View Article Online
Nanoscale
View Journal
Accepted Manuscript This article can be cited before page numbers have been issued, to do this please use: F. Ding, Z. Liang, Z. Xu and T. Yan, Nanoscale, 2013, DOI: 10.1039/C3NR05215J.
Volume 2 | Number 1 | 2010
This is an Accepted Manuscript, which has been through the RSC Publishing peer review process and has been accepted for publication.
www.rsc.org/nanoscale
Volume 2 | Number 1 | January 2010 | Pages 1–156
Nanoscale
Accepted Manuscripts are published online shortly after acceptance, which is prior to technical editing, formatting and proof reading. This free service from RSC Publishing allows authors to make their results available to the community, in citable form, before publication of the edited article. This Accepted Manuscript will be replaced by the edited and formatted Advance Article as soon as this is available. To cite this manuscript please use its permanent Digital Object Identifier (DOI®), which is identical for all formats of publication. More information about Accepted Manuscripts can be found in the Information for Authors.
ISSN 2040-3364
Pages 1–156
COVER ARTICLE Graham et al. Mixed metal nanoparticle assembly and the effect on surface-enhanced Raman scattering
REVIEW Lin et al. Progress of nanocrystalline growth kinetics based on oriented attachment
2040-3364(2010)2:1;1-T
Please note that technical editing may introduce minor changes to the text and/or graphics contained in the manuscript submitted by the author(s) which may alter content, and that the standard Terms & Conditions and the ethical guidelines that apply to the journal are still applicable. In no event shall the RSC be held responsible for any errors or omissions in these Accepted Manuscript manuscripts or any consequences arising from the use of any information contained in them.
www.rsc.org/nanoscale Registered Charity Number 207890
Page 1 of 6
Nano Scale
Nanoscale
Dynamic Article Links ► View Article Online
DOI: 10.1039/C3NR05215J
Cite this: DOI: 10.1039/c0xx00000x
Full Paper
www.rsc.org/xxxxxx
Zilin Liang,a Ziwei Xu,b Tianying Yan,*a and Feng Ding*b Received (in XXX, XXX) Xth XXXXXXXXX 20XX, Accepted Xth XXXXXXXXX 20XX 5
DOI: 10.1039/b000000x
10
Real-time reconstruction of a divacancy in graphene under electron irradiation (EI) is investigated by nonequilibrium molecular dynamic simulation (NEMD). The formation of the amorphous structure is found driven by the generalized Stone-Wales transformations (GSWTs), i.e. C-C bond rotations, around the defective area. The simulation reveals that each step of the reconstruction can be viewed a quasithermal process and thus the formation from a point defect to an amorphous structure favors the minimum energy path. On the other hand, the formation of high energy large defective area is kinetically dominated by the balance between expansion and shrinkage, and a kinetic model was proposed to understand the size of the defective area. The current study demonstrates that the route of the reconstruction in the point defective graphene toward amorphous structure is predictive, though under stochastic EI.
15
Introduction
20
25
30
35
40
45
Point defect in graphene, which accommodates a few additional or vacant carbon atoms within the hexagonal lattices, was first observed by transmission electron microscopy (TEM) in 2004.1 It has been attracting researchers’ considerable attentions,2-4 for it is readily manipulated under TEM, in contrast to the difficulty on managing the defects such as holes, dislocations, and grain boundaries (GB).5-8 Theoretical studies have shown that the point defect, which involves non-hexagonal rings, into graphene layer can alter the mechanical, electronic, and magnetic properties to the sp2 hybridized carbon network.3, 913 Under certain configurations, point defects may be turned into a one dimensional metallic wire14 or a two-dimensional semiconductor15, which can be applied in graphene nanoelectronics. The significance on investigating the behavior of point defect under electron irradiation (EI) is originated from the controllable manipulation of point defect with up-to-date TEM technique.2, 16-23 Therefore, it is of great interest to study the mechanism of point defect’s reconstruction under EI such as the transformation from a point defect to an amorphous structure in graphene. The reconstruction of a point defect is an isomerization reaction,21, 22, 24-27 which can be induced by the C-C bond rotation, i.e., the generalized Stone-Wales transformation (GSWT).28 The energy barrier of the GSWT is ca. 9 - 10 eV on pristine graphene,29, 30 and 5 – 7 eV around a point defect.21, 24 These barriers are too high to be overcame by thermal activation, but can be overcome easily by the sufficient kinetic energy transfer from an incident electron or ion bombardment.26 It was reported that, under EI, a divacancy, V2(5|8|5), can be reconstructed to an amorphous structure V2(5555|6|7777), which is composed of a nearly 30° rotated hexagons (r6’s) surrounded by a GB loop. The GB loop is characterized as four pentagonheptagon (5|7) pairs that are arranged head to tail along a circle. This journal is © The Royal Society of Chemistry [year]
50
55
60
65
70
75
80
Such a transformation can be achieved via successive GSWTs.21 Recently, Banhart and co-workers have developed a highly focus electron beam within 1 Å in diameter,20 and EI is found to be a just tool for tailoring graphene at nanoscale.16-22, 31-33 This opens a way to cultivate a point defect into a two-dimensional amorphous structure, which may provide desired mechanical and electronic properties for various applications. It is interesting that these amorphous structures have much higher formation energy (Ef) than the simple structures, V2(5|8|5) or V2(555|777). How these structures are stabilized under EI? What is the driving force for such a transformation? What is the most probable amorphous structure? Can such processes be tuned by varying the energy of electron beam? Although routes of the reconstructions have been proposed in previous studies,21, 22 the mechanism and the driving force that leads a point defect towards various amorphous structures has never been well understood. In order to address the aforementioned questions, long time-scale nonequilibrium molecular dynamics (NEMD) simulation is desired. In this study, the classical second-generation reactive empirical bond order (REBO2) potential34 is incorporated in the NEMD simulation to simulate the reconstruction of point defect at 2000 K under 80 keV and 60 keV EI (cf. Fig. S1). The realtime evolution to the amorphous structure is simulated with atomistic details. We use divacancy, V2, as an example of point defects because V2 has the lowest Ef among all the point defects in graphene. Details of the NEMD simulation as well as the estimation of the GSWT barriers (∆E’s) and Ef’s with REBO2 potential are provided in the supplementary information. Briefly, we find that the reconstruction of a point defect favors a minimum energy path (MEP). Successive GSWTs happen on the point defect resulted in the competition between its expansion and shrinkage, which can be understood by a kinetic model. The most probable amorphous structure, V2(5555|6|7777), predicated by the model and observed in the NEMD simulation is in good agreement with the TEM observation.21, 22 [journal], [year], [vol], 00–00 | 1
Nanoscale Accepted Manuscript
Published on 14 November 2013. Downloaded by University of Virginia on 16/11/2013 16:53:39.
