Computational Materials Science 93 (2014) 15–21

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Computational Materials Science

journal homepage: www.elsevier .com/locate /commatsci

Irradiation effects in single-walled carbon nanotubes: Density-functionaltheory based treatments

http://dx.doi.org/10.1016/j.commatsci.2014.06.0150927-0256/� 2014 Elsevier B.V. All rights reserved.

⇑ Corresponding author at: The Key Laboratory of Beam Technology and MaterialModification of Ministry of Education, College of Nuclear Science and Technology,Beijing Normal University, Beijing 100875, China. Fax: +86 10 62231 1765.

E-mail address: fszhang@bnu.edu.cn (F.-S. Zhang).

Chao Zhang a,b, Fei Mao a,b, Jinxia Dai a,b, Feng-Shou Zhang a,b,c,⇑a The Key Laboratory of Beam Technology and Material Modification of Ministry of Education, College of Nuclear Science and Technology, Beijing Normal University, Beijing100875, Chinab Beijing Radiation Center, Beijing 100875, Chinac Center of Theoretical Nuclear Physics, National Laboratory of Heavy Ion Accelerator of Lanzhou, Lanzhou 730000, China

a r t i c l e i n f o a b s t r a c t

Article history:Received 11 February 2014Received in revised form 10 June 2014Accepted 12 June 2014

Keywords:Density-functional theoryTight-bindingCarbon nanotubeCollision dynamicsDefect

The collision process of a low-energy carbon ion impinging single-walled carbon nanotubes is studied byusing a self-consistent-charge density-functional tight-binding molecular dynamics method. The simula-tion shows that the outcome of the collision highly depends on the incident kinetic energy and the impactlocation in the nanotube. There are five types of processes observed: adsorption, reflection, substitution,penetration and damage. The adsorption process becomes dominant at energies lower than 20 eV. Defectformation events are observed at energies larger than 20 eV. For this process, 5-1DB, 5-8-5, Stone–Wales,7-4-5-9-5 and 5-7-7-6-5 defects are obtained. The formation processes of the typical defects aredescribed in detail. Moreover, the energy exchange and the charge transfer between the incident carbonion and the nanotube have also been quantitatively studied.

� 2014 Elsevier B.V. All rights reserved.

1. Introduction

Carbon nanotubes (CNTs) [1] are promising building blocks ofnanotechnology for the production of nanoscale devices andnanomachines due to their unique low dimensional nanostructuresand fascinating properties [2–10]. Unfortunately, numerous exper-imental studies reveal that there are various defects present inactual CNTs [11–13], such as vacancies, Stone–Wales (SW) defectand inverse Stone–Wales (ISW) defect. These defects can deterio-rate the properties of the material [14].

On the other hand, defects in CNTs can achieve or enhance somedesired functionalities. The intertube links between nanotube bun-dles can give rise to improvements in the mechanical properties[15]. Arþ ion bombardment of CNTs provokes a dramatic increasein the electrical resistivity of the tube, which indicates that evena small number of defects may significantly modify the conduc-tance of CNTs because of their quasi-one-dimensional structure[16,17]. Therefore, it is necessary to take effective measures tomanipulate the structure of CNTs with desirable goals.

It is an important method to modify material properties byenergetic particle beams irradiation, which has also been used to

harness the structure and properties of CNTs to achieve the desiredfunctionalities [18–22]. Ion beam can be used to cut CNTs or weldthem together to form molecular junctions and multiterminal het-erojunctions which could be incorporated into ultralarge scaleintegrated circuits implemented in CNTs networks [19]. Ion irradi-ation can also be used to chemically functionalize nanotubes, andto fabricate ultrathin metal nanowires with CNTs as masks againstirradiation, as an alternative to the conventional electron-beamlithography [20,21].

Moreover, although a large number of theoretical work has beendevoted to study the irradiation effects in the CNTs [23–25], thereare still some problems that need to be studied further, such asthe location effects on irradiation damage in the CNTs, the collisiondynamical processes of production and evolution of defects, theenergy exchange and the charge transfer between the projectileand the target atoms, and so on.

In this work, we study the collision dynamical process of a low-energy carbon ion impinging single-walled carbon nanotubes byusing a molecular dynamics (MD) method, in which the electronicstructure is computed on the fly within the framework of the self-consistent-charge density-functional tight-binding (SCC-DFTB)theory [26–30]. We specifically investigate the effects of the inci-dent kinetic energy and the impact location on the outcome ofthe collision, the formation processes of some typical defects, andthe energy exchange and the charge transfer between the incidentcarbon ion and the nanotube.

