tP40 carbon: A novel superhard carbon allotrope

doi:10.1088/1674-1056/ab9c01

中国物理B ›› 2020, Vol. 29 ›› Issue (10): 106102-.doi: 10.1088/1674-1056/ab9c01

Heng Liu(刘恒)¹, Qing-Yang Fan(樊庆扬)¹^,†(), Fang Yang(杨放)¹, Xin-Hai Yu(于新海)², Wei Zhang(张伟)³, Si-Ning Yun(云斯宁)⁴^,§‡

收稿日期:2020-03-09 修回日期:2020-05-25 接受日期:2020-06-12 出版日期:2020-10-05 发布日期:2020-10-05
通讯作者: Qing-Yang Fan(樊庆扬), Si-Ning Yun(云斯宁)

tP40 carbon: A novel superhard carbon allotrope

Heng Liu(刘恒)¹, Qing-Yang Fan(樊庆扬)^1,†, Fang Yang(杨放)¹, Xin-Hai Yu(于新海)², Wei Zhang(张伟)³, and Si-Ning Yun(云斯宁)^4,‡

¹ College of Information and Control Engineering, Xi’an University of Architecture and Technology, Xi’an 710055, China
² Department of Mechanical and Electrical Engineering, Hetao College, Bayannur Inner Mongolia 015000, China
³ School of Microelectronics, Xidian University, Xi’an 710071, China
⁴ Functional Materials Laboratory, School of Materials Science and Engineering, Xi’an University of Architecture and Technology, Xi’an 710055, China

Received:2020-03-09 Revised:2020-05-25 Accepted:2020-06-12 Online:2020-10-05 Published:2020-10-05
Contact: ^†Corresponding author. E-mail: qyfan_xidian@163.com; fanqy@xauat.edu.cn ^‡Corresponding author. E-mail: alexsyun1974@aliyun.com; yunsining@xauat.edu.cn
About author:
†Corresponding author. E-mail: qyfan_xidian@163.com
‡Corresponding author. E-mail: fanqy@xauat.edu.cn
§Corresponding author. E-mail: alexsyun1974@aliyun.com
* Project supported by the National Natural Science Foundationof China (Grant Nos. 61804120 and 61901162), the China Postdoctoral Science Foundation (Grant Nos. 2019TQ0243 and 2019M663646), the Young Talent Fund of University Association for Science and Technology in Shaanxi Province, China (Grant No. 20190110), the National Key Research and Development Program of China (Grant No. 2018YFB1502902), and the Key Program for International Science and Technolog Cooperation Projects of Shaanxi Province, China (Grant No. 2019KWZ-03).

摘要/Abstract

Abstract:

In this work, a novel carbon allotrope tP40 carbon with space group P4/mmm is proposed. The structural stability, mechanical properties, elastic anisotropy, and electronic properties of tP40 carbon are investigated systematically by using density functional theory (DFT). The calculated elastic constants and phonon dispersion spectra indicate that the tP40 phase is a metastable carbon phase with mechanical stability and dynamic stability. The B/G ratio indicates that tP40 carbon is brittle from 0 GPa to 60 GPa, while tP40 carbon is ductile from 70 GPa to 100 GPa. Additionally, the anisotropic factors and the directional dependence of the Poisson’s ratio, shear modulus, and Young’s modulus of tP40 carbon at different pressures are estimated and plotted, suggesting that the tP40 carbon is elastically anisotropic. The calculated hardness values of tP40 carbon are 44.0 GPa and 40.2 GPa obtained by using Lyakhov–Oganov’s model and Chen’s model, respectively, which means that the tP40 carbon can be considered as a superhard material. The electronic band gap within Heyd–Scuseria–Ernzerhof hybrid functional (HSE06) is 4.130 eV, and it is found that the tP40 carbon is an indirect and wider band gap semiconductor material.

Key words: novel carbon allotrope, elastic properties, anisotropy, superhard material

中图分类号: (Theory of crystal structure, crystal symmetry; calculations and modeling)

61.50.Ah

61.50.-f (Structure of bulk crystals) 71.20.Nr (Semiconductor compounds) 71.55.Cn (Elemental semiconductors)

Heng Liu(刘恒), Qing-Yang Fan(樊庆扬), Fang Yang(杨放), Xin-Hai Yu(于新海), Wei Zhang(张伟), Si-Ning Yun(云斯宁). [J]. 中国物理B, 2020, 29(10): 106102-.