Atomistic Simulation and the Mechanism of Graphene Amorphization under Electron Irradiation†
Nanoscale
Page 2 of 6 View Article Online
Results and Discussion 50
Published on 14 November 2013. Downloaded by University of Virginia on 16/11/2013 16:53:39.
55
60
5
10
15
20
25
30
35
40
45
Fig. 1 The reconstruction from V2(5|8|5) to V2(r66) by successive GSWTs. The ∆E of individual GSWT as well as the Ef of the corresponding amorphous structures, calculated by the REBO2 potential, are listed for each reaction path. The numbers in the parentheses denote the ∆E and Ef calculated by DFT in literatures, and the superscripts a, b, c and d refer to Ref. 35, Ref. 36, 37, Ref. 13, 24, and Ref. 21, respectively. The red bond with dashed circles highlights the C-C bond upon which GSWT occurs. The insets (a), (b), and (c), provide the atomistic details of the GSWT from V2(5|8|5) to V2(555|777) observed in NEMD simulation. The reconstruction from V2(5|8|5) to V2(555|777) is triggered by the displacement of C2 upon EI, which stimulates the GSWT on C1-C4 bond; (a) Δt=0 fs, the C1-C2 bond is broken by an incident electron and the displaced C2 moves toward C4, as marked by the red arrow; (b) Δt=175 fs, C2 forms bond with C4 and breaks the C3-C4 bond, as marked by the red arrow; (c) Δt=500 fs, C3 moves toward C1 and forms C1-C3 bond. The whole process finalizes in femtosecond time scale. The net result of the GSWT is the 90° rotation of the C2-C3 bond.
For simpler notation, we use the number of r6’s enclosed in the GB loop to denote the amorphous structures, so that V2(5555|6|7777) is denoted as V2(r6), and others are denoted as V2(r66), V2(r666), etc. The reconstruction from V2(5|8|5) to V2(r66), intermediated via V2(555|777) and V2(r6), along with ∆E of individual GSWT as well as Ef of the corresponding amorphous structure, is shown in Fig. 1. The known Density functional theory (DFT) results are also listed in Fig. 1, which shows that the results of REBO2 potential agree with DFT within 1 eV for both ∆E’s and Ef’s. Other reaction paths are of much higher ∆E’s and are rarely observed in the simulation. It clearly demonstrates the step-by-step expansion by three successive GSWTs on the GB loop. Due to the local strain around the point defect,13 it makes the C-C bond on the GB loop easier to be activated by an incident electron, and thus is capable to accomplish the GSWT with lower barrier,38 comparing with the Stone-Wales transformation on pristine lattice of of 8.8 eV by REBO2 (9.2 eV by DFT29). The detailed atomistic dynamics shown in inset of Fig. 1 demonstrate that GSWT is stimulated by the atomic displacement upon EI, and the process closely resembles the “nudge” process proposed by Kotakoski et al.26 The current NEMD simulation shows that the GSWTs of the “wing” bonds (WBs)39 dominant the formation process from V2(5|8|5) to V2(r66), which is in good agreement with previous simulations.21, 22, 24-27 As the reconstruction continues, an amorphous structure can either shrink or expand. Many channels are opened for further expansion of V2(r66) resulting in many isomers. Fig. 2(a) shows 2 | Journal Name, [year], [vol], 00–00
65
four reaction paths that expand V2(r66) to three V2(r666)s and one V2(r6666) via the GSWT. These configurations, though on different amorphous level, are all resulted via one GSWT from V2(r66). With respect to the different arrangement of their r6s, we denote them as V2(r666)-I, V2(r666)-II, V2(r666)-III, and V2(r6666), respectively. Indeed, because of the excess strain for opening a GB loop,40, 41 the V2(r6666) has higher Ef than the other three isomers. Fig. 2(b) shows the probability distribution, P(E), in which E is the relative energy with respect to the Ef of V2(r666)-I. It clearly reveals that the more stable the isomer, the higher the P(E). The blue curve in Fig. 2(b) shows that P(E) is well fitted by the Boltzmann distribution, exp(-E/kbT), in which kb is the Boltzmann constant and T = 2600 K is the fitted temperature. It is important to note that the fitted temperature in the irradiation area is higher than the thermostat temperature of 2000 K, because of the heating imposed by the continuously incident electrons of high intensity. Therefore, the reconstruction of the point defect toward the amorphous structures can be attributed to a quasi-thermal process. Consequently, the step-bystep reconstruction from point defect toward amorphous structure, via successive GSWTs, should follow the minimum energy path (MEP).
