显的变化。立方BC₃的德拜温度随着压力的增大而增加，但随着温度的增大而明显减小。
- 第一性原理 /
- 立方BC₃ /
- 高压 /
- 力学性质 /
- 热力学性质
Abstract: The lattice constant and mechanical properties of cubic BC₃ under ambient and high pressure, including the elastic constants, the elastic modulus, and the mechanical anisotropy, were investigated using the first principle method in the framework of the density functional theory.The thermodynamic properties under high temperature and high pressure were calculated in terms of the quasi-harmonic Debye model.The results obtained show that the cubic BC₃ possesses a large elastic modulus and a high degree of anisotropy under ambient pressure.Under high pressure, the lattice constant, elastic constants, and elastic modulus of cubic BC₃ increase significantly.The results obtained from the thermodynamic calculations suggest that the cubic BC₃ has a large Debye temperature, and the molar heat capacity at constant volume and pressure exhibits obvious variation under high temperature and high pressure.Meanwhile, The Debye temperature of cubic BC₃ increases with the increase of pressure, but decreases with the increase of temperature.
- first principle /
- cubic BC₃ /
- high pressure /
- mechanical properties /
- thermodynamic properties

HTML全文

图 1 立方BC₃的晶体结构

Figure 1. Crystal structure of cubic BC₃

下载: 全尺寸图片幻灯片

图 2 立方BC₃归一化晶格常数a/a₀和密度ρ/ρ₀随压力的变化关系(a)以及能量-体积物态方程(b)

Figure 2. Pressure dependence of normalized lattice constants a/a₀ and density ρ/ρ₀ (a), and the equation of state for cubic BC₃ (b)

下载: 全尺寸图片幻灯片

图 3 立方BC₃弹性常数随压力的变化关系

Figure 3. Pressure dependence of elastic constants for cubic BC₃

下载: 全尺寸图片幻灯片

图 4 杨氏模量各向异性的三维图(a)和平面投影图(b)

Figure 4. Three-dimensional plot (a) and the corresponding projection (b) of anisotropy of Young's modulus

下载: 全尺寸图片幻灯片

图 5 立方BC₃的摩尔定容热容c_V、摩尔定压热容c_p和德拜温度随压力和温度的变化关系

Figure 5. Molar heat capacity c_V, c_p and Debye temperature vs. pressure and temperature for cubic BC₃

下载: 全尺寸图片幻灯片

表 1 不同压力下立方BC₃的体弹性模量、剪切模量和杨氏模量

Table 1. Bulk modulus, shear modulus, and Young's modulus for cubic BC₃ under pressure

Material	Pressure/GPa	B/GPa	G/GPa	Y/GPa
d-BC₃	0	34 5	318	730
	10	381	332	772
	20	416	343	807
	30	450	354	84 1
	4 0	483	363	870
	50	515	371	898
	60	54 7	379	923
	70	578	386	94 8
	80	610	393	971
	90	64 0	399	992
	100	671	4 05	1 012
c-BN^[28]	0	376	390
Diamond^[29-30]	0	432	517	1109

下载: 导出CSV

参考文献(33)

