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Physics Letters A 325 (2004) 283–286

www.elsevier.com/locate/pla

Effect of substitutional atoms in carbon nanocones

Sérgio Azevedo

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

Received 14 February 2004; received in revised form 12 March 2004; accepted 16 March 2004

Communicated by R. Wu

Abstract

We apply first-principles calculations to investigate the effect of introducing substitutional boron or nitrogen in carbonanocones. The studies involve carbon nanocones with one and two pentagons in the tip. Nitrogen is shown to lower tof pentagon defect, while boronincreases. On the other hand boron substitutional, on the pentagon, lowers the gap energy0.95 eV, while nitrogen increases by 0.06eV. This suggests that the substitutional impurity could affect optical properties ocarbon nanocones. 2004 Elsevier B.V. All rights reserved.

Keywords: Nanocone; Defect; Energy

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1. Introduction

Curved nanoscale structures of which the bknown examples are carbon fullerenes and nanotuhave been the focus of increased scientific and teclogical interest, due to their unique electronic and mchanical properties [1–3]. The incorporation of petagonal atomic rings and others, increases the lcurvature and can lead to the closure of the tu[4]. The structure of the cap depends on the incluspecific defect, but generally it has the aspect oconical surface with electronic properties distinctthe bulk material [5]. The full replacement of carbin a graphite sheet by alternating boron and nitroatoms, forming hexagonal boron nitride, results inopening up of a large band gap, which remains es

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

0375-9601/$ – see front matter 2004 Elsevier B.V. All rights reserveddoi:10.1016/j.physleta.2004.03.065

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tially unaltered when the sheet is rolled up to formBN nanotube [6]. Another possibility are the C aBN nanocones [7–9]. An interesting possibility is tpartial substitution of carbon, leading to the formtion of binary CN or CB curve compounds, recenstudied by [10–13]. In the present study, we addrthe relative stability of CxN or B nanocones with onand two pentagons. We determine the formationergy for such nanocones, with an atom substitutioN, on and out defect, respectively. We also have sied the case of a boron atom on the defect. Besideobtain the energy gap for both cases.

A conical structure can be geometrically costructed by a “cut and glue” process, known as Volteprocess [14]. Examples of nanocones built in this wand used in our calculations are shown in Fig.Fig. 1(a) shows C nanocone with a five-membering, 60◦ disclination. Fig. 1(b) shows C nanocowith a N atom on five-membered ring. Fig. 1(c) sho

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284 S. Azevedo / Physics Letters A 325 (2004) 283–286

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Fig. 1. Stable nanocones: carbon, nitrogen and boron atomare represented by gray, blue and yellow, respectively. (a)bon nanocone with a pentagon, disclination of 60◦ , in the tip.(b) and (c) nanocones with substitutional nitrogen on and out derespectively. (d) Boron substitutional on defect, (e) carbon nanocwith two pentagons, disclination of 120◦ , in the tip. (f) Nanoconewith substitutional atom on defect. (For interpretation of the reences to colour in this figure legend, the reader is referred to theversion of this Letter.)

C nanocone with N atom on the six-membered riFig. 1(e), C nanocone with B atom on the pentagonFig. 1(d) C nanocone with two five-membered rin120◦ disclination, and finally Fig. 1(f), nanocone wiN substitutional atom on the pentagons.

Our ab initio methodology is based on the densfunctional theory [15] as implemented in the SIESprogram [16]. We use norm-conserving TroullieMartins pseudopotential [17] in the KleimnanBylander factorized form [18], and a doubleζ basis setcomposed of numerical atomic orbitals of finite ranPolarization orbitals are included for all atoms, andmake use of the generalized gradient approxima(GGA) [19] for the exchange-correlation potentiThe structures of thedoped and undoped nanoconwere obtained by minimization of the total energy uing the Hellmann–Feynmann force. The structuraltimization were performed using a conjugated gradprocedure until the residual force had values smathan 0.1 eV/A◦. The details of these calculations abetter described in Refs. [20,21].

2. Relative stability

We now proceed to a comparative analysis ofenergetic stability of the several nanocones descrin Fig. 1. In order to do so, we introduced the chemipotential theoretically calculatedµN, µB, and µCfor nitrogen, boron, and carbon, respectively. Tchemical potentialµN is obtained from solid nitrogein theα phase, while a metallicα −β is used to obtainthe chemical potentialµB. The chemical potentialµCis obtained from a C planar sheet. Since we are deawith finite clusters, we use hydrogen atoms to satudangling bonds at the edges. To take this additioH–C bonds into account, we introduce the respecchemical potential,µHC, which allow us to write theformation energy as

(1)Eform = Etot − nCµC − nxµx − nHCµHC,

whereEtot is the calculated total energy of the clustIn the above expression,nx is the number of B orN atoms,nC is the number of C atoms, andnHC isthe number of H–C bonds. A first constraint on thydrogen chemical potential is imposed by usingfinite planar sheet of carbon as reference, and ascria null value to its formation energy. This allows uswrite its total energy as

(2)EsheetT = nCCµbulk

CC + nHCµHC,

where nCC is the number of C–C pairs. Using thtotal calculations for the bulk and the finite sheet,find µHC.

