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Three Dimensional Metallic Carbon from Distorting sp3-Bond Yong Cheng, Roderick Melnik, Yoshiyuki Kawazoe, and Bin Wen Cryst. Growth Des., Just Accepted Manuscript • DOI: 10.1021/acs.cgd.5b01490 • Publication Date (Web): 12 Jan 2016 Downloaded from http://pubs.acs.org on January 18, 2016

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Crystal Growth & Design

Three Dimensional Metallic Carbon from Distorting sp3-Bond Yong Cheng,1 Roderick Melnik,2 Yoshiyuki Kawazoe,3,4 and Bin Wen1,* 1

State Key Laboratory of Metastable Materials Science and Technology, Yanshan University, Qinhuangdao 066004, China 2

The MS2Discovery Interdisciplinary Research Institute, Wilfrid Laurier University, 75 University Ave. West, Waterloo, Ontario, Canada N2L 3C5

3

4

New Industry Creation Hatchery Center, Tohoku University, 6-6-4 Aramaki-aza-Aoba, Aoba-ku, Sendai 980-8579, Japan

Institute of Thermophysics, Siberian Branch of the Russian Academy of Sciences, 1, Lavyrentyev Avenue, Novosibirsk 630090, Russia

ABSTRACT Owing to the outstanding properties of metallic carbon as well as their great potential applications, design and synthesis of metallic carbon have long attracted considerable attention. In this work, a new three dimensional metallic carbon (dubbed as Tri-C9) has been built by distorting sp3 hybridization bond. Our first-principles calculations results indicate that Tri-C9 is a metastable metallic carbon, and that the metallic behavior of Tri-C9 originates from the π bonds near Fermi level. This study offers a new way to design all-sp3 hybridized metallic carbon via distorting the sp3-bond. In addition, a feasible synthesis route for Tri-C9 has been proposed by compressing graphite.

_________________________________________________________________________ *Corresponding author. Tel: 011+086-335-8568-761. E-mail: [email protected] 1

ACS Paragon Plus Environment


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1. Introduction As one of the most fascinating elements in the periodic table, carbon can form numerous allotropes with diverse properties, attributed to its versatile sp, sp2 and sp3 hybridized chemical bonds.1 Among these carbon allotropes, metallic carbon has drawn increasing research interests due to its advantageous properties such as the superior catalytic effect,2 phonon-plasmon coupling,3 magnetism4 and superconductivity.5 During the past decades, much effort has been devoted to the studies of metallic carbon, where one dimensional (1D) armchair carbon nanotube6 and two dimensional (2D) graphene7 are successful examples. As for three dimensional (3D) metallic carbon, its design and synthesis process have long been a great challenge. In 2009, a 3D metallic carbon named as K4 carbon was reported by Itoh et al.,8 but it was subsequently proved to be structurally unstable.9 Later, Maetinez-Canales et al. proposed a simple cubic metallic carbon,10 but that particular phase was unstable at ambient pressure.11 Until 2013, inspired by the metallic precursor (e.g. graphene, carbon nanotube and K4 carbon), several stable 3D metallic carbon allotropes have been predicted by theoretical calculations, like the T6-carbon,12 Hex-C2413 and K6 carbon14,15. However, designing new 3D metallic carbon and searching its easy synthesis paths are still far from complete. Recently, many novel pure sp3 hybridized carbon allotropes have been proposed, including bct C4,16 T-carbon,17 L-carbon,18 etc, and they all display semiconductive properties. However, it should be noted that their energy gaps have a decreasing trend in comparison with that of diamond with perfect sp3 hybridized bonds. For instance, for diamond, each carbon atom connects to surrounding four atoms by perfect sp3 hybridization bond, forming a tetrahedron. In this tetrahedron, all six bond angles are 109.5°, as shown in Figure 1(a). At the 2


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same time, the energy gap of diamond is 4.16 eV in GGA level.17 But for bct C4, owing to its distorted sp3-bonds, a bond angle in the tetrahedron is turned to 90° [see Figure 1(b)]. This leads to its energy gap as 2.47 eV in GGA level,17 which is much smaller than that of diamond. The above analysis implies that the electronic property of all-sp3 hybridized carbon may be tuned through distorting the sp3-bonds. It is natural to ask whether it is possible to design a zero energy gap carbon (3D metallic carbon) via further distorting sp3-bond. To answer this open question, a new carbon allotrope with a serious distorted sp3-bond (a bond angle in the tetrahedron is further bent to 60°) has been constructed in this work, as shown in Figure 1(c). Furthermore, our first-principles calculation results have confirmed that this new carbon allotrope is a stable 3D metallic phase rather than semiconductor. Because this new carbon allotrope belongs to a trigonal system crystal, and each unit cell contains 9 carbon atoms, we have termed it as Tri-C9.

