<i>t</i>P40 carbon: A novel superhard carbon allotrope

Heng Liu; Qing-Yang Fan; Fang Yang; Xin-Hai Yu; Wei Zhang; Si-Ning Yun

doi:10.1088/1674-1056/ab9c01

Chinese Physics B, Volume. 29, Issue 10, (2020)

tP40 carbon: A novel superhard carbon allotrope

Heng Liu1... Qing-Yang Fan1,†, Fang Yang1, Xin-Hai Yu2, Wei Zhang3 and Si-Ning Yun4 |Show fewer author(s)

Author Affiliations

¹College of Information and Control Engineering, Xi’an University of Architecture and Technology, Xi’an 70055, China

²Department of Mechanical and Electrical Engineering, Hetao College, Bayannur Inner Mongolia 015000, China

³School of Microelectronics, Xidian University, Xi’an 710071, China

⁴Functional Materials Laboratory, School of Materials Science and Engineering, Xi’an University of Architecture and Technology, Xi’an 710055, China

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Figures & Tables(12)

Fig. 1. Crystal structure of tP40 carbon (a) along the a axis (b) and b axis (c), and crystal structure of P carbon (d).

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Fig. 2. Plots of ratios of (a) a/a₀, c/c₀ and (b) V/V₀versus pressure for tP40 carbon, C₉₆ carbon, P222₁ carbon, c-BN carbon, and diamond.

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Fig. 3. Phonon spectra for tP40 carbon at (a) 0 GPa and (b) 100 GPa.

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Fig. 4. Plots of (a) elastic constants and (b) B, G, and E for tP40 carbon versus pressures.

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Fig. 5. Directional dependence of Young’s modulus at (a) 0 GPa, (b) 50 GPa, and (c) 100 GPa; the shear modulus at (d) 0 GPa, (e) 50 GPa, and (f) 100 GPa; and Passion’s ratio at (g) 0 GPa, (h) 50 GPa, and (i) 100 GPa for tP40 carbon.

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Fig. 6. Electronic band phases according to (a) DFT, (b) HSE06, and (c) DOS for tP40 carbon at zero pressure.

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Table 1. Calculated values of lattice constant (in unit Å), cell volume (in unit Å³), and density (in unit g/cm³) for tP40 carbon, C₆₄, Pnma-BN, C₉₆, and diamond.

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Table 1. Calculated values of lattice constant (in unit Å), cell volume (in unit Å³), and density (in unit g/cm³) for tP40 carbon, C₆₄, Pnma-BN, C₉₆, and diamond.

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

Table 2. Calculated values of elastic constants of C_ij (in unit GPa), bulk modulus B (in unit GPa), shear modulus G (in unit GPa), Young’s modulus E (in unit GPa), Poisson’s ratio v, and B/G ratio for each of tP40 carbon, C₆₄, Pnma-BN, C₉₆, C72, and diamond.

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Table 2. Calculated values of elastic constants of C_ij (in unit GPa), bulk modulus B (in unit GPa), shear modulus G (in unit GPa), Young’s modulus E (in unit GPa), Poisson’s ratio v, and B/G ratio for each of tP40 carbon, C₆₄, Pnma-BN, C₉₆, C72, and diamond.

	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

Table 3. Estimated shear wave velocity (v_s), compressional wave velocity (v_p), average sound velocity v_m, Debye temperature Θ_D, and B/G ratio results for tP40 carbon.

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Table 3. Estimated shear wave velocity (v_s), compressional wave velocity (v_p), average sound velocity v_m, Debye temperature Θ_D, and B/G ratio results for tP40 carbon.

	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

Table 4. Anisotropy factors of tP40 carbon from 0 GPa to 100 GPa.

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Table 4. Anisotropy factors of tP40 carbon from 0 GPa to 100 GPa.

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

Table 5. Mximum values and minimum values of Young’s modulus (in unit GPa), shear modulus (in unit GPa), and Poisson’s ratio and E_max/E_min, G_max/G_min, and v_max/v_min for tP40 carbon.

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Table 5. Mximum values and minimum values of Young’s modulus (in unit GPa), shear modulus (in unit GPa), and Poisson’s ratio and E_max/E_min, G_max/G_min, and v_max/v_min for tP40 carbon.

	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

Table 6. Maximum and minimum Young’s moduli and the values of E_max/E_min in different planes at different pressures for tP40 carbon.

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Table 6. Maximum and minimum Young’s moduli and the values of E_max/E_min in different planes at different pressures for tP40 carbon.

P	(100) (010)			(011) (101)			(001)			(110)			(111)
	E_max	E_min	Ratio	E_max	E_min	Ratio	E_max	E_min	Ratio	E_max	E_min	Ratio	E_max	E_min	Ratio
0	555	480	1.16	562	480	1.17	595	480	1.24	595	548	1.09	595	520	1.14
10	604	490	1.23	595	490	1.21	631	490	1.29	631	585	1.08	631	543	1.16
20	645	500	1.29	618	500	1.24	651	500	1.30	651	613	1.06	651	563	1.16
30	683	607	1.13	627	607	1.03	616	607	1.01	683	615	1.11	642	614	1.05
40	718	614	1.17	645	607	1.06	614	584	1.05	718	584	1.23	660	584	1.13
50	748	626	1.19	662	626	1.06	626	619	1.01	748	619	1.21	683	619	1.10
60	779	635	1.23	688	635	1.08	704	635	1.11	779	688	1.17	710	665	1.07
70	994	626	1.59	708	626	1.13	758	626	1.21	994	708	1.40	765	665	1.15
80	835	621	1.34	713	621	1.15	765	621	1.23	835	711	1.74	765	664	1.15
90	864	615	1.40	720	615	1.17	801	615	1.30	864	713	1.21	801	675	1.19
100	888	604	1.47	735	604	1.22	839	604	1.39	888	725	1.22	839	656	1.28

