M585, a low energy superhard monoclinic carbon phase

Chaoyu He a,b, Jianxin Zhong a,b,n

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

a r t i c l e i n f o

Article history:Received 24 August 2013Received in revised form3 November 2013Accepted 21 November 2013

by J.R. ChelikowskyAvailable online 8 December 2013

Keywords:C. Structure predictionD. SuperhardD. Bulk modulus

a b s t r a c t

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

& 2013 Elsevier Ltd. All rights reserved.

1. Introduction

Many low energy, transparent and superhard carbon allotropes[1–21] have been proposed as potential products of cold-compression of graphite [22–26], such as the sp2–sp3 hybridizedgraphite–diamond structures [1], monoclinic M-carbon [2,3] andF-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 candi-dates for the “superhard graphite” [26] in 2005. But they possessrelatively higher energies and lower hardness. The monoclinic M-carbon was predicted in 2006 [2] and then proposed [3] in 2009 asthe potential candidate for the “superhard graphite” [26]. The bct-C4 phase predicted in 1997 [5] was proposed as a potentialcandidate for the “superhard graphite” in 2010 [4]. In 2011,orthorhombic W-carbon [7] possessing transparent and superhardproperties was predicted and proposed as potential product ofcold-compressing graphite. From a thermodynamical view, W-carbon is more favorable than M-carbon and bct-C4 due to itsrelatively lower energy. However, there still has a wide energy gapof 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 neworthorhombic carbon allotrope, named as Z-carbon, was proposed

and investigated at almost the same time by three independentresearch groups [8–10]. It was shown to be more stable (its cohesiveenergy is about 25 meV per atom lower than that of W-carbon) andharder than the previously proposed W-carbon. To fill the energygap between Z-carbon and diamond (about 140 meV per atom), wehave proposed a special segment combination method [11,12] forcarbon crystal prediction and predicted 6 low energy carbonallotropes, including the H-carbon and S-carbon (about 38 meVper atom lower than Z-carbon) which can be directly translatedfrom AB-stacked graphite [13]. At almost the same time, other threeindependent works [19–21] also proposed similar methods forsystematical searching for low energy carbon phase and predictedmany new superhard carbon allotropes. On the other hand, in theprocess of searching for new superhard materials, 11 new superhardcarbon allotropes were proposed by Zhang et al. [27]. All theseworks enlarged the family of superhard carbon allotropes to a greatextent. Very recently, a new orthorhombic carbon allotrope (oC32)[28] with 16 carbon atoms per unit cell was predicted. Its cohesiveenergy is about 16 meV per atom lower than that of S-carbon.

Topologically, most of all the carbon allotropes in presentsuperhard carbon family can be divided into three types: (i)perfect cubic-diamond and hexagonal-diamonds (with differentstacking manners) with only 6 carbon rings; (ii) hybridizations (5–7 type M-carbon, W-carbon, H-carbon, F-carbon, S-carbon andX-carbon) of cubic-diamond and hexagonal-diamond segmentswith 5–7 rings interface; and (iii) mutations (4–8 type bct-C4,Z-carbon, Y-carbon, and oC32) of the hexagonal-diamond with4–8 ring interface. In present work, we propose a monocliniccarbon phase (M585), which consists of ABCA-stacked cubic-diamond-segments interlinked by interfacial zigzag carbon chains,

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Solid State Communications

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

n Corresponding author at: Hunan Key Laboratory for Micro-Nano EnergyMaterials and Devices, Xiangtan University, Hunan 411105, PR China.Tel.: þ86 732 52665818; fax: þ86 732 58292468.

E-mail address: jxzhong@xtu.edu.cn (J. Zhong).