2. Methods In this work, the crystalline parameters and atomic positions of Tri-C9 are optimized on the basis of density functional theory (DFT),19,20 as implemented in the Vienna ab initio simulation package (VASP).21,22 The all-electron projector augmented wave (PAW) method23 is adopted with 2s22p2 treated as the valence electrons. The exchange-correlation potential is described by the local density approximation (LDA) in the form of Ceperley-Alder.24 To ensure an accurate determination of electronic properties, calculations are repeated using the hybrid Heyd−Scuseria−Ernzerhof functional (HSE06).25,26 The plane-wave cutoff energy of 500 eV has been used in this work. The k-point separation in Brillouin zone of the reciprocal space is sampled as 11×11×13. The conjugate gradient algorithm is used to relax the ions in 3



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their instantaneous ground state, and the convergence threshold of total energy and Hellmann–Feynman force components are set to be within 1×10−6 eV and 10−3 eV/Å, respectively. The phonon dispersion curve is computed using the direct supercell method27 through the VASP and PHONOPY codes,28 and the supercell is set to 3×3×3. The first-principles molecular dynamics simulations are performed in the canonical (NVT) ensemble with a 3×3×3 supercell, each simulation lasted for 6 ps, with a time step of 1 fs. The climbing image nudged elastic band (CI-NEB) method29 is used to simulate the phase transitions path from graphite to Tri-C9. To verify the computational accuracy, benchmark calculations have been performed for diamond. The calculated lattice parameters and elastic constants (see Tables 1 and 2) agreed well with the experimental and other calculated values,30-33 confirming the reliability of our computational scheme.

3. Results and Discussion By means of the first-principles calculations, the crystallographic parameters of Tri-C9 have been successfully optimized, and the results are listed in Table 1 where they are compared with those of graphite30, diamond30,31, bct C4,16 and T-carbon.17 The results indicate that the space group of Tri-C9 is R32 (No. 155), and its equilibrium lattice constants are a = b = 4.083 Å and c = 3.848 Å, respectively. In the unit cell of Tri-C9, only one nonequivalent atom exists, and its atomic Wyckoff position is 9d (0.7842, 0.7842, 0). Two different kinds of C-C bonds exist in Tri-C9, and there are 9 C-C bonds with a bond length of 1.526 Å [d1 in Figure 1(c)], and 9 C-C bonds with a bond length of 1.528 Å [d2 in Figure 1(c)] at ambient pressure, both types of C-C bonds are very close to that of diamond (1.54 Å). All six bond angles in tetrahedron of Tri-C9 (60°, 105.778°, 105.778°, 122.944°, 122.944°, and 123.807°) 4


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are substantially different from that of diamond (109.5°), showing the features of distorted sp3 bond in Tri-C9. To further study the character of chemical bonds of Tri-C9, the bonding charge density for Tri-C9 has been investigated. This density is plotted in Figure 1(f) and compared with that of diamond [Figure 1(d)] and bct C4 [Figure 1(e)], respectively. As can be seen from Figure 1(d)-1(f), the distribution of electrons around C-C bond is symmetric for diamond. However, for bct C4 and Tri-C9, the electrons distributions around C-C bond are asymmetric, especially for Tri-C9. It can be inferred that the asymmetric style of distributed electrons in Tri-C9 may result in peculiar electronic properties, different from diamond. Structural stability is a basic property in the crystal structure study. To check the energetic stability of Tri-C9, the total energy as a function of the volume has been calculated. It is plotted in Figure 2(a) and compared with such energies of diamond, graphite, bct C4 and T-carbon. It can be seen that the corresponding curve of Tri-C9 has a single minimum, signifying that Tri-C9 would be thermodynamically stable. By comparing the total energy per atom of the carbon allotropes studied here, it is found that Tri-C9 is less stable than graphite and diamond, while it is energetically more stable than T-carbon. Remarkably, according to the thermodynamic phase transition theory,34 the critical transition pressure from graphite to Tri-C9 is estimated to be ~66 GPa by calculating the slope of the tangent line (k) between the total energy−volume curves of graphite and Tri-C9 [as shown in inset of Figure 2(a)]. In addition to energetic stability of a crystal structure, the stability of crystal structure is also controlled by its dynamic stability.9 In order to study the dynamic stability of Tri-C9, its phonon spectra at pressure up to 100 GPa have been calculated. The phonon spectra at 0 GPa 5



