Nuclear Instruments and Methods in Physics Research B 326 (2014) 37–40

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Nuclear Instruments and Methods in Physics Research B

journal homepage: www.elsevier .com/locate /n imb

Simulated carbon irradiation of carbon nanotubes – A comparative studyof interatomic potentials

0168-583X/$ - see front matter � 2014 Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.nimb.2013.10.042

⇑ Corresponding author. Address: Departamento de Física, Ingeniería deSistemas y Teoría de la Señal, Universitat de Alicante, 03080 Alicante, Spain.Tel.: +34 965903400 2031.

E-mail address: sheredia@ua.es (S. Heredia-Avalos).

Santiago Heredia-Avalos a,⇑, Juan Carlos Moreno-Marín a, Cristian D. Denton b

a Departament de Física, Enginyeria de Sistemes i Teoria de la Senyal, Universitat d’Alacant, Apartat 99, E-03080 Alacant, Spainb Departament de Física Aplicada, Universitat d’Alacant, Apartat 99, E-03080 Alacant, Spain

a r t i c l e i n f o

Article history:Received 28 June 2013Received in revised form 20 September 2013Accepted 2 October 2013Available online 23 January 2014

Keywords:Carbon nanotubesIon irradiationDefect annealingComputer simulations

a b s t r a c t

We simulate the irradiation of carbon nanotubes (CNT) with carbon ions using a molecular dynamicscode. In order to describe the interaction between carbon ions we use the Tersoff or Brenner potential,both joined smoothly to the Universal ZBL potential at short distances. We have analyzed the defects pro-duced after irradiation, the subsequent modification of the CNT structure, and their dependence on theused interatomic potential, the projectile energy (from 10 eV to 5 keV) and the dose.

For single projectile irradiation, we have obtained that the coordination defect number increases withthe projectile energy, although a saturation value is achieved at high projectile energies (�3 keV). Forcontinuous projectile irradiation, we have observed that for low energies (�10 eV) the accumulation ofadatoms produces a bump in the irradiated region. However, at intermediate energies (�100 eV) the irra-diation produces vacancies which are healed through non-hexagonal rings. This gives rise to a shrinkingof the CNT diameter in the irradiated region. Finally, if the projectile energy is high enough (�1 keV) thecontinuous irradiation produces the breaking of the CNT.

� 2014 Elsevier B.V. All rights reserved.

1. Introduction

Carbon nanotubes (CNTs) have attracted a lot of attention sincetheir discovery in 1991 [1] due to their outstanding electronic andmechanical properties [2]. CNTs can be metals or narrow bandsemiconductors depending on their chirality, so they can be idealcandidates for use in nanoelectronics [3]. CNTs have also extremelyhigh Young modulus and strength [4], so they can be used forreinforcements of other materials [2,5]. Many other excitingapplications for CNTs have emerged in the last years [2].

The irradiation of CNTs with energetic particles such as elec-trons, protons or ions can be used to change their properties [6].Energetic particles can be used to implant foreign atoms, create de-fects, produce amorphous regions or recrystallize the lattice. Thistechnique is specially suited for manipulation of CNTs since thegraphitic structure has a tendency to reconstruct the point defectsby saturating dangling bonds [7]. The irradiation with ion or elec-tron beams can also be used also to coalesce [8], weld [9], link [10]or cut [11] the CNTs.

Therefore, it is important to know how defects are produced onCNTs during irradiation and the changes induced in their structure

due to the saturation of dangling bonds. Several works, both theo-retical and experimental, have been devoted to the study of theeffects of the ionic irradiation in CNTs and related nanostructures[6,12–18].

In this paper we study the production of defects after irradia-tion of CNTs with carbon ions, using molecular dynamics simula-tions. We analyze the structural changes in CNTs after irradiationwith different incident energies and doses [12], and the influenceof the potential used to describe the atomic interactions. The usedenergy range in this study varies from 10 eV to 5 keV.

2. Simulation method

We have developed a simulation code based on classical molec-ular dynamics (MD) [19] in order to simulate the irradiation ofCNTs by carbon projectiles with incident energies from 10 eV to5 keV. It is worth to mention that we have neglected the electronicenergy-loss in our simulations because of the low projectile ener-gies involved in this work.

