M585, a low energy superhard monoclinic carbon phase

Solid State Communications 181 (2014) 24–27

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M585, a low energy superhard monoclinic carbon phase Chaoyu He a,b, Jianxin Zhong a,b,n a b

Hunan Key Laboratory for Micro-Nano Energy Materials and Devices, Xiangtan University, Hunan 411105, RP China Laboratory for Quantum Engineering and Micro-Nano Energy Technology, Xiangtan University, Hunan, 411105, RP China

art ic l e i nf o

a b s t r a c t

Article history: Received 24 August 2013 Received in revised form 3 November 2013 Accepted 21 November 2013

A monoclinic carbon crystal, M585, consisting of ABCA-stacked cubic-diamond-segments interlinked by interfacial zigzag carbon chains is proposed based on first-principles calculations. The formed linear 5–8–5 carbon grain boundary shows a totally new topological manner of carbon phase, which is distinct from those in the previously proposed 4þ8 and 5–7–5 types. M585 is energetically more favorable than the previously proposed M-carbon, W-carbon, H-carbon and S-carbon and is dynamically stable. The calculations on electronic and mechanical properties of M585 indicate that it is optically transparent and mechanically superhard, which has potential applications in mechanical industry. & 2013 Elsevier Ltd. All rights reserved.

by J.R. Chelikowsky Available online 8 December 2013 Keywords: C. Structure prediction D. Superhard D. Bulk modulus

1. Introduction Many low energy, transparent and superhard carbon allotropes [1–21] have been proposed as potential products of coldcompression of graphite [22–26], such as the sp2–sp3 hybridized graphite–diamond structures [1], monoclinic M-carbon [2,3] and F-carbon [16–18], orthorhombic W-carbon [7], Z-carbon [8–10], H-carbon [13,15], S-carbon [13,14] and tetragonal bct-C4 [4–6]. Among these superhard carbons, the sp2–sp3 hybridized graphite– diamond structures [1] were firstly proposed as potential candidates for the “superhard graphite” [26] in 2005. But they possess relatively higher energies and lower hardness. The monoclinic Mcarbon was predicted in 2006 [2] and then proposed [3] in 2009 as the potential candidate for the “superhard graphite” [26]. The bctC4 phase predicted in 1997 [5] was proposed as a potential candidate for the “superhard graphite” in 2010 [4]. In 2011, orthorhombic W-carbon [7] possessing transparent and superhard properties was predicted and proposed as potential product of cold-compressing graphite. From a thermodynamical view, Wcarbon is more favorable than M-carbon and bct-C4 due to its relatively lower energy. However, there still has a wide energy gap of about 165 meV per atom between W-carbon and diamond, indicating that other morestable carbon phases may exist. As expected, after the prediction of W-carbon, another new orthorhombic carbon allotrope, named as Z-carbon, was proposed n Corresponding author at: Hunan Key Laboratory for Micro-Nano Energy Materials and Devices, Xiangtan University, Hunan 411105, PR China. Tel.: þ 86 732 52665818; fax: þ86 732 58292468. E-mail address: [email protected] (J. Zhong).

0038-1098/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ssc.2013.11.035

and investigated at almost the same time by three independent research groups [8–10]. It was shown to be more stable (its cohesive energy is about 25 meV per atom lower than that of W-carbon) and harder than the previously proposed W-carbon. To fill the energy gap between Z-carbon and diamond (about 140 meV per atom), we have proposed a special segment combination method [11,12] for carbon crystal prediction and predicted 6 low energy carbon allotropes, including the H-carbon and S-carbon (about 38 meV per atom lower than Z-carbon) which can be directly translated from AB-stacked graphite [13]. At almost the same time, other three independent works [19–21] also proposed similar methods for systematical searching for low energy carbon phase and predicted many new superhard carbon allotropes. On the other hand, in the process of searching for new superhard materials, 11 new superhard carbon allotropes were proposed by Zhang et al. [27]. All these works enlarged the family of superhard carbon allotropes to a great extent. Very recently, a new orthorhombic carbon allotrope (oC32) [28] with 16 carbon atoms per unit cell was predicted. Its cohesive energy is about 16 meV per atom lower than that of S-carbon. Topologically, most of all the carbon allotropes in present superhard carbon family can be divided into three types: (i) perfect cubic-diamond and hexagonal-diamonds (with different stacking manners) with only 6 carbon rings; (ii) hybridizations (5– 7 type M-carbon, W-carbon, H-carbon, F-carbon, S-carbon and X-carbon) of cubic-diamond and hexagonal-diamond segments with 5–7 rings interface; and (iii) mutations (4–8 type bct-C4, Z-carbon, Y-carbon, and oC32) of the hexagonal-diamond with 4–8 ring interface. In present work, we propose a monoclinic carbon phase (M585), which consists of ABCA-stacked cubicdiamond-segments interlinked by interfacial zigzag carbon chains,

