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

doi:10.7498/aps.68.20182030

Abstract

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.

Keywords:

Authors and contacts

1.
School of Materials and Chemical Engineering, Zhongyuan University of Tecnology, Zhengzhou 451191, China
2.
School of Computer Science and Technology, Henan Polytechnic University, Jiaozuo 454000, China

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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References

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Cited By

图 1 0 GPa和0 K下c-BN和h-BN的总能量与晶胞体积关系

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

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图 2 0 K时, 压力对c-BN和h-BN的弹性常数的影响

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

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图 3 0K和0GPa时c-BN和h-BN的声子谱和声子色散

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

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图 4 温度(a)和压力(b)对c-BN标准元胞体积V/V₀的影响

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

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图 5 c-BN比热容C_V与压力(a)和温度(b)之间的关系

Figure 5. The heat capacity C_V versus temperature and pressure for the c-BN

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图 6 c-BN的热力学膨胀系数α与压力(a)和温度(b)的关系

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

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图 7 c-BN的徳拜温度Θ_D与压力(a)和温度(b)的关系

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

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图 8 c-BN的格林艾森系数γ与压力(a)和温度(b)的关系

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

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图 9 0 GPa和0 K下c-BN (a)和h-BN (b)的能带结构

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

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图 10 0 GPa和0 K下c-BN和h-BN的态密度

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

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图 11 0 K和0 GPa时c-BN和h-BN的复介电函数

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

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图 12 0 K和0 GPa时c-BN和h-BN的吸收系数

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

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图 13 0 K和0 GPa时c-BN和h-BN的反射率

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

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图 14 0 K和0 GPa时c-BN和h-BN的折射率和消光系数

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

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图 15 0 K和0 GPa时c-BN和h-BN的损失函数

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

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图 16 0 K和0 GPa时c-BN和h-BN的光电导率

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

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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]

结构	晶格常数/Å	a	c
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	2.485	6.610
	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]

DownLoad: CSV

表 2 0 K和0 GPa时, c-BN和h-BN的弹性常数C_ij、德拜温度Θ_D和平均声速V_m^{[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	Θ_D/K	V_m/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C_ij, 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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表 4 c-BN和h-BN的带隙宽度^[33,50—57]

Table 4. Bandgap of c-BN and h-BN^[33,50—57]

	c-BN			h-BN
E_g/eV	实验	本文计算	其他计算	实验	本文计算	其他计算
E_g/eV	5.38^[56]	4.391	4.11^[57]	5.955^[58]	4.071	3.378—4.194^[59]
			4.81 ^[33]			4.01 ^[33]
			4.24 ^[60]			4.07 ^[62]
			4.67 ^[61]			4.95^[63]

DownLoad: CSV

map

[1]	许斌, 时永鹏, 吕美哲, 郭全海 2016 人工晶体学报 45 2198 Google Scholar Xu B, Shi Y P, Lv M Z, Guo Q H 2016 J. Synthetic Cryst. 45 2198 Google 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 86 575 Google 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 1154 Google Scholar
[5]	殷红, 赵艳 2015 超硬材料工程 27 49 Google Scholar Yin H, Zhao Y 2015 Superhard Mater. Eng. 27 49 Google Scholar
[6]	Nose K, Yang H S, Yoshida T 2005 Diamond Relat. Mater. 14 1297 Google 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 493 385 Google Scholar
[9]	Gong H R, Wang Q, Chen L, Xiong L 2017 J. Phys. Chem. Solids 104 276 Google Scholar
[10]	Era K, Mishima O, Wada Y, Tanaka J, Yamaoka S 1988 Appl. Phys. Lett. 53 962 Google 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 3725 Google 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 245701 Google Scholar
[14]	Lin Z, McNamara A, Liu Y, Moon K, Wong C P 2014 Compos. Sci. Technol. 90 123 Google Scholar
[15]	Haubner R, Wilhelm M, Weissenbacher R, Lux B 2002 Struct. Bond. 6 1539
[16]	刘娟, 胡锐, 范志强, 张振华 2017 66 238501 Google Scholar Liu J, Hu R, Fan Z Q, Zhang Z H 2017 Acta Phys. Sin. 66 238501 Google Scholar
[17]	Gao B L, Dang C, Wang Y, Wang B 2018 Chin. J. Lumin. 39 1252 Google Scholar
[18]	Weng Q H, Wang X B, Wang X, Bando Y, Golberg D 2016 Chem. Soc. Rev. 45 3989 Google Scholar
[19]	Shayeganfar F, Shahsavari R 2016 Carbon 99 523 Google Scholar
[20]	Zhou J, Wang Q, Sun Q, Jena P 2010 Phys. Rev. B 81 085442 Google Scholar
[21]	候国华, 姜麟麟 2014 吉林大学学报(信息科学版) 32 284 Google Scholar Hou G H, Jiang Q L 2014 J. Jilin Univ.: Inf. Sci. Ed. 32 284 Google Scholar
[22]	Zheng H, Liu M X, Yan H, Yan W, Chu Z D, Bai K K, Dou R F, Zhang Y F, Liu Z F, Nie J C, He L 2013 Phys. Rev. B 87 205405 Google Scholar
[23]	李宇波, 王骁, 戴庭舸, 袁广中, 杨杭生 2013 62 074201 Google Scholar Li Y B, Wang X, Dai T G, Yuan G Z, Yang H S 2013 Acta Phys. Sin. 62 074201 Google Scholar
[24]	王帅 2016 博士学位论文 (兰州: 兰州理工大学) Wang S 2016 Ph. D. Dissertation (Lanzhou: Lanzhou University of Technology) (in Chinese)
[25]	Lu Z S, Liang Y L, Lv P, Cheng Y J, Yang X W 2017 J. Phys. B: At. Mol. Opt. Phys. 34 522
[26]	张宁超, 任娟 2018 四川大学学报(自然科学版) 55 105 Google Scholar Zhang N C , Ren J 2018 J. Sichuan Univ.:Nat. Sci. Ed. 55 105 Google Scholar
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