70
75
80
Fig. 2 (a) Four isomers resulted from the expansion of V2(r66) with one GSWT. I, II, III, and IV refer to the V2(r666)-I, V2(r666)-II, V2(r666)-III, and V2(r6666), respectively. The ∆E of individual GSWT as well as the Ef of the corresponding amorphous structures, calculated by the REBO2 potential, are listed for each reaction path. The colored bonds with dashed circles highlight the C-C bonds upon which the GSWT occurs. The black bond with circle characterizes the “shoulder” bond (SB)39 of the (5|7), on which an SB is the C-C bond on r7 neighboring to the pentagon. (b) The probability distribution, P(E), of the four isomers in (a). The error bars are estimated from 10 independent trajectories with 100 ns MD simulation each. The dashed blue curve is fitted by Boltzmann distribution.
This journal is © The Royal Society of Chemistry [year]
Nanoscale Accepted Manuscript
DOI: 10.1039/C3NR05215J
Page 3 of 6
Nanoscale View Article Online
5
Published on 14 November 2013. Downloaded by University of Virginia on 16/11/2013 16:53:39.
10
It is also notable that the larger the amorphous structure, the higher the Ef. Fig. 3(a) shows the normalized probability distribution of V2, P(V2),of various structures. Larger amorphous structures beyond V2(r666) are rarely observed, and thus make negligible contribution to P(V2). It is clearly shown in Fig. 3(a) that V2(r6) is the most probable isomer in our simulation for both 80 keV and 60 keV EI. In agreement, V2(r6) is also frequently observed experimentally observed amorphous structure under 80 keV EI.21, 22 To further explore the size of amorphous structure in quantity, we adopt the average number of r6’s that are enclosed in the GB loop to denote the level of amorphization (L), L=
∑
P(V2 ) ⋅ nr 6 (V2 ) ,
20
45
(1)
V2 along MEP
15
40
in which nr6(V2) is the number of r6’s enclosed in a GB loop. Thus, nr6(V2) is 0, 0, 1, 2, and 3, respectively, for V2(5|8|5), V2(555|777), V2(r6), V2(r66), and V2(r666). The statistics shown in Fig. 3(a) gives L = 1.1 and L = 0.8, respectively, for the V2 in graphene under 80 keV and 60 keV EI. Since V2(555|777) of L=0 is the most stable V2 isomer, with the lowest Ef among all the V2 isomers (cf. Figs. 1 and 2), it is of interest to investigate the origin of the high probability of V2(r6), instead of V2(555|777).
50
expansion and shrinkage of the GB loop. The size of the amorphous area is thus determined by the balance between the above two competing processes. The barrier threshold of expansion, ∆E, is higher than that of shrinkage, ∆Er, because the expansion leads large amorphous structure and the shrinkage is the reverse process. On the other hand, the number of C-C bonds (Nout) along the outer circumference of the loop for expansion is more than that (Nin) along the inner circumference for shrinkage. Therefore, expansion is energetically unfavorable, but has higher probability to be stimulated upon EI. Based on the above consideration, a kinetic model with a coarse grained (CG) amorphous structure can be applied. As shown in Fig. (3b), the area inside the inner solid circle characterizes the level of amorphization, L, with radius r. While the concentric circle, with width a, between the inner and outer solid circles, represents the GB loop that encloses r6’s. At steady state, the number of events of loop expansion per unit time should be exactly same as that of loop shrinkage, so that
55
Pin ⋅ N in = Pout ⋅ N out ,
60
(2)
in which Pout and Pin denote the probabilities of a GSWT of the outer and inner circumferences, respectively. In order to trigger a GSWT by EI, the transferred energy during a hitting must exceed the ∆E of a GSWT. Therefore, Pout and Pin can be estimated by the probabilities of the transferred energy greater than ∆E and ∆Er, i.e., Pout(Et>∆E) and Pin(Et>∆Er), respectively. For this CG representation, we note that Nout ∝ 2π(r+a) and Nin ∝ 2πr, as illustrated in Fig. 3(b). Therefore, Eq. (2) can be represented as
65
Pin ( Et > ∆Er ) ⋅ 2π r = Pout ( Et > ∆E ) ⋅ 2π ( r + a ) ,
(3)
where a can be roughly estimated as a C-C- bond length in graphene, 1.42 Å. Thus, 70
r=
a
ξ −1
,
(4)
in which
ξ=
75
25
30
35
Fig. 3 (a) Probability distribution, P(V2), of the reconstruction from V2(5|8|5) to V2(r666) along MEP under 80 keV and 60 keV EI, shown as red and green bars, respectively; (b) Pictorial illustration of the coarse grained kinetic model. The ring area between the inner and outer circles represents the GB loop. The area within inner solid circle of radius r characterizes the level of amorphization, L. The outer solid circle of radius r+a characterizes the number of C-C bonds, proportional to 2π(r+a), on which a GSWT expands the amorphous structure. The circle of radius r characterizes the number of C-C bonds, is proportional to 2πr, on which a GSWT shrinks amorphous structure.
