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Chin. Phys. B, 2020, Vol. 29(10): 106102    DOI: 10.1088/1674-1056/ab9c01
CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES Prev   Next  

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
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.

Keywords:  novel carbon allotrope      elastic properties      anisotropy      superhard material  
Received:  09 March 2020      Revised:  25 May 2020      Accepted manuscript online:  12 June 2020
PACS:  61.50.Ah (Theory of crystal structure, crystal symmetry; calculations and modeling)  
  61.50.-f (Structure of bulk crystals)  
  71.20.Nr (Semiconductor compounds)  
  71.55.Cn (Elemental semiconductors)  
Corresponding Authors:  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).

Cite this article: 

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 2020 Chin. Phys. B 29 106102

Fig. 1.  

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

Crystal Method a b c V ρ
tP40 carbon GGAa 8.414 4.383 7.756 2.571
LDAa 8.314 4.329 7.482 2.666
C64 7.180b 2.511 6.022 2.562
Pnma-BN GGAc 4.890 2.589 4.284 13.557
LDAc 4.795 2.557 4.243 13.007
C96 PW91d 9.020 2.700
GGAe 9.004
C72 9.460f 11.760 1.690
Diamond GGAa 3.566 11.341
3.566g 11.337
LDAa 3.526 10.961
3.525g 10.950
Exp.h 3.567 11.346
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.

Fig. 2.  

Plots of ratios of (a) a/a0, c/c0 and (b) V/V0 versus pressure for tP40 carbon, C96 carbon, P2221 carbon, c-BN carbon, and diamond.

tP40 C64a Pnma-BNb C96c C72d P carbone Diamond Diamondf
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 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.

Fig. 3.  

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

vp/(m/s) vs/(m/s) vm/(m/s) ΘD/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 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.

Fig. 4.  

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

Pressure A1 A3 Ba Bc ABa ABc
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 4.  

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

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.

Emax Emin Ratio Gmax Gmin Ratio vmax vmin 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 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.

P (100) (010) (011) (101) (001) (110) (111)
Emax Emin Ratio Emax Emin Ratio Emax Emin Ratio Emax Emin Ratio Emax Emin 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
Table 6.  

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

Fig. 6.  

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

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