Heng Liu(刘恒), Qing-Yang Fan(樊庆扬)†, Fang Yang(杨放), Xin-Hai Yu(于新海), Wei Zhang(张伟), and Si-Ning Yun(云斯宁)‡. tP40 carbon: A novel superhard carbon allotrope[J]. Chin. Phys. B, 2020, 29(10): 106102-.

图/表 12

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Crystal	Method	a	b	c	V	ρ
tP40 carbon	GGA^a	8.414		4.383	7.756	2.571
	LDA^a	8.314		4.329	7.482	2.666
C₆₄		7.180^b		2.511	6.022	2.562
Pnma-BN	GGA^c	4.890	2.589	4.284	13.557
	LDA^c	4.795	2.557	4.243	13.007
C₉₆	PW91^d	9.020				2.700
	GGA^e	9.004
C72		9.460^f			11.760	1.690
Diamond	GGA^a	3.566			11.341
		3.566^g			11.337
	LDA^a	3.526			10.961
		3.525^g			10.950
	Exp.^h	3.567			11.346

	tP40	C₆₄^a	Pnma-BN^b	C₉₆^c	C72^d	P carbon^e	Diamond	Diamond^f
C₁₁	542	598	392	623	273	754	1053	1076
C₁₂	174		99	108	139	152	120	125
C₁₃	82		256			56
C₂₂			770
C₂₃			116
C₃₃	575	677	675			979
C₄₄	240	254	299	194	81	401	563	577
C₅₅			272
C₆₆	261		187			285
B	259	264	298	279	183	334	431	442
G	234	217	227	219	75	360	522
E	540	510	543	521	198	795	1116
v	0.152	0.178			0.310	0.104	0.070
B/G	1.106	1.220			2.46	0.928	0.826

	v_p/(m/s)	v_s/(m/s)	v_m/(m/s)	Θ_D/K	B/G
0	14908	9545	10487	1579	1.106
10	15271	9568	10538	1606	1.229
20	15483	9447	10434	1607	1.352
30	15886	9546	10559	1641	1.435
40	16039	9387	10409	1633	1.586
50	16280	9397	10443	1649	1.668
60	16584	9504	10558	1681	1.712
70	17051	9578	10659	1701	1.847
80	16898	9356	10423	1682	1.929
90	17036	9278	10349	1680	2.039
100	17184	9227	10303	1682	2.134

Pressure	A₁	A₃	B_a	B_c	A_Ba	A_Bc
0	1.008	1.421	807.58	721.47	1.00	0.893
10	0.994	1.487	928.01	817.32	1.00	0.881
20	0.981	1.491	1044.87	908.75	1.00	0.870
30	0.940	1.022	1179.82	990.59	1.00	0.840
40	0.932	0.932	1295.93	1081.51	1.00	0.835
50	0.922	0.984	1403.18	1160.81	1.00	0.827
60	0.910	1.159	1508.43	1241.13	1.00	0.823
70	0.765	1.307	1561.37	1619.36	1.00	1.037
80	0.865	1.338	1724.73	1394.34	1.00	0.808
90	0.825	1.440	1838.87	1456.74	1.00	0.792
100	0.813	1.567	1942.09	1529.97	1.00	0.788

	E_max	E_min	Ratio	G_max	G_min	Ratio	v_max	v_min	Ratio
0	595	480	1.24	261	184	1.42	0.31	0.09	3.44
10	631	490	1.29	272	180	1.51	0.37	0.10	3.70
20	651	500	1.30	283	177	1.60	0.41	0.11	3.73
30	683	607	1.13	282	225	1.25	0.35	0.14	2.50
40	718	584	1.23	286	207	1.38	0.41	0.14	2.93
50	748	619	1.21	293	219	1.34	0.41	0.15	2.73
60	779	635	1.23	314	223	1.41	0.43	0.15	2.87
70	994	626	1.59	368	212	1.74	0.48	0.12	4.00
80	835	621	1.34	335	208	1.61	0.49	0.15	3.27
90	864	615	1.41	348	202	1.72	0.52	0.15	3.47
100	888	604	1.47	358	195	1.84	0.55	0.14	3.92

tP40 carbon: A novel superhard carbon allotrope

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