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Fig. 1. (Color online) Perspective view of M585 in its monoclinic crystalline cell (a), structural character of M585 (b), and the enthalpy per atom for cubic-diamond, M-carbon, Z-carbon, H-carbon, S-carbon, oC32 and M585 as a function of pressure relative to graphite (c).

forming a 5–8–5 carbon rings linear boundary. Such a linear 5–8–5 carbon rings topology manner has never been proposed in any previous carbon phases. The structure, stability, electronic property and mechanical property of M585 are also investigated with first-principles calculations.

2. Calculation methods All calculations of structure optimizations and property investigations are carried out using the density functional theory within local density approximation (LDA) [29,30] as implemented in Vienna ab initio simulation package (VASP) [31,32]. The interactions between nucleus and the 2s22p2 valence electrons of carbon are described by the projector augmented wave (PAW) method [33,34]. A plane-wave basis with a cutoff energy of 500 eV is used to expand the wave functions and the Brillouin Zone (BZ) sample meshes are set to be dense enough (less than 0.21 Å  1) to ensure the accuracy of our calculations. Crystal lattices and atom positions of M585 and all the reference systems studied in present work are fully optimized up to the residual force on every atom less than 0.005 eV/Å through the conjugate-gradient algorithm. The vibrational properties of M585 are investigated by the phonon package [35] with the forces calculated from VASP to evaluate its dynamical stability. The elastic constants of M585 and all the reference systems studied in this work are calculated as the second-order coefficient in the polynomial function of distortion parameter δ used to fit their total energies according to Hooke's law. In view of their differences in crystal symmetries, different groups of deformations are applied on different allotropes. The bulk modulus (B) and shear modulus (G) are evaluated according to Hill's formula [36] based on the calculated elastic constants. To further analyze the hardness of these carbon allotropes, we adopt the recently introduced empirical scheme [37] to evaluate their Vicker's hardness (Hv ) which is determined by their B and G as Hv ¼ 2(G3/B2)0.585  3.

Fig. 2. (Color online) Phonon band structure of M585.

3. Results and discussion The structure of M585 was constructed through our previously proposed segment-combination-method. The optimized structural characteristics of M585 are shown in Fig. 1 (a) and (b), including its crystalline cell (in perspective view) and compositions of ABCAstaked cubic diamond segments and interfacial zigzag carbon chains. It has a monoclinic cell with lattice parameters of a ¼ 9:631 Å, b ¼ 2:497 Å, c ¼ 4:306 Å and β ¼81.3151 and belongs to space group P21/m (No. 11). Nine inequivalent atoms in this crystal occupy the positions at (0.847, 0.750, 0.809), (0.638, 0.750, 0.536), (0.804, 0.750, 0.481), (0.370, 0.750, 0.959), (0.998, 0.750, 0.893), (0.582, 0.250, 0.719), (0.421, 0.250, 0.774), (0.786, 0.250, 0.987) and (0.852, 0.250, 0.291). Its equilibrium volume of 5.69 Å3 per atom indicates a density of 3.507 g/cm3, which is comparable to that of diamond. Interestingly, M585 possesses a new topological type of 5–8–5, which is distinct from the previously proposed two types of 5 þ7 and 4 þ8. It can be considered as a combination of ABCA-stacked cubic-diamond-segments interlinked by

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Table 1 Space group, lattice parameters (LP), density (g/cm3), band gap (Eg: eV), cohesive energy (Ecoh: eV), bulk modulus (B0: Gpa) and Vicker's hardness (Hv: GPa) for diamond, M-carbon, Z-carbon, H-carbon, S-carbon, oC32 and M585. Systems

Space group

LP

Density

Eg

Ecoh

B0

Hv

Diamond M-carbon Z-carbon H-carbon S-carbon oC32 M585

Fd-3m C2/m Cmmm Pbam Cmcm Cmmm P21/m

a ¼ b ¼ c ¼ 3:536 Å a ¼ 9:093 Å, b ¼ 2:498 Å, c ¼ 4:108 Å, β ¼ 96.961 a ¼ 8:677 Å, b ¼ 4:211 Å, c ¼ 2:489 Å a ¼ 7:792 Å, b ¼ 4:757 Å, c ¼ 2:497 Å a ¼ 2:496 Å, b ¼ 11:293 Å, c ¼ 4:857 Å a ¼ 17:283 Å, b ¼ 4:171 Å, c ¼ 2:486 Å a ¼ 9:631 Å, b ¼ 2:497 Å, c ¼ 4:306 Å, β ¼ 81.3151