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are shown in Figure 2(b), where it can be seen that there exist no imaginary frequencies, suggesting that Tri-C9 is dynamically stable at ambient pressure. In the phonon spectra at 0 GPa, the highest phonon frequency is about 36.74 THz, which is about 7%~8% lower than that of diamond (our calculated value: 39.63 THz, 1322 cm-1, others’ theoretical value in LDA level35: 1324 cm-1, experimental value36: 1332 cm-1). Furthermore, no imaginary frequencies exist in the phonon spectra of Tri-C9 at pressures of 50 and 100 GPa (see supporting information Figure S2). Because Tri-C9 is dynamically stable at ambient pressure and even at pressures up to 100 GPa, Tri-C9 may be synthesized under high pressure and further it can be quenched to ambient pressure. To further verify the stability of Tri-C9, the first-principle molecular dynamics simulations at 300 K are also performed with a 3×3×3 supercell of Tri-C9. It is found that the structure of Tri-C9 is kept after 6000 steps with a time step of 1 fs, which strongly demonstrates its structural stability. In order to investigate the mechanical properties of Tri-C9 and to confirm its mechanical stability, single crystal elastic constants for Tri-C9 have been calculated. They are listed in Table 2 where they are compared with diamond, bct C4 and T-carbon.17,32,33,37 Our calculated elastic constants satisfy the mechanical stability criteria38: C11 - |C12| > 0, (C11+C12)C33 2C132 > 0, (C11-C12)C44 - 2C142 > 0, and this result further confirms the dynamical stability of Tri-C9

deduced

from

phonon

spectra

calculation.

By

using

Voigt–Reuss–Hill

approximations,39 the polycrystalline bulk and shear moduli of Tri-C9 have also been evaluated, and they are listed in Table 2. It is noted that Tri-C9 has a relatively large bulk modulus (365 GPa), and it is ~3/4 of diamond bulk modulus (466 GPa), indicating that Tri-C9 is resistant to hydrostatic compression. According to Chen’s model,40 the Vickers hardness (Hv) 6


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of Tri-C9 is calculated to be 34.8 GPa, which is ~50% of cubic boron nitride’s (c-BN) Hv (63 ± 5 GPa).41 Although bulk modulus of Tri-C9 is comparable to that of c-BN (369 ± 14 GPa),42,43 its shear modulus (272 GPa) is much smaller than that of c-BN (409 GPa), and this leads to a relatively smaller Hv compared to c-BN. Owing to the particular electrons distribution around Tri-C9 C-C bond, we expect that the electronic properties of Tri-C9 are of particular interest. To explore the electronic properties of Tri-C9, the densities of states and electronic band structure of Tri-C9 have been calculated and they are plotted in Figures 3(a) and 3(b), respectively. It can be seen that several electronic bands cross the Fermi level, resulting in an electron density of states at 0.42 states/eV at the Fermi level. Therefore, Tri-C9 can be considered as a 3D metallic carbon. To further affirm the electronic band structures of Tri-C9, more accurate calculations have been performed by using the screened hybrid functional HSE06, and they are also plotted in Figure 3(b) in comparison with the results of LDA calculations. It can be easily seen from Figure 3(b) that some electronic bands also cross the Fermi level. This result is consistent with the one obtained by LDA method. It further confirms that Tri-C9 indeed behave in a metallic manner. To uncover the origin of metallic properties, the local density of states of Tri-C9 has been calculated, as presented in Figure 3(a). As can be seen from Figure 3(a), the 2p orbital is predominant near the Fermi level, which results in metallicity of Tri-C9. Supplemental Figure S3 also indicates that the contributions of 2px, 2py and 2pz orbitals to the Fermi level are almost the same, which leads to high degeneracy in its projected density of states. This result demonstrates that metallicity of Tri-C9 is contributed from 2px, 2py and 2pz orbitals, and this characteristic is distinguished from graphite. For graphite, its metallicity only originates from 7