The forces acting on each particle were modelled by means ofempirical interatomic potentials. In order to make a comparativeanalysis, we describe the C–C interactions using two differentpotentials, i.e. the Tersoff potential [12,20] and the Brenner poten-tial [21]. In the case of the Brenner potential we have omitted thetime-consuming bond conjugation terms because they are not rel-evant for energetic collisions. In order to describe realistically close

Fig. 1. Average coordination defect number as a function of the incident projectileenergy, when using the Tersoff (open symbols) or Brenner (solid symbols) potentialto describe the atomic interactions, before (circles) and after the annealing stage(triangles). The dashed curves are depicted to guide the eye.

38 S. Heredia-Avalos et al. / Nuclear Instruments and Methods in Physics Research B 326 (2014) 37–40

collisions the empirical potentials were smoothly linked [12] to theZiegler–Biersack–Littmark (ZBL) universal potential at short inter-atomic distances [22].

We have used the velocity Verlet algorithm [19] to numericallysolve the equations of motion of all interacting atoms. In order todecrease the computing time, our code uses a variable time stepDt which depends on the maximum velocity and force.

To avoid the displacement of the CNT during the irradiationwith carbon projectiles, we have kept fixed the atoms at both endsof the CNT during the simulation. The CNT temperature is con-trolled using the Berendsen thermostat [23].

We have studied in our simulations a single-walled CNT, arm-chair (10, 10), with �100 Å in length, �7 Å in radius, and with itsaxis parallel to the z-axis. The CNT is attached by its ends, so bothends have fixed positions. The velocity of the carbon atoms locatedin a region of 5% of the total length of the CNT, next to its fixedends, are scaled according to the Berendsen thermostat, as de-scribed previously. The carbon projectiles bombard the CNT inthe direction perpendicular to the nanotube axis, although theexact impact coordinates are randomly distributed on a centralregion of 10% of the total length of the CNT.

We have divided our simulation in three consecutive stages: (i)the bombardment of the CNT with a carbon projectile and the sim-ulation of the dynamics of the system during 10 ps, with a thermo-stat temperature of 300 K; (ii) the annealing of the CNT during100 ps, being 2500 K (or 1500 K) the temperature of the Berendsenthermostat when using Tersoff [12,20] (or Brenner [21]) potential;and (iii) the cooling of the CNT to a temperature of 0 K during20 ps. The annealing temperature was chosen in such a mannerthat it is the highest possible, in order to stimulate the healing ofdefects, but without producing misleading defects on the CNT.We have observed that we can use higher temperatures whenusing the Tersoff potential.

The main damage mechanism during irradiation stage is thetransfer of energy from the projectile to the CNT, which resultsin the displacement of the atoms of the CNT structure, resultingin vacancies. Depending on the transferred energy, the primaryatoms can be backscattered, can replace or extract atoms of theCNT, or even they can be added to the CNT (adatoms).

In this work, we have studied two different situations in oursimulations: (i) we have evaluated the damage produced in theCNT due to single-ion irradiation and (ii) we have also analyzedthe damage caused by consecutive-ion irradiation.

3. Results and discussion

The bombardment of the CNT with carbon atomic projectilescauses damage, which can be evaluated through the formation ofdefects in the structure. According to previous authors [14], we as-sume that the coordination defect number N reflects quantitativelythe irradiation damage produced. This magnitude is defined as thenumber of carbon atoms with coordination number different thanthree.

In the following, we have studied how N depends on the projec-tile energy and on the potential used to describe the atomic inter-actions during single-ion irradiation. Because of the statisticalfluctuations on N, due to the fact that in our simulations the impactcoordinates of the projectile are randomly distributed on a centralregion of 10% of the total length of the CNT, we have made 200independent simulations for each incident energy, in order to getthe average of the coordination defect number hNi as a representa-tive value of N.

In Fig. 1 we present the results of the average coordination de-fect number hNi obtained after single-ion irradiation with carbonions of different incident energies, before (solid and open circles)