As illustrated in Figs. 1 and 2, a GSWT on the outer GB loop generally expands the amorphous area, while a GSWT inside the GB loop generally shrinks the amorphous area. Thus, the V2 reconstruction can be viewed as the competition between This journal is © The Royal Society of Chemistry [year]
80
85
Pin ( Et > ∆Er ) , Pout ( Et > ∆E )
(5)
For such CG amorphous model, ∆E and ∆Er may be estimated by averaging the barriers for the expansion from V2(r6) to V2(r666), as shown in Figs. 1 and 2, which gives ∆E = 7.7 eV. For the shrinkage from V2(r666) to V2(r6), the average of the three reverse barriers gives ∆Er = 5.6 eV. The difference between ∆E and ∆Er, i.e., 2.1 V, is reasonable as the formation energy of a pentagon-heptagon pair in graphene is of the similar level.35 Eq. (5) may be estimated via Eq. (S1) in the computational methods section, which gives ξ = 1.79 and ξ = 2.27, respectively, under 80 keV and 60 keV EI. Therefore, the radius, r, of the average amorphous area is 1.81 Å and 1.12 Å for 80 keV and 60 keV EI from Eq. (4). Further coarse graining r6 as a circle of r = 1.42 Å, the level of amorphization, which gives the number of r6 enclosed by the GB loop, may be estimated to be L = 1.6 and L = Journal Name, [year], [vol], 00–00 | 3
Nanoscale Accepted Manuscript
DOI: 10.1039/C3NR05215J
Nanoscale
Page 4 of 6 View Article Online
5
Published on 14 November 2013. Downloaded by University of Virginia on 16/11/2013 16:53:39.
10
15
0.6, respectively, under 80 keV and 60 keV EI. The above two L’s agree well with the level of amorphization, i.e., L = 1.1 and L = 0.8, respectively, from the simulation in quality. Thus, the kinetic model is validated, from which the level of the amorphization may be understood for the competition between expansion and shrinkage of the amorphous structure. It is important to note that the discrepancy between the kinetic model and the simulation may be stemmed from the following factors: (i) the rough estimation of the threshold barrier that triggers a GSWT, which should be higher than the exact barrier of bond rotation because of the lattice vibrations at finite temperature and energy dissipation in real experiments and simulations; 24, 42, 43 (ii) the rough estimation of the loop width; (iii) the CG kinetic model may not well applicable for a very system like r6; and (iv) the inaccuracy of the empirical REBO2 potential.34
60
65
70
Conclusion
20
25
30
In summary, we have simulated the real-time reconstruction of a divacancy from point defect to various amorphous structures in graphene under EI via NEMD simulation. The reconstruction is found through a series of generalized Stone-Wales transformation (GSWT). During such evolution, although under stochastic EI of high intensity, the GSWT that leads to less energy rising occurs more frequently and can be described by the Boltzmann distribution. In addition, the level of amorphization, i.e., the number of r6’s that are enclosed by the GB loop, can be understood by a coarse grained kinetic model, which accounts for the competition between expansion and shrinkage of the amorphous structure. Thus, the route of amorphous structure is predictable, with the structure following MEP, and the level of amorphization within the framework of a kinetic model. This finding greatly improved our understanding on the reconstruction of amorphous structure in point defective graphene under EI, and provides a model to estimate the amorphous area in quantity
75
80
85
90
Acknowledgements 35
40
This work done in Nankai is supported by NSFC (21373118, 21073097), Natural Science Foundation of Tianjin (12JCYBJC13900), NCET-10-0512, and National Innovative Research Program for Undergraduates (201210055035). The work done in Hong Kong Polytechnic University is supported by
Hong Kong GRF research grant (B-Q35N, B-Q26K), Hong Kong PolyU Internal grants (G-YM60, G-UC49 G-UB57, APM35, A-PK89, A-PJ50) and NSFC grant (21273189) The simulations were performed on TianHe-1A Supercomputer Center in Tianjin, China.
45
95
at
National
100
Notes and References a
50
55
Tianjin Key Laboratory of Metal- and Molecule-Based Material Chemistry, Synergetic Innovation Center of Chemical Science and Engineering (Tianjin), Key Laboratory of Advanced Energy Materials Chemistry (Ministry of Education), Institute of New Energy Material Chemistry, College of Chemistry, Nankai University, Tianjin 300071, China. Email: [email protected] b Institute of Textiles and Clothing, Hong Kong Polytechnic University, Hung Hom, Hong Kong, China. Email: [email protected] † Electronic supplementary information (ESI) available: Computational methods
4 | Journal Name, [year], [vol], 00–00
105
110