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the delocalization of electrons in 2pz orbital.44 To better understand the spatial density distributions and the number of states characterized by s and/or p orbital of Tri-C9, the partial valence electron density of Tri-C9 has been calculated, and the results are presented in Figure 3(c). For the low energy range (state I), the electronic states are mainly contributed from 2s orbital, hence s-s type bonds appear predominantly. With increases of energy (state II), the contribution of 2p orbital becomes stronger and the electron density is reduced in the middle part of each bond, resulting in appearance of sp3-sp3 type bonds. For states I and II, the bond is pure sp3 hybridized chemical bond, and it is similar to the sp3 hybridized chemical bond in diamond. Then, when the energy reaches to the vicinity of the Fermi level (state III), the electronic states from 2s orbital become fairly small, and p-p (π) type bonds appear predominantly. This phenomenon illustrates that the distortion of sp3-bonds causes the valence electrons in the Tri-C9 to recombine and result in the asymmetric electrons distribution around Tri-C9 C-C bond [see Figure 1(f)], which features π hybridization. Therefore, Tri-C9 exhibits the metallic property instead of semiconductive property. As we suggested above, the phase transformation from graphite to Tri-C9 can be observed at pressure above ~66 GPa. To confirm this and further explore possible synthesis paths for this new 3D metallic carbon, the transformation from graphite toward Tri-C9 has been calculated by using the CI-NEB method.29 In this CI-NEB calculation, a 36-atom supercell is used, and the phase transformation path under pressures at 30, 50, and 70 GPa have been built. They are shown in Figure 4. As can be seen from Figure 4, Tri-C9 is thermodynamically less stable than graphite at pressures of 30 and 50 GPa, and the energy 8


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barriers from graphite to Tri-C9 are ~0.71 and 0.56 eV/atom, respectively. When the pressure reaches to 70 GPa, the Tri-C9 becomes thermodynamically more favorable than graphite, and the energy barrier from graphite to Tri-C9 is further reduced to ~0.46 eV/atom. These computational results indicate that Tri-C9 may be synthesized by compressing graphite at pressure larger than 70 GPa, which is consistent with our previous thermodynamically stable calculations. To identify this new 3D metallic carbon in experiments, the X-ray diffraction (XRD) patterns of Tri-C9 with wavelength 1.54056 Å have been simulated. The results are plotted in Figure S4 and compared with that of graphite, diamond, bct C4, T-carbon and experimental XRD patterns of n-diamond. It can be found that the XRD patterns of Tri-C9 can be easily distinguished from other carbon allotropes, and its XRD peaks are located at 2θ = 34.41°, 44.33°, 54.23°, 75.19° and 89.14°, respectively, which corresponding to the (101), (110), (10 _

_

2), (211), (212) crystal planes of Tri-C9. Interestingly, it can be found that some XRD peaks of Tri-C9 match well with that of experimentally synthesized 3D carbon named n-diamond,45 implying our work may be helpful for the structural identification of n-diamond.46

4. Conclusions In summary, a novel carbon polytype (named Tri-C9) has been constructed by distorting sp3-bond. Our first-principles calculations results demonstrate that Tri-C9 is a metastable carbon with a considerable bulk modulus of 365 GPa. The electronic property calculations on Tri-C9 indicated that it is a metallic carbon, and its metallic behavior result from 2p orbitals electrons. In particular, our study opens a new way to design all-sp3 hybridized metallic carbon via distorting the sp3-bond. 9



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ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (Grant No.’s 51121061, 51131002 and 51372215), and the Natural Science Foundation for Distinguished Young Scholars of Hebei Province of China (Grant No. E2013203265). R. M. acknowledges the support from the NSERC and CRC programs, Canada. The authors also would like to thank the staff of the Center for Computational Materials Science, Institute for Materials Research, Tohoku University for computer support. Y.K. is thankful to the Russian Megagrant Project No. 14.B25.31.0030.

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Figures and Tables

Figure 1. (color on line) (a)-(c) Building block (top) and corresponding crystal structure (bottom) for diamond, bct C4 and Tri-C9 (1×2×1 supercell), respectively. (d)-(f) Bonding charge density (top) and its 2D slices (bottom) for diamond, bct C4 and Tri-C9, respectively. The bonding charge density is the difference between the total charge density of the structure and the superposition of the charge density of the neutral constituent atoms. The isosurface of the bonding charge density is 0.2 e/ Å3. The red and blue colors in the slices indicate the electron accumulation and depletion, respectively.

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Figure 2. (a) Total energy as a function of volume for Tri-C9, diamond, graphite, bct C4 and T-carbon. The inset shows the common tangent between the graphite and Tri-C9 for calculating the transition pressure. (b) Calculated phonon band structures of Tri-C9 at pressure of 0 GPa. The high symmetry path in the Brillouin zone is chosen as: Γ (0, 0, 0) → K (-1/3, 2/3, 0) → H (-1/3, 2/3, 1/2) → A (0, 0, 1/2) → Γ (0, 0, 0) → Μ (0, 1/2, 0) →L (0, 1/2, 1/2) →A (0, 0, 1/2).