16 C. Zhang et al. / Computational Materials Science 93 (2014) 15–21

After the introduction, we briefly review the simulation methodand the model system in Section 2. In Section 3, we review theresults for the incident energy and the impact location effects onirradiation damage in carbon nanotube, the formation processesof typical defects, as well as the charge transferred from the nano-tube to the incident carbon ion. The conclusion is presented at theend of the paper.

Fig. 1. Schematic representation of the simulation setup. The inset shows theselected points where the incident carbon ion hits the nanotube. According to thesymmetry of the nanotube, ten group points are chosen, which are labeled as: filledcircles (Group a), filled down triangles (Group b), filled pentagons (Group c),filled triangles (Group d), filled squares (Group e), open hexagons (Group f), opentriangles (Group g), open circles (Group h), open squares (Group i) and opendown triangles (Group j), respectively.

2. Methods

The SCC-DFTB method has already been described at length inseveral publications [31–33], and therefore we present here onlythe details essential for this study. The total energy for thedensity-functional theory (DFT) is expanded to the second orderaround a given reference electron density q0ð~rÞ:

Etot ¼Xocc

i¼1

hWijbH0jWii �12

Z Z 0 q0q00j~r �~r0jd

~r0d~r

þ Excðq0Þ �Z

Vxcðq0Þq0d~r þ Eii

þ 12

Z Z 0 1j~r �~r0j þ

d2Exc

dqdq0jq0

!dqdq0d~r0d~r; ð1Þ

where bH0 and Wi represent the Kohn–Sham (KS) Hamiltonian andorbitals expanded in a minimal basis of pseudoatomic orbitals(Wi ¼

Plcli/l), respectively. Exc and Vxc denote the exchange–cor-

relation (xc) energy and potential, respectively. The term Eii indi-cates the ion–ion repulsion potential.

The density fluctuations dqð~rÞ ¼ qð~rÞ � q0ð~rÞ in the second-order term are written as a superposition of atomic contributionsdqa. The dqa is approximated by atomic charge fluctuations Dqa,

dq ¼X

adqa �

Xa

Dqa ¼X

aðqa � q0

aÞ: ð2Þ

The charge difference between the atom in the molecule (qa) and itsneutral form (q0

a) is calculated via a Mulliken analysis.This article concentrates on a (10,0) single-walled CNT, with the

supercell containing 400 carbon atoms. Periodic boundary condi-tion along the tube axis is used. Test calculations for longer nano-tubes give essentially the same results. The initial temperature ofthe target atoms is zero. For direct analogy with experiments, werefer to the incoming atoms as ions throughout the text. This illus-trates that the initial charge of the incoming particle is zero. Theincident carbon ion with the incident energy ranging from 0.01to 100 eV moves perpendicularly to the center axis of the tubefrom a site, which is initially located with sufficient separationabove the tube to ensure no interaction with the atoms in thenanotube. In addition, ten symmetric points are chosen to studythe impact location effect on irradiation damage. The simulationsetup is shown schematically in Fig. 1.

Nuclear motion is followed by Newton’s equation with thevelocity Verlet algorithm. To ensure proper total momentum andenergy conservations, the timestep is chosen 0.1 fs during the col-lision phase. For each collision event, the evolution time is at least10 ps in order to obtain energetically favorable configuration. Inorder to improve convergence in the iterative self-consistent-charge scheme, we employ a Fermi–Dirac smearing with electronictemperature Tel ¼ 1000 K, which has a similar effect to averageover many electronic states near the Fermi level. One should notethat the energy of the electronic subsystem (including the projec-tile, the nanotube and the interactions between the projectile andthe nanotube) is fixed by the conservation of the number ofelectrons in the system. When the projectile collides with thenanotube, the electronic energy level of the nanotube will change

because of the charge transfer between the projectile and thenanotube. Thus the Fermi energy of the nanotube is not fixed.

3. Results and discussion

3.1. Incident energy dependence of the dynamical process

Fig. 2a–c and d–f show the time evolutions of the kinetic energy(Ek), the change in the potential energy (DEp) of the system and thedistance (D) between the projectile and the center of mass of thenanotube when the incident energy (Ein) is 13 eV and 100 eV forthe group a (see Fig. 1), respectively.