Solid State Communications 181 (2014) 24–27

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

2. Calculation methods

All calculations of structure optimizations and property inves-tigations are carried out using the density functional theory withinlocal density approximation (LDA) [29,30] as implemented inVienna ab initio simulation package (VASP) [31,32]. The interac-tions between nucleus and the 2s22p2 valence electrons of carbonare described by the projector augmented wave (PAW) method[33,34]. A plane-wave basis with a cutoff energy of 500 eV is usedto expand the wave functions and the Brillouin Zone (BZ) samplemeshes are set to be dense enough (less than 0.21 �1) to ensurethe accuracy of our calculations. Crystal lattices and atom positionsof M585 and all the reference systems studied in present work arefully optimized up to the residual force on every atom less than0.005 eV/Šthrough the conjugate-gradient algorithm. The vibra-tional properties of M585 are investigated by the phonon package[35] with the forces calculated from VASP to evaluate its dynami-cal stability.

The elastic constants of M585 and all the reference systemsstudied in this work are calculated as the second-order coefficientin the polynomial function of distortion parameter δ used to fittheir total energies according to Hooke's law. In view of theirdifferences in crystal symmetries, different groups of deformationsare applied on different allotropes. The bulk modulus (B) andshear modulus (G) are evaluated according to Hill's formula [36]based on the calculated elastic constants. To further analyze thehardness of these carbon allotropes, we adopt the recentlyintroduced empirical scheme [37] to evaluate their Vicker's hard-ness (Hv) which is determined by their B and G as Hv¼2(G3/B2)0.585 �3.

3. Results and discussion

The structure of M585 was constructed through our previouslyproposed segment-combination-method. The optimized structuralcharacteristics of M585 are shown in Fig. 1 (a) and (b), including itscrystalline cell (in perspective view) and compositions of ABCA-staked cubic diamond segments and interfacial zigzag carbonchains. It has a monoclinic cell with lattice parameters ofa¼ 9:631 Å, b¼ 2:497 Å, c¼ 4:306 Å and β¼81.3151 and belongsto space group P21/m (No. 11). Nine inequivalent atoms in thiscrystal 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 comparableto that of diamond. Interestingly, M585 possesses a new topolo-gical type of 5–8–5, which is distinct from the previously proposedtwo types of 5þ7 and 4þ8. It can be considered as a combinationof ABCA-stacked cubic-diamond-segments interlinked by

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).

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

C. He, J. Zhong / Solid State Communications 181 (2014) 24–27 25

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 structu-rally related to perfect graphite. However, we find no any potentialpathways for transition from perfect graphite to M585. But it ismore energetically stable than M-carbon, Z-carbon, H-carbon andS-carbon. At zero pressure, its cohesive energy of �8.911 eV peratom (comparable to that of �8.913 eV per atom for the recentlyproposed 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 pressurerelative to graphite is shown in Fig. 1(c). The results indicate thatM585 and oC32 are more stable than graphite when the externalpressure is larger than 5 GPa. M585 and oC32 possess comparablestability 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 bepositive in previous literatures [3,9,10,13,28]. In this work, tofurther confirm the dynamic stability of M585, we investigate itsvibrational properties by PHONON package with atomic forcesapplied from VASP. The phonon band structure is shown in Fig. 2.We can see that there have been no any imaginary frequencies inthe phonon band structure, and we confirm that there have beenno any imaginary vibration modes in the phonon density of stateof M585. That is to say, M585 is a promising new carbon allotropein views of its remarkable energetic stability and positive dyna-mical stability.

We then investigate the electronic and mechanical propertiesof M585 and some other carbon allotropes for reference. Spacegroup, density, band gap, cohesive energy, bulk modulus andVicker's hardness of diamond, M-carbon, Z-carbon, H-carbon,S-carbon, oC32 and M585 are summarized in Table 1. Our resultsindicate that, as superhard intermediate phases between graphiteand diamond, M-carbon, Z-carbon, H-carbon, S-carbon, oC32possess densities, bulk modulus and Vicker's hardness close tothat of diamond, which are in good consistent with previousinvestigations. M585 possesses mass density of 3.507 g/cm3,which is comparable to that of diamond and equal to that ofZ-carbon. Its bulk modulus and Vicker's hardness values are462.30 GPa and 78.85 GPa, respectively, which are comparable tothose of all the previously proposed superhard carbon phases,indicating that M585 is also a superhard material.

