Physics Letters A 351 (2006) 109–112

www.elsevier.com/locate/pla

Energetic stability of B–C–N monolayer

Sérgio Azevedo

Departamento de Física, Universidade Estadual de Feira de Santana, km-03, Br-116 Norte, 44031-460 Feira de Santana, Ba, Brazil

Received 26 July 2005; received in revised form 19 October 2005; accepted 19 October 2005

Available online 27 October 2005

Communicated by R. Wu

Abstract

We investigate the relative stability of several BCN structures with 32-atoms unit cell using first-principles calculations. The compounds havethe topology of a graphite layer with carbon, nitrogen or boron atoms on each site. Our results indicated that formation energy of island-likeconfigurations is comparable to the strip-like pattern. We also find compounds that have the same number of B–N and C–N bonds presentdifferent energetic stability. In addition, we showed that C–N is favored over C–B bonds.© 2005 Elsevier B.V. All rights reserved.

PACS: 71.20.Tx; 71.15.Mb; 61.48.+c

1. Introduction

Considerable interest has recently centered on new ternaryBCN compounds that are attractive as superhard materials [1]and also as electrical materials [2–5]. The compounds in lay-ered structures are expected to behave as semiconductors withvarious band gap energies that can be controlled by their atomiccomposition, since intermediate between graphite and hexag-onal BN are expected to behave between a semi-metal andan insulator. This similarity has motivated the synthesis ofgraphite-like layered compounds where carbon atoms are par-tially substituted by boron and nitrogen. There has been mucheffort to synthesize the new BCN compounds, the first of whichwas reported by Badzian et al. [6], who tried a chemical va-por deposition (CVD) process with BC�3, CC�4, N2, and H2 asstarting materials. More recently [7–9], it were prepared amor-phous BC2N powders by mechanical milling with hexagonalBN and graphite as starting materials and CVD, respectively.

Theoretical researches on structures stability of such com-pounds were developed using first-principles methods, basedon pseudopotential local-orbital approach, semi-empirical, andsemi-classical method [2–4]. The theoretical study described inRef. [2] conclude that, using 8-atoms unit cell, the most stable

E-mail address: sazevedo@mail.uefs.br (S. Azevedo).

0375-9601/$ – see front matter © 2005 Elsevier B.V. All rights reserved.doi:10.1016/j.physleta.2005.10.053

structures seem to optimize the chemical bond energy by maxi-mizing the number of C–C and B–N bonds. In a recent work [3],a strip-like model was substituted by a chain-like one. Takingthe strips, containing from 1 to 4 chains of C–C and B–N withcells from 4 to 16 atoms, it was shown that the approach to seg-regation limit is energetically favorable for a BC2N system. InRef. [4], Nozaki and Itoh investigated the structural propertyof the layered compound, BC2N, by means of a semi-classicalmethod. From calculations, it has been found that the most sta-ble structures of BC2N are formed so as increase the number ofboth C–C and B–N bonds. In addition it is shown that structureswith the same number of nearest neighbor has the same ener-getic stability. In all these works the compound with strip-likepattern is the most stable.

In this work, first-principles calculations are applied to in-vestigate the relative stability of B–C–N monolayer, using dif-ferent models from these described in [1,2,4]. The study of32-atoms unit cell rather than 8-atoms, as described in [3,4],permit us to investigate, in addition strip-like pattern, island-like models. Namely, the analysis of the structural stability ofBCN systems based on the large-sized unit cell models, per-mit us to examine the dependence on the size of unit cell. Fromthis investigation we hope to contribute to understanding theformation of these structures, since there has been a contro-versy in the literature: some experiments suggest partial segre-gation between C and BN resulting in a island-like or strip-like

110 S. Azevedo / Physics Letters A 351 (2006) 109–112

Fig. 1. Seven stable structures BC2N with island, (a)–(d), and stripe patterns,(e)–(g), and two stable structures NC3, and BC3, (h) and (i), respectively. Ineach case, the unit cell shown contains thirty two atoms. Boron, carbon andnitrogen atoms are represented by white, grey, and black colors, respectively.

configurations [10], while others [11,12] favor to a model inwhich C, B, and N atoms are mixed.