At Ein ¼ 13 eV, one can find that from Fig. 2a the Ek increasesslightly to the maximum 14.7 eV at about 126 fs, while the DEp

(see Fig. 2b) decreases slightly to the minimum �1.8 eV. The rea-son is that the target atoms of the nanotube attract the incidentcarbon ion. After 126 fs, the Ek is followed with a sudden fall andthen rise, and the DEp rises and then drops promptly. This isascribed to the incident carbon ion colliding with the primaryknock-on atom (PKA) and occupying the original position of thePKA. As shown in Fig. 2c, the distance between the incident carbonion and the center of mass of the nanotube is finally about 3.95 Å,which is close to the radius (3.90 Å) of the (10,0) single-walledCNTs. After obtaining the energy from the projectile, the PKA even-tually moves towards the rear surface of the tube, and finally isadsorbed on the rear surface in the nanotube.

At Ein ¼ 100 eV, there are two local minimums for the Ek (seeFig. 2d) at about 48 fs and 67 fs, respectively, and two local maxi-mums for the DEp (see Fig. 2e). The first local maximum is due tothe projectile impinging the PKA and occupying its original posi-tion (see Fig. 2f), which is similar to that for Ein ¼ 13 eV. The reasonfor the second local maximum is that the PKA collides with the sec-ondary knock-on atom (SKA) on the rear surface of the nanotube,and occupies the original position of the SKA, finally the SKAescapes out of the nanotube. The phenomenon can be easilyobserved in the CNTs with the even chiral indices, because thePKA can easily penetrate through the hexagonal ring within therear surface for odd chiral indices, but for even ones a nearlyhead-on collision between the PKA and the SKA on the rear surfacewill occur [25].

3.2. Incident energy and impact location effects on irradiation damage

In this section, we will show, when the incident energy rangesfrom 0.01 to 100 eV, the effects of the incident energy and theimpact location on the irradiation damage.

0

8

16

24

t (fs)

(d)

D (

Å)

(a)

(e)

(b)

(f)(c)

00 120 180 240 300 0 30 6 0 60 9 1200

8

16

24

t (fs)

6

9

12

15

Ek (

eV)

50

75

100

0

3

6

0

25

50D

Ep (

eV)

D (

Å)

DE

p (eV

) E

k (eV

)

Fig. 2. Time evolutions of the kinetic energy (Ek), the change in the potential energy (DEp), and the distance (D) between the projectile and the center of mass of the nanotubeare shown in (a–c) and (d–f), corresponding to the incident energies of 13 eV and 100 eV for the group a, respectively.

C. Zhang et al. / Computational Materials Science 93 (2014) 15–21 17

The interactions between the projectile and the nanotube in thebombardment simulations reveal five processes: adsorption,reflection, substitution, penetration and damage. Fig. 3 shows theprobabilities of the five processes as functions of the incidentenergy. At energies lower than 10 eV, the adsorption process isdominant (the projectile is adsorbed on the nanotube after colli-sion). The probability for this process is almost 100%. As the inci-dent energy increases, the probability decreases rapidly, almostzero at 70 eV.

For Ein > 10 eV, the substitution process is observed. In thiscase, the projectile collides with a target atom in the nanotubeand occupies the original position of the target atom. The targetatom leaves its original position after collision. Finally, it becomesan adatom on the nanotube or escapes out of the nanotube. Thereis a non-monotonic trend in the relationship between the probabil-ity for the substitution process and the incident energy. The prob-ability reaches the maximum 70.27% at Ein ¼ 30 eV, and decreasesto 16.22% at Ein ¼ 100 eV.

In addition, damage is observed at energies greater than 20 eV.The probability of the damage increases with the incident energyincreasing, which increases to 75.68% at 100 eV (see Fig. 3). Theresult is similar to that obtained by using empirical potentialssimulations reported in Tolvanen et al. for the (8,8) single-walled

Fig. 3. Probabilities of adsorption, reflection, substitution, penetration and damageas functions of the incident kinetic energy. The probabilities are calculated bymultiplying the weight value associated with the symmetry of the tube.

CNTs [23]. In the Ref. [23], the total number of defects rapidlyincreases in the incident energy ranging from 50 eV to 700 eV.The discrepancy for the minimum kinetic energy of incident ionsrequired to create defects is attributed to the different diametersand chiralities of the CNTs, and the different bonding interactions[34].