3.611 3.443 3.507 3.440 3.489 3.553 3.507

4.648 3.532 3.414 4.512 4.451 3.282 4.212

 8.997  8.821  8.857  8.845  8.896  8.913  8.911

514.15 447.33 497.87 466.92 486.29 476.93 462.30

88.02 75.45 80.51 83.29 83.50 80.47 78.85

interfacial zigzag carbon chains, forming the 5–8–5 ring boundary. We know that all the previously proposed M-carbon, bct-C4, W-carbon, Z-carbon, H-carbon, S-carbon and oC32 can be structurally related to perfect graphite. However, we find no any potential pathways for transition from perfect graphite to M585. But it is more energetically stable than M-carbon, Z-carbon, H-carbon and S-carbon. At zero pressure, its cohesive energy of  8.911 eV per atom (comparable to that of  8.913 eV per atom for the recently proposed oC32) is only 87 meV higher than that of diamond. The enthalpy per atom for cubic diamond, M-carbon, Z-carbon, H-carbon, S-carbon, oC32 and M585 as a function of pressure relative to graphite is shown in Fig. 1(c). The results indicate that M585 and oC32 are more stable than graphite when the external pressure is larger than 5 GPa. M585 and oC32 possess comparable stability and are always more favorable than M-carbon, Z-carbon, H-carbon and S-carbon. The dynamical stabilities of M-carbon, Z-carbon, H-carbon, S-carbon and oC32 have been confirmed to be positive in previous literatures [3,9,10,13,28]. In this work, to further confirm the dynamic stability of M585, we investigate its vibrational properties by PHONON package with atomic forces applied from VASP. The phonon band structure is shown in Fig. 2. We can see that there have been no any imaginary frequencies in the phonon band structure, and we confirm that there have been no any imaginary vibration modes in the phonon density of state of M585. That is to say, M585 is a promising new carbon allotrope in views of its remarkable energetic stability and positive dynamical stability. We then investigate the electronic and mechanical properties of M585 and some other carbon allotropes for reference. Space group, density, band gap, cohesive energy, bulk modulus and Vicker's hardness of diamond, M-carbon, Z-carbon, H-carbon, S-carbon, oC32 and M585 are summarized in Table 1. Our results indicate that, as superhard intermediate phases between graphite and diamond, M-carbon, Z-carbon, H-carbon, S-carbon, oC32 possess densities, bulk modulus and Vicker's hardness close to that of diamond, which are in good consistent with previous investigations. M585 possesses mass density of 3.507 g/cm3, which is comparable to that of diamond and equal to that of Z-carbon. Its bulk modulus and Vicker's hardness values are 462.30 GPa and 78.85 GPa, respectively, which are comparable to those of all the previously proposed superhard carbon phases, indicating that M585 is also a superhard material. All the previously proposed superhard carbon allotropes are optically transparent due to their wide energy band gaps. As summarized in Table 1, we can see that our calculated band gaps for these carbon allotropes distribute in a range of 3.41–4.61 eV, exceeding the maximum energy value of the visible light. These results are in good consistent with previous calculations. The electronic band structure of M585 at zero pressure is shown in Fig. 3. We can see that it is an indirect band-gap semiconductor with a band-gap of 4.21 eV, indicating that M585 is optically transparent too.

Fig. 3. (Color online) Electronic band structure of M585.

4. Conclusion Based on segment-combination-method, we have proposed a low energy, optically transparent and mechanical superhard carbon phase (M585) between graphite and diamond. It is more favorable than the previously proposed M-carbon, Z-carbon, H-carbon and S-carbon and confirmed dynamically stable. M585 can be considered as the combination of ABCA-stacked cubic diamond segments interlinked by interfacial zigzag carbon chains. The interfacial boundary of 5–8–5 carbon ring in M585 suggests a new topological manner for predicting new carbon phases, which is distinct to the previously proposed two types of 4 þ8 and 5 þ7. Our calculations indicate that M585 is an optically transparent insulator with remarkable Vicker's hardness comparable to diamond.

Acknowledgments This work is supported by the National Natural Science Foundation of China (Grant nos. 11074211 and 51172191), the National Basic Research Program of China (2012CB921303), and the Hunan Provincial Innovation Foundation for Postgraduate (Grant No. CX2013A010).

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