We developed calculation for an isolated monolayer, sincethe main properties are expected to be dominated by the atomicarrangements in the graphite-like layers. Besides, the layerstacking problem along the y-axis is a difficult problem fromthe point of view of total energy considerations. The B–C–Nmonolayers studied are thus composed of periodically repeatedx–z plane layers, with thirty-two atoms, with an interlayer dis-tance d = 15 Å along the y-axis so that neighboring layers donot interact. In Fig. 1(a) exists a detailed description of the unitcell, from which the infinite monolayer is generating. The vec-tors �a1 and �b1 generate the 32-atoms unit cell, while the vectors

�a2 and �b2 translated the components of this unit cell, in such away that build the infinite monolayer.

Our ab initio methodology is based on the functional den-sity [13] as implemented in the SIESTA program [14]. We usenon-conserving Troullier–Martins pseudo-potentials [15] in theKleinman–Bylander factorized form [16], and a double ζ ba-sis set composed of numerical atomic orbital of finite range.Polarization orbital is included for all atoms, and we makeuse of the generalized gradient approximation (GGA) [17]for the exchange-correlation potential. The BC2N compoundswere obtained by minimization of the total energy using theHellman–Feynman force. The structural optimization were per-formed using a conjugated gradient procedure until the residualforce reached values smaller than 0.05 eV/Å.

The lattice parameter was optimized for each structure. Thebond lengths in the relaxed structures are dCC = 1.44 Å, dCN =1.40 Å, dCB = 1.53 Å, and dBN = 1.45 Å.

2. Energetic stability

In order to address the energetic of BCN monolayer, we mustdistinguish the different techniques that can be employed intheir synthesis. In each case, we introduce suitable theoreticalchemical potentials for nitrogen (μN), boron (μB), and carbon(μC). For the case in which the BCN monolayer is obtained bylaser ablation, arch discharge, or solid-state reaction inducedby electron-beam irradiation, we can have either a nitrogen ora boron-rich environment, depending on the atomic reservoiremployed. In the N-rich environment μN = −270.22 eV is thetotal energy per atom of the α–N2 phase of solid nitrogen, whilea metallic α–B phase, μB = −77.23 eV, is used as the reservoirfor the B-rich environment. In both cases, μN and μB are linkedby the thermodynamic constraint

(1)μN + μB = μlayerBN ,

where μlayerBN = −350.17 eV, is the chemical potential per BN

pair in the infinite planar sheet.The chemical potential for carbon, similarly to boron nitride,

is obtained from a graphite sheet calculation, which result inμCC = −309.72 eV. Using these chemical potentials, and tak-ing as reference of energy to be the completely segregated limit(energy of C2 and BN dimmers respectively in pure graphiteand hexagonal BN), and ascribing a null value to its formationenergy, the formation energies of the BCN monolayers can bewritten as

(2)Eform = Etot − nBμB − nNμN − nCμC,

where Etot is total energy of a monolayers derived from a su-percell calculation of thirty-two atoms. The factors nB, nN, andnC are numbers of B, N, and C atoms, respectively. Besides, onthe basis of such total energy calculation, Eq. (2), it is clear thatin the thermodynamic limit, BC2N compounds will be driventoward complete segregation.

In the case of the BC2N compounds nBN = nCC = 8, there-fore Eq. (2) can be rewritten as

(3)Eform = Etot − 8(μBN + μCC).

S. Azevedo / Physics Letters A 351 (2006) 109–112 111

Then we can conclude from Eq. (3), that the formation energyof the BC2N independent on the environment. On the otherhand, BC3 or NC3 structures, nB(N) = 8 and nCC = 12, leadus

(4)Eform = Etot − 8μB(N) − 12μCC.

In the case of the BC3 monolayer, we have N-rich envi-ronment, therefore the chemical potential μN = −270.22 eV,α–N2 phase of solid nitrogen, and chemical potential for theboron is given by

(5)μB = μBN − μN = −350.17 + 270.22 = −79.97 eV.