For this process, we not only observe the formation of the5-1DB [35], 5-8-5 and SW defects (see Fig. 4a–c), but also find7-4-5-9-5 (74595) and 5-7-7-6-5 (57765) defects (see Fig. 4e andf, respectively). Meanwhile, a carbon trimer, C3, is observed inthe hollow core of the nanotube, as shown in Fig. 4d. The probabil-ities for the reflection process and the penetration process arelower in the range of energies. The probability of the penetrationprocess is only about 8.1% at 100 eV. The reason is that the incidentcarbon ion not only penetrates through the front wall of the nano-tube but also the rear wall in this case.

We next investigate the impact location effect on the radiationdamage formed in the nanotube. The types of processes for eachimpact location in a wide range of incident energies are presentedin Table 1. For Ein 6 1 eV, the type of event is independent of theimpact position and the incident energy. The incident carbon ionsare adsorbed on the bridge site, which can be clearly seen in VideoS1. At Ein ¼ 10 eV, adsorption is still the preferred process at mostof the impact positions unless in the group f. The reason is that therepulsive interaction is dominant when the incident ion rapidlymoves to the center of the hexagon. However, there is not enoughkinetic energy for the projectile to overcome the potential barrierso that it is finally reflected for the group f (see Video S2). At20 eV, the substitution process is observed in the groups a, h andj, while for the group f, the incident carbon ion penetrates throughthe front surface of the tube, and finally is adsorbed on the rearsurface inwardly (see Video S3). Moreover, we study the irradia-tion process of single-walled CNTs with a carbon ion at Ein ¼20 eV for the group f by employing the non-SCC DFTB method[31], and find that the incident carbon ion not only easily pene-trates through the front surface, but also the rear surface of thetube (see Video S4), which is not the same with the result calcu-lated by using the SCC-DFTB method. This shows that the chargetransfer between the incident carbon ion and the nanotube cer-tainly plays a significant role in the collision process.

For 30 eV 6 Ein 6 100 eV, there are a variety of dynamic pro-cesses related to the impact position and the incident energy. For

18 C. Zhang et al. / Computational Materials Science 93 (2014) 15–21

the group a, the incident carbon ion occupies the original positionof the PKA after collision. The PKA collides with the secondaryknock-on atom (SKA) on the rear surface of the nanotube, andoccupies the original position of the SKA. Finally the SKA escapesout of the CNTs. For the group f, the incident carbon ion penetratesthrough the hexagonal rings in the front wall and the rear wall ofthe nanotube, respectively. Therefore, for the groups a and f, thereis no damage observed in the tube, and the nanotube remainsone-dimensional crystal structure after collision. For the groups eand j, we observe the formation of the 5-8-5 defect, which is from

Fig. 4. Typical defect configurations after the energetic carbon ion colliding withthe (10,0) single-walled CNTs. (a)–(f) show the 5-1DB defect, 5-8-5 defect, SWdefect, the carbon trimer C3, 7-4-5-9-5 (74595) and 5-7-7-6-5 (57765) defects,respectively. Carbon atoms in the vicinity of the defect are labeled as dark blue ball.The green balls in (d) and (e) indicate the incident carbon ions. (For interpretation ofthe references to color in this figure legend, the reader is referred to the web versionof this article.)

Table 1Results of irradiating the (10,0) single-walled CNTs with a carbon ion at several impact pre = reflection, sub = substitution, DB = 5-1DB defect, 585 = 5-8-5 defect, SW = Stone–WaC3 ¼ carbon trimer. E1/E2 deNotes 1/2 target atom(s) escaping from the nanotube, respec

Impact positions/Ein 0.01 eV 0.1 eV 1 eV 10 eV

Group a Ads Ads Ads AdsGroup b Ads Ads Ads AdsGroup c Ads Ads Ads AdsGroup d Ads Ads Ads AdsGroup e Ads Ads Ads Ads

Group f Ads Ads Ads ReGroup g Ads Ads Ads AdsGroup h Ads Ads Ads AdsGroup i Ads Ads Ads AdsGroup j Ads Ads Ads Ads

the reconstruction of divacancies. What’s more, a carbon trimer C3

is also found in the hollow core of the nanotube, which consists ofthe incident carbon ion and two target atoms (see Fig. 4d). Thereare many impact locations where the target atoms are able toescape out of the nanotube, such as the groups b, d, h, i and j.