1. A. Hashimoto, K. Suenaga, A. Gloter, K. Urita and S. Iijima, Nature, 2004, 430, 870-873. 2. A. V. Krasheninnikov and F. Banhart, Nat. Mater., 2007, 6, 723-733. 3. F. Banhart, J. Kotakoski and A. V. Krasheninnikov, ACS Nano, 2010, 5, 26-41. 4. A. V. Krasheninnikov and K. Nordlund, J. Appl. Phys., 2010, 107, 071301-071370. 5. Ç. Ö. Girit, J. C. Meyer, R. Erni, M. D. Rossell, C. Kisielowski, L. Yang, C.-H. Park, M. F. Crommie, M. L. Cohen, S. G. Louie and A. Zettl, Science, 2009, 323, 1705-1708. 6. J. H. Warner, E. R. Margine, M. Mukai, A. W. Robertson, F. Giustino and A. I. Kirkland, Science, 2012, 337, 209-212. 7. S. Kurasch, J. Kotakoski, O. Lehtinen, V. Skákalová, J. Smet, C. E. Krill, A. V. Krasheninnikov and U. Kaiser, Nano Lett., 2012, 12, 3168-3173. 8. O. Lehtinen, S. Kurasch, A. V. Krasheninnikov and U. Kaiser, Nat Commun, 2013, 4, 2098. doi:2010.1038/ncomms3098. 9. R. Khare, S. L. Mielke, J. T. Paci, S. Zhang, R. Ballarini, G. C. Schatz and T. Belytschko, Phys. Rev. B, 2007, 75, 075412. 10. O. V. Yazyev and L. Helm, Phys. Rev. B, 2007, 75, 125408. 11. M. T. Lusk and L. D. Carr, Phys. Rev. Lett., 2008, 100, 175503. 12. A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov and A. K. Geim, Rev. Mod. Phys., 2009, 81, 109-162. 13. O. Cretu, A. V. Krasheninnikov, J. A. Rodríguez-Manzo, L. Sun, R. M. Nieminen and F. Banhart, Phys. Rev. Lett., 2010, 105, 196102. 14. J. Lahiri, Y. Lin, P. Bozkurt, I. I. Oleynik and M. Batzill, Nat. Nanotech., 2010, 5, 326-329. 15. D. J. Appelhans, Z. Lin and M. T. Lusk, Phys. Rev. B, 2010, 82, 073410. 16. J. Li and F. Banhart, Nano Lett., 2004, 4, 1143-1146. 17. F. Banhart, J. Li and M. Terrones, Small, 2005, 1, 953-956. 18. F. Banhart, J. X. Li and A. V. Krasheninnikov, Phys. Rev. B, 2005, 71, 241408. 19. J. C. Meyer, C. Kisielowski, R. Erni, M. D. Rossell, M. F. Crommie and A. Zettl, Nano Lett., 2008, 8, 3582-3586. 20. J. A. Rodriguez-Manzo and F. Banhart, Nano Lett., 2009, 9, 22852289. 21. J. Kotakoski, A. V. Krasheninnikov, U. Kaiser and J. C. Meyer, Phys. Rev. Lett., 2011, 106, 105505. 22. A. W. Robertson, C. S. Allen, Y. A. Wu, K. He, J. Olivier, J. Neethling, A. I. Kirkland and J. H. Warner, Nat. Commun., 2012, 3, 1144. 23. A. Zobelli, A. Gloter, C. P. Ewels and C. Colliex, Phys. Rev. B, 2008, 77, 045410. 24. G.-D. Lee, C. Z. Wang, E. Yoon, N.-M. Hwang, D.-Y. Kim and K. M. Ho, Phys. Rev. Lett., 2005, 95, 205501. 25. G.-D. Lee, C. Z. Wang, E. Yoon, N.-M. Hwang and K. M. Ho, Phys. Rev. B, 2006, 74, 245411. 26. J. Kotakoski, J. C. Meyer, S. Kurasch, D. Santos-Cottin, U. Kaiser and A. V. Krasheninnikov, Phys. Rev. B, 2011, 83, 245420. 27. Z. Wang, Y. G. Zhou, J. Bang, M. P. Prange, S. B. Zhang and F. Gao, J. Phys. Chem. C, 2012, 116, 16070-16079. 28. A. J. Stone and D. J. Wales, Chem. Phys. Lett., 1986, 128, 501-503. 29. L. Li, S. Reich and J. Robertson, Phys. Rev. B, 2005, 72, 184109. 30. J. Ma, D. Alfé, A. Michaelides and E. Wang, Phys. Rev. B, 2009, 80, 033407.
This journal is © The Royal Society of Chemistry [year]
Nanoscale Accepted Manuscript
DOI: 10.1039/C3NR05215J
Page 5 of 6
Nanoscale View Article Online
DOI: 10.1039/C3NR05215J
10
15
20
25
This journal is © The Royal Society of Chemistry [year]
Nanoscale Accepted Manuscript
Published on 14 November 2013. Downloaded by University of Virginia on 16/11/2013 16:53:39.
5
31. B. Song, G. g. F. Schneider, Q. Xu, G. g. Pandraud, C. Dekker and H. Zandbergen, Nano Lett., 2011, 11, 2247-2250. 32. F. Börrnert, L. Fu, S. Gorantla, M. Knupfer, B. Büchner and M. H. Rümmeli, ACS Nano, 2012, 6, 10327-10334. 33. C. J. Russo and J. A. Golovchenko, Proc. Natl. Acad. Sci. USA, 2012, 109, 5953-5957. 34. D. W. Brenner, O. A. Shenderova, J. A. Harrison, S. J. Stuart, B. Ni and S. B. Sinnott, J. Phys.: Condens. Matter, 2002, 14, 783-802. 35. Y. Kim, J. Ihm, E. Yoon and G.-D. Lee, Phys. Rev. B, 2011, 84, 075445. 36. A. A. El-Barbary, R. H. Telling, C. P. Ewels, M. I. Heggie and P. R. Briddon, Phys. Rev. B, 2003, 68, 144107. 37. A. V. Krasheninnikov, P. O. Lehtinen, A. S. Foster and R. M. Nieminen, Chem. Phys. Lett., 2006, 418, 132-136. 38. T. Dumitrica and B. I. Yakobson, Appl. Phys. Lett., 2004, 84, 27752777. 39. F. Ding, K. Jiao, M. Wu and B. I. Yakobson, Phys. Rev. Lett., 2007, 98, 075503. 40. Y. Liu and B. I. Yakobson, Nano Lett., 2010, 10, 2178-2183. 41. B. I. Yakobson and F. Ding, ACS Nano, 2011, 5, 1569-1574. 42. J. C. Meyer, F. Eder, S. Kurasch, V. Skakalova, J. Kotakoski, H. J. Park, S. Roth, A. Chuvilin, S. Eyhusen, G. Benner, A. V. Krasheninnikov and U. Kaiser, Phys. Rev. Lett., 2012, 108, 196102. 43. J. C. Meyer, F. Eder, S. Kurasch, V. Skakalova, J. Kotakoski, H. J. Park, S. Roth, A. Chuvilin, S. Eyhusen, G. Benner, A. V. Krasheninnikov and U. Kaiser, Phys. Rev. Lett., 2013, 110, 239902.