[1]	HAINES J, LÉGER J M, BOCQUILLON G.Synthesis and design of superhard materials[J]. Annual Review of Materials Research, 2001, 31(1):1-23. doi: 10.1146/annurev.matsci.31.1.1
[2]	TIAN Y, XU B, ZHAO Z.Microscopic theory of hardness and design of novel superhard crystals[J]. International Journal of Refractory Metals and Hard Materials, 2012, 33:93-106. doi: 10.1016/j.ijrmhm.2012.02.021
[3]	NOVIKOV N V.Synthesis of superhard materials[J]. Journal of Materials Processing Technology, 2005, 161(1):169-172. https://www.sciencedirect.com/science/article/pii/S0924013604009094
[4]	SOLOZHENKO V L, GREGORYANZ E.Synthesis of superhard materials[J]. Materials Today, 2005, 8(11):44-51. doi: 10.1016/S1369-7021(05)71159-7
[5]	NOVIKOV N V, DUB S N.Fracture toughness of diamond single crystals[J]. Journal of Hard Materials, 1991, 2(1):3-11. https://www.researchgate.net/publication/284697397_Fracture_toughness_of_diamond_single_crystals
[6]	SOLOZHENKO V L, DUB S N, NOVIKOV N V.Mechanical properties of cubic BC₂N, a new superhard phase[J]. Diamond and Related Materials, 2001, 10(12):2228-2231. doi: 10.1016/S0925-9635(01)00513-1
[7]	ZININ P V, MING L C, ISHⅡ H A, et al.Phase transition in BC_x system under high-pressure and high-temperature:synthesis of cubic dense BC₃ nanostructured phase[J]. Journal of Applied Physics, 2012, 111(11):114905. doi: 10.1063/1.4723275
[8]	SOLOZHENKO V L, KURAKEVYCH O O, ANDRAULT D, et al.Ultimate metastable solubility of boron in diamond:synthesis of superhard diamondlike BC₅[J]. Physical Review Letters, 2009, 102(1):015506. doi: 10.1103/PhysRevLett.102.015506
[9]	SOLOZHENKO V L, ANDRAULT D, FIQUET G, et al.Synthesis of superhard cubic BC₂N[J]. Applied Physics Letters, 2001, 78(10):1385-1387. doi: 10.1063/1.1337623
[10]	BADZIAN A R.Superhard material comparable in hardness to diamond[J]. Applied Physics Letters, 1988, 53(25):2495-2497. doi: 10.1063/1.100528
[11]	CHUNG H Y, WEINBERGER M B, LEVINE J B, et al.Synthesis of ultra-incompressible superhard rhenium diboride at ambient pressure[J]. Science, 2007, 316(5823):436-439. doi: 10.1126/science.1139322
[12]	GOU H, DUBROVINSKAIA N, BYKOVA E, et al.Discovery of a superhard iron tetraboride superconductor[J]. Physical Review Letters, 2013, 111(15):157002. doi: 10.1103/PhysRevLett.111.157002
[13]	CROWHURST J C, GONCHAROV A F, SADIGH B, et al.Synthesis and characterization of the nitrides of platinum and iridium[J]. Science, 2006, 311(5765):1275-1278. doi: 10.1126/science.1121813
[14]	KUMAR N R S, CHANDRA S, AMIRTHAPANDIAN S, et al.Investigations of the high pressure synthesized osmium carbide by experimental and computational techniques[J]. Materials Research Express, 2015, 2(1):016503. doi: 10.1088/2053-1591/2/1/016503
[15]	DOMNICH V, REYNAUD S, HABER R A, et al.Boron carbide:structure, properties, and stability under stress[J]. Journal of the American Ceramic Society, 2011, 94(11):3605-3628. doi: 10.1111/jace.2011.94.issue-11
[16]	GLASS C W, OGANOV A R, HANSEN N.Uspex-evolutionary crystal structure prediction[J]. Computer Physics Communications, 2006, 175(11):713-720.
[17]	LYAKHOV A O, OGANOV A R, STOKES H T, et al.New developments in evolutionary structure prediction algorithm uspex[J]. Computer Physics Communications, 2013, 184(4):1172-1182. doi: 10.1016/j.cpc.2012.12.009
[18]	WANG Y, LV J, ZHU L, et al.CALYPSO:a method for crystal structure prediction[J]. Computer Physics Communications, 2012, 183(10):2063-2070. doi: 10.1016/j.cpc.2012.05.008
[19]	ZHANG M, LIU H, LI Q, et al.Superhard BC₃ in cubic diamond structure[J]. Physical Review Letters, 2015, 114(1):015502. doi: 10.1103/PhysRevLett.114.015502
[20]	KRESSE G, FURTHMVLLER J.Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set[J]. Physical Review B, 1996, 54(16):11169-11186. doi: 10.1103/PhysRevB.54.11169
[21]	PERDEW J P, BURKE K, ERNZERHOF M.Generalized gradient approximation made simple[J]. Physical Review Letters, 1996, 77(18):3865-3868. doi: 10.1103/PhysRevLett.77.3865
[22]	KRESSE G, JOUBERT D.From ultrasoft pseudopotentials to the projector augmented-wave method[J]. Physical Review B, 1999, 59(3):1758-1775. doi: 10.1103/PhysRevB.59.1758
[23]	HILL R.The elastic behaviour of a crystalline aggregate[J]. Proceedings of the Physical Society Section A, 1952, 65(5):349-354. doi: 10.1088/0370-1298/65/5/307
[24]	OTERO-DE-LA-ROZA A, LUAÑA V.Gibbs 2:a new version of the quasi-harmonic model code.Ⅰ.robust treatment of the static data[J]. Computer Physics Communications, 2011, 182(8):1708-1720. doi: 10.1016/j.cpc.2011.04.016
[25]	BIRCH F.Finite elastic strain of cubic crystals[J]. Physical Review, 1947, 71(11):809-824. doi: 10.1103/PhysRev.71.809
[26]	MOUHAT F, COUDERT F X.Necessary and sufficient elastic stability conditions in various crystal systems[J]. Physical Review B, 2014, 90(22):224104. doi: 10.1103/PhysRevB.90.224104
[27]	WU Z, ZHAO E, XIANG H, et al.Crystal structures and elastic properties of superhard IrN₂ and IrN₃ from first principles[J]. Physical Review B, 2007, 76(5):054115. doi: 10.1103/PhysRevB.76.054115
[28]	ZHANG R F, VEPREK S, ARGON A S.Anisotropic ideal strengths and chemical bonding of wurtzite BN in comparison to zincblende BN[J]. Physical Review B, 2008, 77(17):998-1002.
[29]	WANG Y J, WANG C Y.Mechanical properties and electronic structure of superhard diamondlike BC₅:a first-principles study[J]. Journal of Applied Physics, 2009, 106(4):043513. doi: 10.1063/1.3195082
[30]	ZHANG R F, LIN Z J, VEPREK S.Anisotropic ideal strengths of superhard monoclinic and tetragonal carbon and their electronic origin[J]. Physical Review B, 2011, 83(15):4400-4408.
[31]	CAZZANI A, ROVATI M.Extrema of Young's modulus for cubic and transversely isotropic solids[J]. International Journal of Solids and Structures, 2003, 40(7):1713-1744. doi: 10.1016/S0020-7683(02)00668-6
[32]	KLEIN C A.Anisotropy of Young's modulus and Poisson's ratio in diamond[J]. Materials Research Bulletin, 1992, 27(12):1407-1414. doi: 10.1016/0025-5408(92)90005-K
[33]	ZHENG B, ZHANG M, LUO H G.Pressure effect on structural, elastic, and thermodynamic properties of tetragonal B₄C₄[J]. AIP Advances, 2015, 5(3):436-439. http://www.osti.gov/scitech/biblio/22454476