3.3. Formation processes of typical defects

To understand the formation processes of defect configurationsafter colliding, the time evolutions of SW and 57765 defects aredescribed in Figs. 5 and 6, respectively. Fig. 5 shows atomic pro-cesses for the group h at the incident energy of 70 eV. At 53 fs,the incident carbon ion labeled as 1 forms new bonds with atoms2, 4 and 5. At 65 fs, atom 2 breaks bonds with atoms 1, 3, 4 and 5.At the same time, atom 1 breaks bonds with 4 and 5, and pene-trates through the front surface of the nanotube. As time proceeds,atom 1 eventually moves towards the rear surface of the tube, andis adsorbed on the rear surface outwardly at the end of thesimulation.

At 73 fs, atom 3 breaks bonds with atoms 6 and 7, and a diva-cancy is formed on the front surface. The defective lattice area isenergetically unstable due to the dangling bonds. Atoms nearbythe divacancy will saturate the dangling bonds during the relaxa-tion process. Atoms 2 and 3 diffuse to make bonds with the unsat-urating atoms 5 and 6 in the time range from 99 to 150 fs,respectively. At about 200 fs, a similar 5-8-5 defect with two ada-toms is formed.

Lee et al. [36] have found that adatom generation in the processof reconstruction can accelerate the structure transformation to amore stable structure. As shown in Fig. 5, adatom 2 breaks thebond with atom 5 and forms a new bond with atom 9 at 235 fs.At the same time, adatom 3 forms a new bond with atom 8. At287 fs, atom 2 breaks the bond with atom 9, and make bonds withatoms 4 and 5, respectively. Finally, atom 2 forms a new bond withatom 3, and a SW defect is created at 320 fs. At 10 ps, the SW defectstill remains (see Fig. 4c). This illustrates that the SW defect is anenergetically favorable configuration.

We have once studied the irradiation process of (9,0) single-walled CNTs with a carbon ion by employing the classical MD withan empirical potential, and observed the SW defect when the pro-jectile with the incident energy of 40 eV moves perpendicularly tothe center axis of the tube and approaches a target atom [25]. Thediscrepancy for the impact location effect on the radiation damageformed in the nanotube is attributed to chiral indices of the CNTsand the different simulation methods. The SCC-DFTB method canbe soft to simulate the irradiation process because of allowing forthe self-consistent-charge of charge-transfer effects, while theempirical potential simulation can be hard. Moreover, the SWdefect has also been observed experimentally [37], confirmingthe accuracy of our calculations.

ositions for the incident energy Ein ¼ 0:01 � 100 eV. Table legend: ads = adsorption,les defect, 74595 = 7-4-5-9-5 defect, 57765 = 5-7-7-6-5 defect, pene = penetration,tively. The character p indicates no damage (perfect) in the nanotube after colliding.

20 eV 30 eV 50 eV 70 eV 100 eV

Sub Sub/E1/p Sub/E1/p Sub/E1/p Sub/E1/pAds Sub Sub Sub DB/E1Ads Ads DB DB 585Ads Sub Sub 74595 DB/E1Ads Ads SW 585/C3 57765

Ads Pene/p Pene/p Pene/p Pene/pAds Ads Ads Pene/p Pene/pSub Sub DB SW DB/585/E2Ads Sub Sub Sub/E1(p) 585/E2Sub 585/C3 DB DB/E1 DB/E1

Fig. 5. Atomic processes for the group h at Ein ¼ 70 eV. In order to see the evolution processes more clearly, the carbon atoms on the rear surface of the tube are concealed.The green balls indicate the incident carbon ions. The red balls indicate two adatoms, which will play an important role in the process of reconstruction. (For interpretation ofthe references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 6. Atomic processes for the group e at Ein ¼ 100 eV. In order to see the evolution processes more clearly, the carbon atoms on the rear surface of the tube are concealed.The green balls indicate the incident carbon ions. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

C. Zhang et al. / Computational Materials Science 93 (2014) 15–21 19

Fig. 6 shows atomic processes for the group e at the incidentenergy of 100 eV. At 45 fs, the incident carbon ion labeled as 1forms new bonds with atoms 2 and 3, respectively. At 65 fs, atoms2 and 3 break bonds with neighboring atoms, and atom 1 pene-trates through the front surface of the nanotube. Meanwhile, atom4 breaks bonds with atoms 8 and 9, and atom 5 breaks bonds with

atoms 10 and 11, respectively. As time proceeds, atom 1 eventuallymoves towards the rear surface of the tube, and finally is adsorbedon the rear surface outwardly.