The results obtained for the formation of the nancones, using the above procedure, are shown in Tafor nanocones with one and two pentagons, and boand nitrogen as substitutional impurity on defepentagon, or out defect, on hexagon. The underlinumbers in Table 1 indicate the most stable structuWe found, from Table 1, that the presence of nitrogon pentagon, actually lowers the formation eneof the nanocone by 0.94 eV. On the other hand,presence of nitrogen, out defect, lowers the energ0.31 eV. These results were obtained by calculathe difference in the total energy between a nanocin which the nitrogen is placed on the defect or odefect, and the pure carbon nanocone. This shthat the nitrogen lowers the energy cost for formatof pentagons. For the nanocone with substitutioboron, on the defect, the formation energy increa

S. Azevedo / Physics Letters A 325 (2004) 283–286 285

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Table 1Formation energies (in eV) of the carbon nanocones shown in Fig. 1 (third column). The electronic bandgap of each structure, at the GGA lis indicated in the fourth column. The underlined values indicate the most stable structure and lower gap energy respectively

Nanocone Impurity Position Eform (eV) Egap (eV)

one pentagon N on defect 4.01 1.21one pentagon N out defect 4.64 0.96one pentagon B on defect 5.73 0.26one pentagon (C) not not 4.95 1.15two pentagons N on defect 7.56 0.47two pentagons N out defect 8.14 0.47two pentagons (C) not not 8.21 0.93

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by 0.78 eV. For the case of nanocones with tpentagons in the tip, we obtain the formation enefor substitutional nitrogen on defect, out defect, apure carbon nanocone. Table 1, are given by 78.14, and 8.21 eV, respectively. Again here the Ndefect lowers the cost formation energy by 0.65compared to the pure carbon nanocone. This reconfirms the fact that N lowers the cost formatienergy of the pentagons.

We also investigated the reactivity of these strtures, with N or B like substitutional impurity. In Table 1, we can see the calculated gaps of nanocwith one pentagon in tip, a nitrogen atom on hexagFig. 1(c), the pure carbon nanocone Fig. 1(a), andone with boron atom on the defect Fig. 1(d), are 0.1.15 and 0.26 eV, respectively. These results indicthat substitutional boron, on pentagon, or nitrogen,defect, enhances the reactivity of the system and mfield-emission easier. Meantime the gap for the subtutional nitrogen on defect is 1.21 eV, therefore it dcreases the reactivity. For the case of nanoconestwo pentagons in the tip, the nitrogen as impurity sstitutional on the pentagons, and on hexagon, out dfect, has the same energy gap given by 0.47 eV. Thfore, we can conclude that exists an enhance ofreactivity.

3. Conclusions

In summary, we have investigated the energstability of substitutional atoms in carbon structuwith disclination, called nanocones. In this work wstudy nanocones with disclinations of 60◦ and 120◦,that corresponds to the nanocones with one andpentagons, respectively. We show that the more

,

ble structure are that presents nitrogen on the deNamely, our results confirm that the role of nitrogenthe formation of CN nanocones, it is lower the enecost for formations of pentagons. On the other hathe boron substitutional enhances the energy cosformations of pentagons. Besides, we investigatereactivity of these structures. We show that nitrogesubstitutional on the defect, and on the hexagon, incase with one pentagon in tip of nanocone, enhanthe gap energy by 0.06 eV and lowers by 0.19 eVspectively compared to carbon pure nanocone. Thethe boron substitutional on defect, in the with one ptagon, lower the energy gap by 0.89 eV. Therefore,can conclude that boron substitutional on defect, incase of nanocones with one pentagon, is more reathan nitrogen ones. For the case of two pentagonthe tip of nanocones, the gap energy for nitrogen sstitutional on and out defect is reduced by 0.46 eVboth cases, compared to carbon pure nanocone.the nitrogen substitutional becomes the structure mreactive in any place.

Acknowledgements

This work has been supported by CNPq. The coputational work was carried out at the LaboratórioEstrutura Eletrônica, Departamento de Física, Unisidade Federal de Minas Gerais.

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