and after (solid and open triangles) the annealing stage of theCNT; the dashed curves were depicted to guide the eye. Opensymbols represent the results when using the Tersoff potential todescribe the atomic interactions, whereas solid symbols representthe results obtained for Brenner potential. All situations shownthat hNi reaches saturation values for incident energies higher that3 keV. As expected, after the irradiation, the annealing of the CNThelps the migration of vacancies and their recombination, so thatthe average coordination defect number significantly decreases. Itis worth to notice that before annealing, the use of Brenner poten-tial to describe the atomic interactions produces more defects thanthe use of Tersoff potential, which suggests that carbon atoms re-main more linked to the structure when using the Tersoff potential.These results show that hNi reaches different saturation values forhigh incident energies. In order to explain these results, we havecalculated the threshold displacement energies Eth for Brennerand Tersoff potentials using our simulation code. Our results showthat Eth,Brenner = 22.9 eV, whereas Eth,Tersoff = 24.3 eV, so these re-sults can explain that more defects are produced on the CNTs whenusing the Brenner potential. However, although using Tersoff andBrenner potentials give differences on hNi before the annealingstage, our simulations show that after the annealing, the use ofboth potentials give similar results, i.e. the coordination defectnumber increases with incident ion energy up to 3 keV, reachinga saturation value hNi � 9 at high energies.

Regarding the kind of defects generated, we have observed inour simulations that the irradiation with a carbon ion with lowenergies (E < 30 eV) causes the adhesion of the carbon atom tothe CNT wall (single adatom), which evolves after annealing tothe formation of a double-coordinated atom (bridge defect). How-ever, for higher projectile energies, the irradiation of the projectilealso causes the formation of vacancies, resulting in different sizeholes that can evolve after the annealing stage to non-hexagonalstructures.

On the other hand, we have studied the damage produced onthe CNT when it is successively irradiated with 200 carbon ionswith incident energies from 10 eV to 1 keV. We have depicted inFig. 2 the average coordination defect number as a function ofthe number of incident carbon ions; solid (or open) blue circlesrepresent the results when the incident energy of the carbonprojectiles is 10 eV and Tersoff (or Brenner) potential is used todescribe the atomic interactions, whereas solid (or open) red trian-gles are the results when the incident energy is 100 eV and Tersoff

Fig. 2. Average coordination defect number as a function of the number of ions thatbombard the CNT. Solid (or open) blue circles correspond to 10 eV incident energyand Brenner (or Tersoff) potential, whereas solid (or open) red triangles correspondto 100 eV incident energy and Brenner (or Tersoff) potential. The dashed curves aredepicted to guide the eye. (For interpretation of the references to colour in thisfigure legend, the reader is referred to the web version of this article.)

Fig. 3. Appearance of CNT after irradiation with 100 consecutive carbon ions withdifferent energies when using the Brenner potential to describe the atomicinteractions. Colours indicate the coordination number: white (1), red (2), blue(3), and violet (4). The green lines define the region under irradiation. (Forinterpretation of the references to colour in this figure legend, the reader is referredto the web version of this article.)

Fig. 4. Average CNT radius as a function of the CNT z-axis for different incidentenergies and doses. We have used Brenner potential to describe the atomicinteractions.

S. Heredia-Avalos et al. / Nuclear Instruments and Methods in Physics Research B 326 (2014) 37–40 39

(or Brenner) potential is used. The dashed curves are depicted toguide the eye. As expected, we have found in our simulations thatthe average coordination defect number grows with the ionic doseand incident energy. It is worth to mention that, regardless theinteratomic potential used, a saturation is observed for �50 projec-tiles with 100 eV incident energy. However, the results obtainedfor 10 eV projectiles suggest that higher doses are required toachieve the saturation on hNi. Fig. 2 also shows significant differ-ences on hNi when using Tersoff or Brenner potentials; the laterresulting in higher hNi. As the projectile incident energy increases,the number of defects created by each projectile grows and thesaturation value is reached for lower doses. The saturation valuesdepend on the potential used in the simulation, being lower forthe Tersoff potential, because the CNT is stiffer when using thispotential and it is more difficult to produce defects, which is inagreement with the different threshold displacement energiesobtained for both potentials. Notice that for a single projectile,the difference between the average coordination defect numberobserved for both potentials is almost hidden by the statisticalfluctuations of the simulation, however this systematic differencegives significant discrepancies as the number of incidentprojectiles increases.