At 118 fs, atoms 2 and 3 form new bonds with atoms 6 and 7,respectively, and form new bonds with atoms 12 and 13 at190 fs, respectively. Therefore, two pentagonal rings are created

0 40 80 120 160 200

-0.4

-0.2

0.0

Dq (

e)

30

40

50

(f)

103 fs88 fs

(c)

(b)

EI k

(eV

)

(a)

73 fs

(d) (e)

0

8

16

24

D (

Å)

t (fs)

Fig. 7. Time evolutions of the kinetic energy (EIk) (a) of the incident carbon ion, the

charge transferred (Dq) (b) from the nanotube to the incident carbon ion, and thedistance (D) (c) between the projectile and the center of mass of the nanotube atEin= 50 eV for the group f. Atomic structures from the front view at 73 fs (d), fromthe side view at 88 fs (e) and from the rear view at 103 fs (f), corresponding to threedash lines above, respectively, are also shown. The green balls indicate the incidentcarbon ions. (For interpretation of the references to color in this figure legend, thereader is referred to the web version of this article.)

20 C. Zhang et al. / Computational Materials Science 93 (2014) 15–21

in the tube. At 197 fs, atom 2 forms a new bond with atom 3, and at212 fs, atoms 8 and 10 form new bonds with atoms 9 and 11,respectively. A 5665 defect (consisting of two pentagons and twoadjacent hexagons) is formed in the nanotube. At 276 fs, atoms 4and 5 form news bonds with atoms 9 and 11, respectively, and at302 fs, form news bonds with atoms 14 and 15, respectively. Onecan find that there is a pair of 57765 defects created in the tube.At 10 ps, the defect configuration remains (see Fig. 4f), confirmingthat the configuration is an energetically favorable structure.

3.4. Kinetic energy and charge transfer of the collision dynamicalprocess

Another two factors analyzed in the projectile-target interac-tion are the kinetic energy of the projectile and the charge trans-ferred from the nanotube to the projectile. The ratio of thekinetic energy of the projectile after collision to the initial kineticenergy is a measurement of the degree of interaction and theamount of energy gained by the nanotube structure. From Table 1,one can find that the incident carbon ion has almost transferred itsenergy entirely to the target atoms of the nanotube except for thegroup f (for Ein ¼ 10 eV and Ein P 30 eV) and the group g (forEin P 70 eV) after colliding. For the groups f (for Ein ¼ 10 eV andEin P 30 eV) and g (for Ein P 70 eV), the projectile either reboundsor penetrates through the nanotube with residual energy aftercolliding.

Fig. 7 shows the time evolutions of the kinetic energy (EIk) of the

incident carbon ion, the charge transferred (Dq) from the nanotubeto the incident carbon ion, and the distance (D) between the pro-jectile and the center of mass of the nanotube at Ein ¼ 50 eV forthe group f. From Fig. 7a, one can note that the EI

k increases slightlyduring the time from 63 fs to 67 fs because of the attractive inter-actions among the target atoms in the nanotube. After 67 fs, the EI

k

decreases first, reaches the local minimum at about 73 fs and thenrises. The reason is that the repulsive force is dominant when theincident carbon ion approaches the target atoms in the front wallof the tube (see Fig. 7d).

At about 88 fs, the projectile locates at the center axis of thetube (see Fig. 7e). This is illustrated in Fig. 7c where the distancebetween the projectile and the center of mass of the nanotube isabout 0 Å. At this time, the EI

k is temporary constant (45.29 eV)(see Fig. 7a). After 88 fs, the projectile will move towards the rearwall of the nanotube. At about 91 fs, the EI

k increases once again,and declines abruptly after 96 fs. It decreases to the minimum at103 fs (see Fig. 7a), and then increases. It tends to be constant value(40.28 eV) after 130 fs, which illustrates that the projectile hasescaped out of the nanotube. For this case, the ratio of the kineticenergy of the projectile after collision to the initial kinetic energyis about 80.56%.