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Figure 3. (color on line) (a) Total and local densities of states (DOS) for Tri-C9, the inset shows the Brillouin zone of Tri-C9 (b) Electronic band structures of Tri-C9, the blue lines are obtained from LDA calculations, the red lines are obtained from HSE06 calculations, the Fermi level is shifted 0.0 eV. (c) Partial valence electron density of Tri-C9 in different energy ranges (I, III and III) corresponding to band structure [right side of (b)], respectively.

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Figure 4. (a) Enthalpy vs pathway steps for the transition from graphite to Tri-C9 at pressures of 30, 50, 70 GPa, respectively. The letter IS refers to the initial state: graphite, CS refers to the critical state, TS stands for the transition state, and FS is the final state: Tri-C9. (b) The corresponding structures of IS, CS, TS, and FS.

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Table 1. The space group, equilibrium lattice constants (a and c in Å), Wyckoff position, mass density (ρ in g/cm3), bond length (d in Å), cohesive energy (Ecoh in eV/atom) and energy gap (Eg in eV) for Tri-C9 at zero pressure, in comparison with the available experimental and other theoretical values for diamond, graphite, bct C4 and T-carbon. Structure

Space groups

Tri-C9

R32 (155)

Graphite

P6/mmm (191)

a

c

Wyckoff position

d

Ecoh

Eg

(g/cm )

(Å)

(eV/atom)

(eV)

3.232

1.526, 1.528

7.994

metal

2.323

1.413

8.979

2.770-2.280

1.420

7.374

ρ 3

Source

(Å)

(Å)

4.083

3.848

2.447

6.622

2.460

6.642-6.716

2.443

6.679

2.301

1.410

9.001

3.536

—

3.610

1.531

8.990

4.19

Our work

3.567

—

3.520

1.54

7.37

5.45

Expt.b

3.530

—

3.625

1.529

9.004

4.25

Cal.a

4.333

2.486

3.418

1.563, 1.508

8.479

2.48

Our work

2.56

Cal.c

(0.7842, 0.7842, 0)

(0, 0, 0.25)

Our work Our work

metal

Expt.a

(0.3333, 0.6667, 0.25)

_

Diamond

Fd3m (227)

bct C4

I4/mmm (139)

T-carbon

Fd3m (227)

_

(0.1804, 0.1804, 0) 4.329

2.483

7.448

—

7.450 a

(0.0, 0.0, 0.0)

Cal.a

—

1.562, 1.506 1.544

1.487, 1.404

7.479

2.13

Our work

1.540

1.488, 1.404

7.503

2.22

Cal.d

(0.0706,0.0706,0.0706)

Ref.30. b Ref.31. c Ref.16. dRef.17.

17



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Page 18 of 19

Table 2. The calculated elastic constants (Cij in GPa), bulk modulus (B in GPa), shear modulus (G in GPa) and G/B value for Tri-C9, compared to the available experimental and other theoretical values for diamond, graphite, bct C4 and T-carbon. Structure

C11

C12

C13

C14

C33

C44

C66

B

G

G/B

Source

Tri-C9

645

194

171

111

961

348

—

365

272

0.75

Our work

1099

149

—

—

—

590

—

466

541

1.16

Our work

1076

125

—

—

—

577

—

442

534

1.21

Expt.e

1107

145

—

—

—

598

—

466

548

1.18

Cal.f

978

191

74

—

1256

465

316

431

401

0.93

Our work

932.6

172.1

58.5

—

1189.6

446.7

324.5

403.6

420.9

1.04

Cal.g

202

152

—

—

—

69

—

169

53

0.27

Our work

204

153

—

—

—

71

—

170

47

0.28

Cal.h

Diamond

bct C4

T-carbon e

Ref.32. f Ref.33. g Ref.37. hRef.14.

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For Table of Contents Only TOC-Synopsis Table of Contents Graphic:

Synopsis: Our study opens a new way to design all-sp3 hybridized metallic carbon via distorting the sp3-bond. Tile: Three Dimensional Metallic Carbon from Distorting sp3-Bond Authors: Yong Cheng,1 Roderick Melnik,2 Yoshiyuki Kawazoe3,4, and Bin Wen1,*

19


Three Dimensional Metallic Carbon from Distorting ... - ACS Publications

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