All the previously proposed superhard carbon allotropes areoptically transparent due to their wide energy band gaps. Assummarized in Table 1, we can see that our calculated band gapsfor these carbon allotropes distribute in a range of 3.41–4.61 eV,exceeding the maximum energy value of the visible light. Theseresults are in good consistent with previous calculations. Theelectronic band structure of M585 at zero pressure is shown inFig. 3. We can see that it is an indirect band-gap semiconductorwith a band-gap of 4.21 eV, indicating that M585 is opticallytransparent too.

4. Conclusion

Based on segment-combination-method, we have proposed alow energy, optically transparent and mechanical superhard car-bon phase (M585) between graphite and diamond. It is morefavorable than the previously proposed M-carbon, Z-carbon,H-carbon and S-carbon and confirmed dynamically stable. M585can be considered as the combination of ABCA-stacked cubicdiamond segments interlinked by interfacial zigzag carbon chains.The interfacial boundary of 5–8–5 carbon ring in M585 suggests anew topological manner for predicting new carbon phases, whichis distinct to the previously proposed two types of 4þ8 and 5þ7.Our calculations indicate that M585 is an optically transparentinsulator with remarkable Vicker's hardness comparable todiamond.

Acknowledgments

This work is supported by the National Natural Science Foun-dation of China (Grant nos. 11074211 and 51172191), the NationalBasic Research Program of China (2012CB921303), and the HunanProvincial Innovation Foundation for Postgraduate (Grant No.CX2013A010).

References

[1] F.J. Ribeiro, P. Tangney, S.G. Louie, M.L. Cohen, Phys. Rev. B 72 (2005) 214109.[2] A.R. Oganov, C.W. Glass, J. Chem. Phys. 124 (2006) 244704.[3] Q. Li, Y.M. Ma, A.R. Oganov, H.B. Wang, H. Wang, Y. Xu, T. Cui, H.K. Mao,

G.T. Zou, Phys. Rev. Lett. 102 (2009) 175506.[4] K. Umemoto, R.M. Wentzcovitch, S. Saito, T. Miyake, Phys. Rev. Lett. 104 (2010)

125504.[5] R.H. Baughman, A.Y. Liu, C. Cui, P.J. Schields, Synth. Met. 86 (1997) 2371.[6] H.S. Domingos, J. Phys.: Condens. Matter. 16 (2004) 9083.[7] J.T. Wang, C.F. Chen, Y. Kawazoe, Phys. Rev. Lett. 106 (2011) 075501.[8] D. Selli, I.A. Baburin, R. Martoňák, S. Leoni, Phys. Rev. B 84 (2011) 161411(R).

Table 1Space 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 Fd-3m a¼ b¼ c¼ 3:536 Å 3.611 4.648 �8.997 514.15 88.02M-carbon C2/m a¼ 9:093 Å, b¼ 2:498 Å, c¼ 4:108 Å, β¼96.961 3.443 3.532 �8.821 447.33 75.45Z-carbon Cmmm a¼ 8:677 Å, b¼ 4:211 Å, c¼ 2:489 Å 3.507 3.414 �8.857 497.87 80.51H-carbon Pbam a¼ 7:792 Å, b¼ 4:757 Å, c¼ 2:497 Å 3.440 4.512 �8.845 466.92 83.29S-carbon Cmcm a¼ 2:496 Å, b¼ 11:293 Å, c¼ 4:857 Å 3.489 4.451 �8.896 486.29 83.50oC32 Cmmm a¼ 17:283 Å, b¼ 4:171 Å, c¼ 2:486 Å 3.553 3.282 �8.913 476.93 80.47M585 P21/m a¼ 9:631 Å, b¼ 2:497 Å, c¼ 4:306 Å, β¼81.3151 3.507 4.212 �8.911 462.30 78.85

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

C. He, J. Zhong / Solid State Communications 181 (2014) 24–2726

[9] M. Amsler, J.A. Flores-Livas, L. Lehtovaara, F. Balima, S.A. Ghasemi, D. Machon,S. Pailhès, A. Willand, D. Caliste, S. Botti, A.S. Miguel, S. Goedecker, M.A.L. Marques, Phys. Rev. Lett. 108 (2012) 065501.