With the same method, we calculate the ratio for Ein ¼ 10 eV,30 eV, 70 eV and 100 eV for the group f is about 21.81%, 40.20%,89.28% and 94.38%, respectively. The ratio for Ein ¼ 70 eV and100 eV for the group g is about 15.56% and 64.17%, respectively.One can find that as the incident energy increases, the interactionbetween the projectile and target atoms is weaker for the groups fand g, and the energy exchange between the projectile and thenanotube decreases. The reason is that the projectile-target inter-action time reduces as the incident energy of the projectileincreases, leading to the reduction in the exchange energy. In addi-tion, the exchange energy depends on the impact position, which ishigher for the group g than that for the group f for a certain inci-dent energy.

Moreover, one can note that the trend for the charge transfer issimilar to that for the kinetic energy of the incident ion. FromFig. 7b, one can find that the Dq increases slightly during the timefrom 63 fs to 67 fs. This illustrates that the charge is transferred

from the nanotube to the projectile when the incident ion movesgradually towards the atoms of the front surface of the nanotube.The reason is that the Coulombic attraction between the projectileand the target atoms in the tube is dominant. After 67 fs, itdecreases sharply (see Fig. 7b), which shows that the charge ofthe projectile is transferred to the nanotube. At about 73 fs, theDq decreases to the minimum. After 73 fs, it increases once again,and slightly drops after about 80 fs. After about 95 fs, there is stilla local minimum for the Dq at about 103 fs. During this phase, theprojectile will penetrate through the rear surface of the nanotube,as shown in Fig. 7f. At about 104 fs, the nonuniform change of thecharge is due to the minor thermal fluctuations of carbon atoms inthe nanotube. One should note that the charge transfer is zero after130 fs, which illustrates that the projectile is still neutral at the endof the simulation.

4. Conclusions

By using the quantum chemical SCC-DFTB method, we studythe collision process of a low-energy carbon ion impinging a(10,0) single-walled carbon nanotubes. Five types of processesare observed: adsorption, reflection, substitution, penetration anddamage. At energies lower than 20 eV, the adsorption process isdominant. For the adsorption events, adatom defects are formed.Moreover, there is a non-monotonic trend in the relationshipbetween the probability for the substitution process and the inci-dent energy. Defect formation events are observed at energies lar-ger than 20 eV. The probabilities of the reflection process and thepenetration process are lower in the range of energies. Further-more, we study the energy exchange between the projectile andthe nanotube, and find that the closer the impact locationapproaches a lattice atom, the higher the energy exchange. This

C. Zhang et al. / Computational Materials Science 93 (2014) 15–21 21

work provides the analysis of physical process and sheds light onunderstanding the effects of irradiation in carbon nanotube-basednanosensors and nanoelectronics.

Acknowledgments

This work was supported by the National Natural Science Foun-dation of China under Grant Nos. 11025524 and 11161130520, theNational Basic Research Program of China under Grant No.2010CB832903, the European Commission’s 7th Framework Pro-gramme (FP7-PEOPLE-2010-IRSES) under Grant Agreement ProjectNo. 269131, and the introduced doctor’s startup fund from theAnhui University of Science and Technology.

Appendix A. Supplementary material

Supplementary data associated with this article can be found,in the online version, at http://dx.doi.org/10.1016/j.commatsci.2014.06.015.

References

[1] S. Iijima, Nature (London) 354 (1991) 56.[2] R.H. Baughman, A.A. Zakhidov, W.A. de Heer, Science 297 (2002) 787.[3] Q. Li, C. Liu, X. Wang, S. Fan, Nanotechnology 20 (2009) 145702.[4] M. Fujii, X. Zhang, H. Xie, H. Ago, K. Takahashi, T. lkuta, H. Abe, T. Shimizu, Phys.

Rev. Lett. 95 (2005) 065502.[5] Z. Xu, M.J. Buehler, ACS Nano 3 (2009) 2767.[6] F. Han, Y. Azdoud, G. Lubineau, Comput. Mater. Sci. 81 (2014) 641.[7] P. He, D. Xu, T.S. Lin, Z. Jiao, Comput. Mater. Sci. 72 (2013) 38.[8] Y. Kinoshita, M. Murashima, M. Kawachi, N. Ohno, Comput. Mater. Sci. 70

(2013) 1.[9] B. Li, Comput. Mater. Sci. 74 (2013) 27.

[10] V. Vijayaraghavan, C.H. Wong, Comput. Mater. Sci. 71 (2013) 184.[11] A.V. Krasheninnikov, K. Nordlund, J. Appl. Phys. 107 (2010) 071301.[12] J.Y. Huang, S. Chen, Z.F. Ren, Z. Wang, K. Kempa, M.J. Naughton, G. Chen, M.S.