Journal Name, [year], [vol], 00–00 | 5
Nanoscale Accepted Manuscript
Published on 14 November 2013. Downloaded by University of Virginia on 16/11/2013 16:53:39.
Nanoscale View Article Online
Page 6 of 6
DOI: 10.1039/C3NR05215J
Table of Contents (TOC) Graphic
Nanoscale
View Journal
Accepted Manuscript This article can be cited before page numbers have been issued, to do this please use: F. Ding, Z. Liang, Z. Xu and T. Yan, Nanoscale, 2013, DOI: 10.1039/C3NR05215J.
Volume 2 | Number 1 | 2010
This is an Accepted Manuscript, which has been through the RSC Publishing peer review process and has been accepted for publication.
www.rsc.org/nanoscale
Volume 2 | Number 1 | January 2010 | Pages 1–156
Nanoscale
Accepted Manuscripts are published online shortly after acceptance, which is prior to technical editing, formatting and proof reading. This free service from RSC Publishing allows authors to make their results available to the community, in citable form, before publication of the edited article. This Accepted Manuscript will be replaced by the edited and formatted Advance Article as soon as this is available. To cite this manuscript please use its permanent Digital Object Identifier (DOI®), which is identical for all formats of publication. More information about Accepted Manuscripts can be found in the Information for Authors.
ISSN 2040-3364
Pages 1–156
COVER ARTICLE Graham et al. Mixed metal nanoparticle assembly and the effect on surface-enhanced Raman scattering
REVIEW Lin et al. Progress of nanocrystalline growth kinetics based on oriented attachment
2040-3364(2010)2:1;1-T
Please note that technical editing may introduce minor changes to the text and/or graphics contained in the manuscript submitted by the author(s) which may alter content, and that the standard Terms & Conditions and the ethical guidelines that apply to the journal are still applicable. In no event shall the RSC be held responsible for any errors or omissions in these Accepted Manuscript manuscripts or any consequences arising from the use of any information contained in them.
www.rsc.org/nanoscale Registered Charity Number 207890
Page 1 of 6
Nano Scale
Nanoscale
Dynamic Article Links ► View Article Online
DOI: 10.1039/C3NR05215J
Cite this: DOI: 10.1039/c0xx00000x
Full Paper
www.rsc.org/xxxxxx
Zilin Liang,a Ziwei Xu,b Tianying Yan,*a and Feng Ding*b Received (in XXX, XXX) Xth XXXXXXXXX 20XX, Accepted Xth XXXXXXXXX 20XX 5
DOI: 10.1039/b000000x
10
Real-time reconstruction of a divacancy in graphene under electron irradiation (EI) is investigated by nonequilibrium molecular dynamic simulation (NEMD). The formation of the amorphous structure is found driven by the generalized Stone-Wales transformations (GSWTs), i.e. C-C bond rotations, around the defective area. The simulation reveals that each step of the reconstruction can be viewed a quasithermal process and thus the formation from a point defect to an amorphous structure favors the minimum energy path. On the other hand, the formation of high energy large defective area is kinetically dominated by the balance between expansion and shrinkage, and a kinetic model was proposed to understand the size of the defective area. The current study demonstrates that the route of the reconstruction in the point defective graphene toward amorphous structure is predictive, though under stochastic EI.
15
Introduction
20
25
30
35
40
45
Point defect in graphene, which accommodates a few additional or vacant carbon atoms within the hexagonal lattices, was first observed by transmission electron microscopy (TEM) in 2004.1 It has been attracting researchers’ considerable attentions,2-4 for it is readily manipulated under TEM, in contrast to the difficulty on managing the defects such as holes, dislocations, and grain boundaries (GB).5-8 Theoretical studies have shown that the point defect, which involves non-hexagonal rings, into graphene layer can alter the mechanical, electronic, and magnetic properties to the sp2 hybridized carbon network.3, 913 Under certain configurations, point defects may be turned into a one dimensional metallic wire14 or a two-dimensional semiconductor15, which can be applied in graphene nanoelectronics. The significance on investigating the behavior of point defect under electron irradiation (EI) is originated from the controllable manipulation of point defect with up-to-date TEM technique.2, 16-23 Therefore, it is of great interest to study the mechanism of point defect’s reconstruction under EI such as the transformation from a point defect to an amorphous structure in graphene. The reconstruction of a point defect is an isomerization reaction,21, 22, 24-27 which can be induced by the C-C bond rotation, i.e., the generalized Stone-Wales transformation (GSWT).28 The energy barrier of the GSWT is ca. 9 - 10 eV on pristine graphene,29, 30 and 5 – 7 eV around a point defect.21, 24 These barriers are too high to be overcame by thermal activation, but can be overcome easily by the sufficient kinetic energy transfer from an incident electron or ion bombardment.26 It was reported that, under EI, a divacancy, V2(5|8|5), can be reconstructed to an amorphous structure V2(5555|6|7777), which is composed of a nearly 30° rotated hexagons (r6’s) surrounded by a GB loop. The GB loop is characterized as four pentagonheptagon (5|7) pairs that are arranged head to tail along a circle. This journal is © The Royal Society of Chemistry [year]
50
55
60
65
70
75
80
Such a transformation can be achieved via successive GSWTs.21 Recently, Banhart and co-workers have developed a highly focus electron beam within 1 Å in diameter,20 and EI is found to be a just tool for tailoring graphene at nanoscale.16-22, 31-33 This opens a way to cultivate a point defect into a two-dimensional amorphous structure, which may provide desired mechanical and electronic properties for various applications. It is interesting that these amorphous structures have much higher formation energy (Ef) than the simple structures, V2(5|8|5) or V2(555|777). How these structures are stabilized under EI? What is the driving force for such a transformation? What is the most probable amorphous structure? Can such processes be tuned by varying the energy of electron beam? Although routes of the reconstructions have been proposed in previous studies,21, 22 the mechanism and the driving force that leads a point defect towards various amorphous structures has never been well understood. In order to address the aforementioned questions, long time-scale nonequilibrium molecular dynamics (NEMD) simulation is desired. In this study, the classical second-generation reactive empirical bond order (REBO2) potential34 is incorporated in the NEMD simulation to simulate the reconstruction of point defect at 2000 K under 80 keV and 60 keV EI (cf. Fig. S1). The realtime evolution to the amorphous structure is simulated with atomistic details. We use divacancy, V2, as an example of point defects because V2 has the lowest Ef among all the point defects in graphene. Details of the NEMD simulation as well as the estimation of the GSWT barriers (∆E’s) and Ef’s with REBO2 potential are provided in the supplementary information. Briefly, we find that the reconstruction of a point defect favors a minimum energy path (MEP). Successive GSWTs happen on the point defect resulted in the competition between its expansion and shrinkage, which can be understood by a kinetic model. The most probable amorphous structure, V2(5555|6|7777), predicated by the model and observed in the NEMD simulation is in good agreement with the TEM observation.21, 22 [journal], [year], [vol], 00–00 | 1
Nanoscale Accepted Manuscript
Published on 14 November 2013. Downloaded by University of Virginia on 16/11/2013 16:53:39.