Similarly for the NC3 compound, in B-rich environment, μB =−77.23 eV, and the chemical for the nitrogen can be obtainedby

(6)μN = μBN − μB = −350.17 + 77.23 = −272.94 eV.

Details of this approach are better described in Refs. [18–21].

3. First-principles results

There are not experimental data for detailed crystal struc-tural of BC2N, and the size of the unit cell of this material isnot known at the present, because of the lack of high qualityBC2N samples. In systems where thirty two constituent atomsare constrained in the unit cell, 46 898 310 polymorphic struc-tures, without any B–B and N–N bonds, are possible [4] whenthe structural model is restricted to monolayer unit cells. It wasshown [1,3,4] that the more stable compounds display the max-imum number of C–C and B–N bonds. Therefore, in this work,we investigate BC2N monolayer with strip and island patternwhere the number of C–C and B–N bonds are maximized. Be-sides, we studied the BC3 and NC3 structures with the goal ofverify whether B–C are favored over N–C bonds or vice versa.

The unit cells of our BCN sheet are shown in Fig. 1.We considered three different stoichiometries, namely, BC2N(Fig. 1(a)–(g)), NC3 (Fig. 1(h)), and BC3 (Fig. 1(i)). The BC2Ncompounds present island (Fig. 1(a)–(d)) and strip (Fig. 1(e)–(g)) pattern. Fig. 1(a) and (b), (e) and (g) have the same numberof B–N, C–C, B–C, and N–C bonds.

Our first-principles results for the formation energy of theseveral structures, described in Fig. 1, are presented in Table 1.The second column shows the formation energy of these struc-tures; in other columns are displayed the bond number for theseveral island-like and strip-like structures.

Among all structures with a BC2N stoichiometry investi-gated, we found to be most stable, underlined values, the com-pounds that display maximum number of C–C and B–N bonds.Therefore, our results confirm the same trend obtained in earlyworks, where was used unit cell with 8 and 16 atoms, respec-tively.

We can see from Table 1, that a and f monolayer, most sta-bles, display strip and island pattern, respectively. The differ-ence for the formation energy between these two structures iswithin 0.01 eV/atom. Soon this energy difference is not mean-ingful, since it is within of the numerical uncertainty. Therefore,

Table 1Formation energies (in eV/atom), second column, and number of bonds, fromthird to sixth column, of the BCN monolayer shown in Fig. 1. The underlinednumbers exhibit the two most stable structures, as indicated in the second col-umn

Structure Eform (eV)/atom B–N C–C B–C N–C

a 0.18 19 19 5 5b 0.19 19 19 5 5c 0.24 18 18 6 6d 0.28 17 17 7 7e 0.25 16 16 8 8f 0.17 20 20 4 4g 0.36 16 16 8 8h 0.91 24 0 0 24i 1.01 24 0 24 0

such results permit us to conclude, that it is not possible, at leastfrom the point of view of energetic, to decide whether BC2Ncompounds, with unit cell of thirty-two atoms, can present strip-like or island-strip segregation. Besides it is shown that infinitemonolayer with the same number of C–C, B–N, N–C, and B–Cbonds can present different values for formation energy. As wecan see, the BC2N geometries present first-neighbor configu-ration energetically degenerate, namely configurations with thesame bonding topology displaying different values for forma-tion energy. For example, the values for structures a and b, ande and g, are 0.01 and 0.11 eV/atom, respectively. Again, thefirst one is not meaningful, however the second one is meaning-ful. Therefore, such results lead to conclude that the approachof stability based on first-neighbor (number bonds), only, doesnot describe totally such systems. We also found, see Table 1(Fig. 1(h) and (i)), that the compounds with same number ofC–C and B–N bonds, and different numbers of N–C and B–Cones, present different formation energy. Namely, compoundsthat display N–C is more stable than their similar with B–Cones. Therefore, we can conclude that N–C are favored overB–C bonds.