Dresselhaus, Phys. Rev. Lett. 98 (2007) 185501.[13] A.J. Stone, D.J. Wales, Chem. Phys. Lett. 128 (1986) 501.

[14] B. Peng, M. Locascio, P. Zapol, S. Li, S.L. Mielke, G.C. Schatz, H.D. Espinosa,Nature Nanotech. 3 (2008) 626.

[15] A.V. Krasheninnikov, F. Banhart, Nature Mater. 6 (2007) 723.[16] C. Gómez-Navarro, P.J. De Pablo, J. Gómez-Herrero, B. Biel, F.J. Garcia-Vidal, A.

Rubio, F. Flores, Nature Mater. 4 (2005) 534.[17] E. Polizzi, N. Neophytou, D. Kienle, M.P. Anantram, Appl. Phys. Lett. 88 (2006)

242106.[18] A. Tolvanen, G. Buchs, P. Ruffieux, P. Gröning, O. Gröning, A.V. Krasheninnikov,

Phys. Rev. B 9 (2009) 125430.[19] M.S. Raghuveer, P.G. Ganesan, J. D’Arcy-Gall, G. Ramanath, M. Marshall, I.

Petrov, Appl. Phys. Lett. 84 (2004) 4484.[20] H. Schittenhelm, D.B. Geohegan, G.E. Jellison, A.A. Puretzky, M.J. Lance, P.F.

Britt, Appl. Phys. Lett. 81 (2002) 2097.[21] W.S. Yun, J. Kim, K.H. Park, J.S. Ha, Y.J. Ko, K. Park, S.K. Kim, Y.J. Doh, H.J. Lee, J.P.

Salvetat, L. Forró, J. Vac. Sci. Technol. A 18 (2000) 1329.[22] Z.J. Xu, W. Zhang, Z.Y. Zhu, C.L. Ren, Y. Li, P. Huai, J. Appl. Phys. 106 (2009)

043501.[23] A. Tolvanen, J. Kotakoski, A.V. Krasheninnikov, K. Nordlund, Appl. Phys. Lett. 91

(2007) 173109.[24] A.V. Krasheninnikov, F. Banhart, J.X. Li, A.S. Foster, Phys. Rev. B 72 (2005)

125428.[25] C. Zhang, F. Mao, F.S. Zhang, Y. Zhang, Chem. Phys. Lett. 541 (2012) 92.[26] Th. Frauenheim, G. Seifert, M. Elstner, Th. Niehaus, Ch. Köhler, M. Amkreutz, M.

Sternberg, Z. Hajnal, A. Di Carlo, S. Suhai, J. Phys.: Condens. Matter. 14 (2002)3015.

[27] G. Seifert, J. Phys. Chem. A 111 (2007) 5609.[28] R. Scholz, R. Luschtinetz, G. Seifert, T. Jägeler-Hoheisel, C. Körner, K. Leo, M.

Rapacioli, J. Phys.: Condens. Matter. 25 (2013) 473201.[29] I. Belabbas, J. Chen, Ph. Komninou, G. Nouet, Comput. Mater. Sci. 79 (2013)

118.[30] V.C. Fuertes, C.F.A. Negre, M.B. Oviedo, F.P. Bonafé, F.Y. Oliva, C.G. Sánchez, J.

Phys.: Condens. Matter. 25 (2013) 115304.[31] M. Elstner, D. Porezag, G. Jungnickel, J. Elsner, M. Haugk, Th. Frauenheim, S.

Suhai, G. Seifert, Phys. Rev. B 58 (1998) 7260.[32] M. Elstner, Theor. Chem. Acc. 116 (2006) 316.[33] C.F.A. Negre, E.M. Perassi, E.A. Coronado, C.G. Sánchez, J. Phys.: Condens.

Matter. 25 (2013) 125304.[34] S.J. Zhao, J.M. Xue, Y.G. Wang, S. Yan, Appl. Phys. A 108 (2012) 313.[35] A.J. Lu, B.C. Pan, Phys. Rev. Lett. 92 (2004) 105504.[36] G.D. Lee, C.Z. Wang, E.J. Yoon, N.M. Hwang, K.M. Ho, Appl. Phys. Lett. 92 (2008)

043104.[37] K. Suenaga, H. Wakabayashi, M. Koshino, Y. Sato, K. Urita, S. Iijima, Nat.

Nanotech. 2 (2007) 358.