[10] Z.S. Zhao, B. Xu, X.F. Zhou, L.M. Wang, B. Wen, J.L. He, Z.Y. Liu, H.T. Wang,Y.J. Tian, Phys. Rev. Lett. 107 (2011) 215502.

[11] C.Y. He, L.Z. Sun, C.X. Zhang, X.Y. Peng, K.W. Zhang, J.X. Zhong, Phys. Chem.Chem. Phys. 14 (2012) 8410.

[12] C.Y. He, L.Z. Sun, J.X. Zhong, J. Superhard Mater. 34 (2012) 386.[13] C.Y. He, L.Z. Sun, C.X. Zhang, X.Y. Peng, K.W. Zhang, J.X. Zhong, Solid State

Commun. 152 (2012) 1560.[14] D. Li, K. Bao, F.B. Tian, Z.W. Zeng, Z. He, B.B. Liu, T. Cui, Phys. Chem. Chem. Phys.

14 (2012) 4347.[15] J.T. Wang, C.F. Chen, Y. Kawazoe, Phys. Rev. B 85 (2012) 033410.[16] F. Tian, X. Dong, Z.S. Zhao, J.L. He, H.T. Wang, J. Phys: Condens. Matter. 24

(2012) 165504.[17] M. Amsler, J.A. Flores-Livas, S. Botti, M.A.L. Marques, S. Geodecker, arXiv:1202.

6030v1.[18] J.T. Wang, C.F. Chen, Y. Kawazoe, J. Chem. Phys. 137 (2012) 024502.[19] H.Y. Niu, X.Q. Chen, S.B. Wang, D.Z. Li, W.L. Mao, Y.Y. Li, Phys. Rev. Lett. 108

(2012) 135501.[20] R.L. Zhou, X.C. Zeng, J. Am. Chem. Soc. 134 (2012) 7530.

[21] Q. Zhu, Q. Zeng, A.R. Oganov, Phys. Rev. B 85 (2012) 201407.[22] F.P. Bundy, J. Chem. Phys. 46 (1967) 3437.[23] A.F. Goncharov, I.N. Makarenko, S.M. Stishov, Sov. Phys. JETP 69 (1989) 380.[24] M. Hanfland, H. Beister, K. Syassen, Phys. Rev. B 39 (1989) 12598.[25] W. Utsumi, T. Yagi, Science 252 (1991) 1542.[26] W.L. Mao, H. Mao, P.J. Eng, T.P. Trainor, M. Newville, C.C. Kao, D.L. Heinz,

J.F. Shu, Y. Eng, R.J. Hemley, Science 302 (2003) 425.[27] X.X. Zhang, Y.C. Wang, J. Lv, C.Y. Zhu, Q. Li, M. Zhang, Q. Li, Y.M. Ma, J. Chem.

Phys. 138 (2013) 114101.[28] M. Zhang, H.Y. Liu, Y.H. Du, X.X. Zhang, Y.C. Wang, Q. Li, Phys. Chem. Chem.

Phys. 15 (2013) 14120.[29] D.M. Ceperley, B.J. Alder, Phys. Rev. Lett. 45 (1980) 566.[30] J.P. Perdew, A. Zunger, Phys. Rev. B 23 (1981) 5048.[31] G. Kresse, J. Furthmüller, Phys. Rev. B 54 (1996) 11169.[32] G. Kresse, J. Furthmüller, Comput. Mater. Sci. 6 (1996) 15.[33] P.E. Blöchl, Phys. Rev. B 50 (1994) 17953.[34] G. Kresse, D. Joubert, Phys. Rev. B 59 (1999) 1758.[35] K. Parlinski, Z-.Q. Li, Y. Kawazoe, Phys. Rev. Lett. 78 (1997) 4063.[36] R. Hill, Proc. Phys. Soc. A 65 (1952) 349.[37] H.Y. Niu, P.Y. Wei, Y. Sun, X.Q. Chen, C. Franchini, D.Z. Li, Y.Y. Li, Appl. Phys. Lett.

99 (2011) 031901.

C. He, J. Zhong / Solid State Communications 181 (2014) 24–27 27