4. Conclusions

We used first-principles calculation to address the questionof how stable are BC2N, with 32-atoms in cell unit, compoundsdisplaying island-like and strip-like configurations respectively,in addition of NC3 and BC3 monolayer. It has been shown thatthe formation energy of island pattern can be compared to stripone. Soon, ours results indicated that island-like is so probablyas strip-like segregation, result that is not possible to obtain, us-ing models with eight or sixteen atoms. Also, we found thatstructures with identical numbers of C–C, B–N, C–N, and B–Cbonds can present different stability. This suggest that it is nec-essary, in addition to approach of numbers bonds, a method thatinclude, maybe, second neighboring to explain energetic sta-bility. Besides, we showed that N–C is more stable than B–Cbonds. Then, we can conclude, from the results obtained in thiswork, that most stable monolayer maximize C–C, B–N bondsfavored C–N ones. Namely, the BC2N system is always thermo-dynamically unstable towards segregation of carbon and boronnitride, which minimize the number of C–N and C–B bonds.

112 S. Azevedo / Physics Letters A 351 (2006) 109–112

Acknowledgements

We acknowledge to the financial support from the BrazilianAgency CNPq, and Fundação de Amparo a Pesquisa do Estadoda Bahia, FAPESB.

References

[1] A.Y. Amy, M.L. Cohen, Science 245 (1989) 841.[2] A.Y. Amy, M.L. Cohen, Phys. Rev. B 41 (1990) 10727.[3] X. Blase, J.-Ch. Charlier, A. de Vita, R. Car, Appl. Phys. A 68 (1999) 293.[4] H. Nozaki, S. Itoh, J. Phys. Chem. Solids 57 (1996) 41.[5] S. Azevedo, M.S.C. Mazzoni, H. Chacham, R.W. Nunes, Appl. Phys.

Lett. 82 (2003) 2323.[6] A.R. Badzian, T. Niemysky, E. Olkunisk, in: F.A. Glaski (Ed.), Proceed-

ings of the International Conference on Chemical Vapor Deposition, vol. 3,American Nuclear Society, Hinsdale, IL, 1972, p. 717.

[7] B. Yao, W.J. Chen, L. Amy, B.Z. Ding, W.H. Su, J. Appl. Phys. 84 (1998)1412.

[8] T. Sasaki, M. Akaishi, S. Yamaoka, Y. Fujiki, T. Oikawa, Chem. Mater. 5(1993) 695.

[9] J. Kouvetakis, T. Sasaki, C. Chen, R. Hagiwara, M. Lemer, K.M. Krisnan,N. Barlett, Synth. Met. 34 (1989) 1.

[10] Y. Zhang, K. Suenaga, C. Colliex, S. Iijima, Science 68 (1996) 2962.[11] D. Golberg, P. Dorozhkin, Y. Bando, M. Haregawa, Z.-C. Dong, Chem.

Phys. Lett. 359 (2002) 220.[12] M.O. Watanabe, S. Itoh, K. Mizushima, Appl. Phys. Lett. 68 (1996) 2962.[13] W. Kohn, L.J. Shan, Phys. Rev. 140 (1965) A1133.[14] D. Sanchez-Portal, P. Ordejon, E. Artacho, J.M. Soler, Int. J. Quantum

Chem. 65 (1997) 453.[15] N. Troullier, J.L. Martins, Phys. Rev. B 43 (1991) 1993.[16] L. Kleinman, D.M. Bylander, Phys. Rev. Lett. 48 (1982) 1425.[17] J.P. Perdew, K. Burke, M. Enrzerhof, Phys. Rev. Lett. 77 (1996) 3865.[18] S.S. Alexandre, H. Chacham, R.W. Nunes, Phys. Rev. B 63 (4) (2001)

045402.[19] S.S. Alexandre, M.S.C. Mazzoni, H. Chacham, Appl. Phys. Lett. 75

(1999) 61.[20] R.J. Baierle, S.B. Fagan, R. Mota, A.J.R. da Silva, A. Fazzio, Phys. Rev.

B 64 (2001) 085413.[21] S. Azevedo, M.S.C. Mazzoni, R.W. Nunes, H. Chacham, Phys. Rev. B 70

(2004) 205412.