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Heng Liu, Qing-Yang Fan, Fang Yang, Xin-Hai Yu, Wei Zhang, Si-Ning Yun. tP40 carbon: A novel superhard carbon allotrope[J]. Chinese Physics B, 2020, 29(10):

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Paper Information

Received: Mar. 9, 2020

Accepted: --

Published Online: Apr. 21, 2021

The Author Email: Fan Qing-Yang (yunsining@xauat.edu.cn)

DOI:10.1088/1674-1056/ab9c01

Topics

Nuclear physics

Particles and fields

Particle and nuclear astrophysics and cosmology

Table 1. Calculated values of lattice constant (in unit Å), cell volume (in unit Å3), and density (in unit g/cm3) for tP40 carbon, C64, Pnma-BN, C96, and diamond.

Table 1. Calculated values of lattice constant (in unit Å), cell volume (in unit Å3), and density (in unit g/cm3) for tP40 carbon, C64, Pnma-BN, C96, and diamond.

Table 2. Calculated values of elastic constants of Cij (in unit GPa), bulk modulus B (in unit GPa), shear modulus G (in unit GPa), Young’s modulus E (in unit GPa), Poisson’s ratio v, and B/G ratio for each of tP40 carbon, C64, Pnma-BN, C96, C72, and diamond.

Table 2. Calculated values of elastic constants of Cij (in unit GPa), bulk modulus B (in unit GPa), shear modulus G (in unit GPa), Young’s modulus E (in unit GPa), Poisson’s ratio v, and B/G ratio for each of tP40 carbon, C64, Pnma-BN, C96, C72, and diamond.

Table 3. Estimated shear wave velocity (vs), compressional wave velocity (vp), average sound velocity vm, Debye temperature ΘD, and B/G ratio results for tP40 carbon.

Table 3. Estimated shear wave velocity (vs), compressional wave velocity (vp), average sound velocity vm, Debye temperature ΘD, and B/G ratio results for tP40 carbon.

Table 4. Anisotropy factors of tP40 carbon from 0 GPa to 100 GPa.

Table 4. Anisotropy factors of tP40 carbon from 0 GPa to 100 GPa.

Table 5. Mximum values and minimum values of Young’s modulus (in unit GPa), shear modulus (in unit GPa), and Poisson’s ratio and Emax/Emin, Gmax/Gmin, and vmax/vmin for tP40 carbon.

Table 5. Mximum values and minimum values of Young’s modulus (in unit GPa), shear modulus (in unit GPa), and Poisson’s ratio and Emax/Emin, Gmax/Gmin, and vmax/vmin for tP40 carbon.

Table 6. Maximum and minimum Young’s moduli and the values of Emax/Emin in different planes at different pressures for tP40 carbon.

Table 6. Maximum and minimum Young’s moduli and the values of Emax/Emin in different planes at different pressures for tP40 carbon.

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Table 1. Calculated values of lattice constant (in unit Å), cell volume (in unit Å³), and density (in unit g/cm³) for tP40 carbon, C₆₄, Pnma-BN, C₉₆, and diamond.

Table 1. Calculated values of lattice constant (in unit Å), cell volume (in unit Å³), and density (in unit g/cm³) for tP40 carbon, C₆₄, Pnma-BN, C₉₆, and diamond.

Table 2. Calculated values of elastic constants of C_ij (in unit GPa), bulk modulus B (in unit GPa), shear modulus G (in unit GPa), Young’s modulus E (in unit GPa), Poisson’s ratio v, and B/G ratio for each of tP40 carbon, C₆₄, Pnma-BN, C₉₆, C72, and diamond.

Table 2. Calculated values of elastic constants of C_ij (in unit GPa), bulk modulus B (in unit GPa), shear modulus G (in unit GPa), Young’s modulus E (in unit GPa), Poisson’s ratio v, and B/G ratio for each of tP40 carbon, C₆₄, Pnma-BN, C₉₆, C72, and diamond.

Table 3. Estimated shear wave velocity (v_s), compressional wave velocity (v_p), average sound velocity v_m, Debye temperature Θ_D, and B/G ratio results for tP40 carbon.

Table 3. Estimated shear wave velocity (v_s), compressional wave velocity (v_p), average sound velocity v_m, Debye temperature Θ_D, and B/G ratio results for tP40 carbon.

Table 5. Mximum values and minimum values of Young’s modulus (in unit GPa), shear modulus (in unit GPa), and Poisson’s ratio and E_max/E_min, G_max/G_min, and v_max/v_min for tP40 carbon.

Table 5. Mximum values and minimum values of Young’s modulus (in unit GPa), shear modulus (in unit GPa), and Poisson’s ratio and E_max/E_min, G_max/G_min, and v_max/v_min for tP40 carbon.

Table 6. Maximum and minimum Young’s moduli and the values of E_max/E_min in different planes at different pressures for tP40 carbon.

Table 6. Maximum and minimum Young’s moduli and the values of E_max/E_min in different planes at different pressures for tP40 carbon.