Atomistic Simulation and the Mechanism of Graphene Amorphization under Electron Irradiation†
Nanoscale
Page 2 of 6 View Article Online
Results and Discussion 50
Published on 14 November 2013. Downloaded by University of Virginia on 16/11/2013 16:53:39.
55
60
5
10
15
20
25
30
35
40
45
Fig. 1 The reconstruction from V2(5|8|5) to V2(r66) by successive GSWTs. The ∆E of individual GSWT as well as the Ef of the corresponding amorphous structures, calculated by the REBO2 potential, are listed for each reaction path. The numbers in the parentheses denote the ∆E and Ef calculated by DFT in literatures, and the superscripts a, b, c and d refer to Ref. 35, Ref. 36, 37, Ref. 13, 24, and Ref. 21, respectively. The red bond with dashed circles highlights the C-C bond upon which GSWT occurs. The insets (a), (b), and (c), provide the atomistic details of the GSWT from V2(5|8|5) to V2(555|777) observed in NEMD simulation. The reconstruction from V2(5|8|5) to V2(555|777) is triggered by the displacement of C2 upon EI, which stimulates the GSWT on C1-C4 bond; (a) Δt=0 fs, the C1-C2 bond is broken by an incident electron and the displaced C2 moves toward C4, as marked by the red arrow; (b) Δt=175 fs, C2 forms bond with C4 and breaks the C3-C4 bond, as marked by the red arrow; (c) Δt=500 fs, C3 moves toward C1 and forms C1-C3 bond. The whole process finalizes in femtosecond time scale. The net result of the GSWT is the 90° rotation of the C2-C3 bond.
For simpler notation, we use the number of r6’s enclosed in the GB loop to denote the amorphous structures, so that V2(5555|6|7777) is denoted as V2(r6), and others are denoted as V2(r66), V2(r666), etc. The reconstruction from V2(5|8|5) to V2(r66), intermediated via V2(555|777) and V2(r6), along with ∆E of individual GSWT as well as Ef of the corresponding amorphous structure, is shown in Fig. 1. The known Density functional theory (DFT) results are also listed in Fig. 1, which shows that the results of REBO2 potential agree with DFT within 1 eV for both ∆E’s and Ef’s. Other reaction paths are of much higher ∆E’s and are rarely observed in the simulation. It clearly demonstrates the step-by-step expansion by three successive GSWTs on the GB loop. Due to the local strain around the point defect,13 it makes the C-C bond on the GB loop easier to be activated by an incident electron, and thus is capable to accomplish the GSWT with lower barrier,38 comparing with the Stone-Wales transformation on pristine lattice of of 8.8 eV by REBO2 (9.2 eV by DFT29). The detailed atomistic dynamics shown in inset of Fig. 1 demonstrate that GSWT is stimulated by the atomic displacement upon EI, and the process closely resembles the “nudge” process proposed by Kotakoski et al.26 The current NEMD simulation shows that the GSWTs of the “wing” bonds (WBs)39 dominant the formation process from V2(5|8|5) to V2(r66), which is in good agreement with previous simulations.21, 22, 24-27 As the reconstruction continues, an amorphous structure can either shrink or expand. Many channels are opened for further expansion of V2(r66) resulting in many isomers. Fig. 2(a) shows 2 | Journal Name, [year], [vol], 00–00
65
four reaction paths that expand V2(r66) to three V2(r666)s and one V2(r6666) via the GSWT. These configurations, though on different amorphous level, are all resulted via one GSWT from V2(r66). With respect to the different arrangement of their r6s, we denote them as V2(r666)-I, V2(r666)-II, V2(r666)-III, and V2(r6666), respectively. Indeed, because of the excess strain for opening a GB loop,40, 41 the V2(r6666) has higher Ef than the other three isomers. Fig. 2(b) shows the probability distribution, P(E), in which E is the relative energy with respect to the Ef of V2(r666)-I. It clearly reveals that the more stable the isomer, the higher the P(E). The blue curve in Fig. 2(b) shows that P(E) is well fitted by the Boltzmann distribution, exp(-E/kbT), in which kb is the Boltzmann constant and T = 2600 K is the fitted temperature. It is important to note that the fitted temperature in the irradiation area is higher than the thermostat temperature of 2000 K, because of the heating imposed by the continuously incident electrons of high intensity. Therefore, the reconstruction of the point defect toward the amorphous structures can be attributed to a quasi-thermal process. Consequently, the step-bystep reconstruction from point defect toward amorphous structure, via successive GSWTs, should follow the minimum energy path (MEP).