The effects of the continuous irradiation on the CNT structure,depending on the energy of the incident projectile, are shown inFig. 3, in which we have depicted the appearance of the CNT afterirradiation with 100 carbon projectiles when using the Brennerpotential to describe the atomic interactions. The colours of theatoms represent their coordination number: white (1), red (2), blue(3), and violet (4). It is worth to notice the consequences of irradi-ation for different projectile energies. For projectiles with lowenergy (�10 eV), we observe the formation of adatoms in the wallsof the CNT, which evolve into bumps on the irradiated region,increasing the CNT radius. In this case, the number of carbon atomson the irradiated area increases, because the projectiles have notenough energy to extract atoms from the nanotube and they areusually captured. However, when the projectiles have higher ener-gies (�100 eV), we observe the formation of vacancies during theirradiation stage, which evolve into polygonal shapes during theannealing, and a progressive reduction of the CNT radius. Thereduction of the CNT radius can be explained by considering thatthe number of carbon atoms on the irradiated area decreases withthe dose, because in this case the projectiles have enough energy to

extract atoms from the CNT. Increasing the incident energy of theprojectile (�1000 eV) results in a higher damage, which could evenbreak the CNT in the irradiated area.

In order to quantify the changes in the structure after irradia-tion we have calculated the CNT radius R along the CNT. As thereare statistical fluctuation of R, due to the fact that the impactcoordinates of the projectile are randomly distributed on a centralregion of 10% of the total length of the CNT, we have made 10 inde-pendent simulations in order to get representative values of hRi inall the results shown in the following.

We have depicted in Fig. 4 the average CNT radius hRi along theCNT z-axis in order to analyse how it depends on the incident en-ergy and dose. Brenner potential is used to make these simulations.As expected, for low incident energies (10 eV), we have observedthat hRi significantly increases on the irradiated area, whereas forhigher incident energy (100 eV), hRi decreases; these changes onCNT radius increase with the dose.

Our simulations also show that the potential used to describethe atomic interactions affects the results obtained for hRi. Wehave depicted in Fig. 5 the average CNT radius has a function of

Fig. 5. Average CNT radius as a function of the CNT z-axis for different incidentenergies and potentials to describe the atomic interactions, after irradiation with200 consecutive projectiles.

Fig. 6. Extreme average CNT radius as a function of the number of ions thatbombard the CNT. Blue symbols correspond to a projectile energy of 10 eV, whilered symbols correspond to 100 eV. Full (open) symbols show the results when usingthe Brenner (Tersoff) interatomic potential. (For interpretation of the references tocolour in this figure legend, the reader is referred to the web version of this article.)

40 S. Heredia-Avalos et al. / Nuclear Instruments and Methods in Physics Research B 326 (2014) 37–40

the CNT z-axis for different incident energies after irradiation with200 consecutive projectiles; solid symbols correspond to the re-sults obtained when using the Brenner potential, whereas opensymbols correspond to those obtained when using Tersoff poten-tial. As previously observed, the CNT is more stiff when using theTersoff potential, being more difficult to produce defects, andtherefore, to change the CNT radius.

Finally, we have depicted in Fig. 6 the extreme (maximum orminimum) average radius hRiext of the CNT for 10 eV (or 100 eV)incident energy as a function of the dose. As expected, the hRiext in-creases with the dose for 10 eV incident energies, whereas hRiext

decreases with the dose for 100 eV incident energies. Howeverthere is a saturation of hRiext with the dose for both energiesconsidered here. As noted previously the changes of hRiext are morepronounced when using the Brenner potential.

4. Conclusions

We have developed a code based on molecular dynamics tosimulate the irradiation of nanostructures with atomic projectiles.In this work, we have used this code to study the damage producedon CNTs after irradiation with carbon ions with different energiesand doses. We have also studied how the potential used to describethe atomic interactions affects the simulation of the CNT damage.

We have observed that for low projectile incident energies(�10 eV) the defects are only adatoms, while vacancies are alsoobserved for higher energies. These defects evolve after annealingthrough the saturation of dangling bonds. The number of defectsgenerated by a single ion grows with projectile energy butsaturates at �3 keV.

We have also studied the effect of continuous irradiation of theCNT. For low energies the accumulation of adatoms produces abump in the irradiated region, which significantly increase theCNT radius. At intermediate energies the irradiation producesvacancies which evolve to non-hexagonal rings. This results intoa shrinking of the CNT radius in the irradiated region, which hasbeen observed before [13]. If the projectile energy is high enoughthe continuous irradiation produces the breaking of the CNT.Although the CNT structure after irradiation is qualitatively similarwith both interatomic potentials considered here, there are notice-able quantitative differences in the resulting radius of the CNT.

Acknowledgments

This work has been financially supported by the Spanish Minis-terio de Economía y Competitividad and the European RegionalDevelopment Fund (Project FIS2010-17225).

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