70
75
80
Fig. 2 (a) Four isomers resulted from the expansion of V2(r66) with one GSWT. I, II, III, and IV refer to the V2(r666)-I, V2(r666)-II, V2(r666)-III, and V2(r6666), respectively. The ∆E of individual GSWT as well as the Ef of the corresponding amorphous structures, calculated by the REBO2 potential, are listed for each reaction path. The colored bonds with dashed circles highlight the C-C bonds upon which the GSWT occurs. The black bond with circle characterizes the “shoulder” bond (SB)39 of the (5|7), on which an SB is the C-C bond on r7 neighboring to the pentagon. (b) The probability distribution, P(E), of the four isomers in (a). The error bars are estimated from 10 independent trajectories with 100 ns MD simulation each. The dashed blue curve is fitted by Boltzmann distribution.
This journal is © The Royal Society of Chemistry [year]
Nanoscale Accepted Manuscript
DOI: 10.1039/C3NR05215J
Page 3 of 6
Nanoscale View Article Online
5
Published on 14 November 2013. Downloaded by University of Virginia on 16/11/2013 16:53:39.
10
It is also notable that the larger the amorphous structure, the higher the Ef. Fig. 3(a) shows the normalized probability distribution of V2, P(V2),of various structures. Larger amorphous structures beyond V2(r666) are rarely observed, and thus make negligible contribution to P(V2). It is clearly shown in Fig. 3(a) that V2(r6) is the most probable isomer in our simulation for both 80 keV and 60 keV EI. In agreement, V2(r6) is also frequently observed experimentally observed amorphous structure under 80 keV EI.21, 22 To further explore the size of amorphous structure in quantity, we adopt the average number of r6’s that are enclosed in the GB loop to denote the level of amorphization (L), L=
∑
P(V2 ) ⋅ nr 6 (V2 ) ,
20
45
(1)
V2 along MEP
15
40
in which nr6(V2) is the number of r6’s enclosed in a GB loop. Thus, nr6(V2) is 0, 0, 1, 2, and 3, respectively, for V2(5|8|5), V2(555|777), V2(r6), V2(r66), and V2(r666). The statistics shown in Fig. 3(a) gives L = 1.1 and L = 0.8, respectively, for the V2 in graphene under 80 keV and 60 keV EI. Since V2(555|777) of L=0 is the most stable V2 isomer, with the lowest Ef among all the V2 isomers (cf. Figs. 1 and 2), it is of interest to investigate the origin of the high probability of V2(r6), instead of V2(555|777).
50
expansion and shrinkage of the GB loop. The size of the amorphous area is thus determined by the balance between the above two competing processes. The barrier threshold of expansion, ∆E, is higher than that of shrinkage, ∆Er, because the expansion leads large amorphous structure and the shrinkage is the reverse process. On the other hand, the number of C-C bonds (Nout) along the outer circumference of the loop for expansion is more than that (Nin) along the inner circumference for shrinkage. Therefore, expansion is energetically unfavorable, but has higher probability to be stimulated upon EI. Based on the above consideration, a kinetic model with a coarse grained (CG) amorphous structure can be applied. As shown in Fig. (3b), the area inside the inner solid circle characterizes the level of amorphization, L, with radius r. While the concentric circle, with width a, between the inner and outer solid circles, represents the GB loop that encloses r6’s. At steady state, the number of events of loop expansion per unit time should be exactly same as that of loop shrinkage, so that
55
Pin ⋅ N in = Pout ⋅ N out ,
60
(2)
in which Pout and Pin denote the probabilities of a GSWT of the outer and inner circumferences, respectively. In order to trigger a GSWT by EI, the transferred energy during a hitting must exceed the ∆E of a GSWT. Therefore, Pout and Pin can be estimated by the probabilities of the transferred energy greater than ∆E and ∆Er, i.e., Pout(Et>∆E) and Pin(Et>∆Er), respectively. For this CG representation, we note that Nout ∝ 2π(r+a) and Nin ∝ 2πr, as illustrated in Fig. 3(b). Therefore, Eq. (2) can be represented as
65
Pin ( Et > ∆Er ) ⋅ 2π r = Pout ( Et > ∆E ) ⋅ 2π ( r + a ) ,
(3)
where a can be roughly estimated as a C-C- bond length in graphene, 1.42 Å. Thus, 70
r=
a
ξ −1
,
(4)
in which
ξ=
75
25
30
35
Fig. 3 (a) Probability distribution, P(V2), of the reconstruction from V2(5|8|5) to V2(r666) along MEP under 80 keV and 60 keV EI, shown as red and green bars, respectively; (b) Pictorial illustration of the coarse grained kinetic model. The ring area between the inner and outer circles represents the GB loop. The area within inner solid circle of radius r characterizes the level of amorphization, L. The outer solid circle of radius r+a characterizes the number of C-C bonds, proportional to 2π(r+a), on which a GSWT expands the amorphous structure. The circle of radius r characterizes the number of C-C bonds, is proportional to 2πr, on which a GSWT shrinks amorphous structure.
As illustrated in Figs. 1 and 2, a GSWT on the outer GB loop generally expands the amorphous area, while a GSWT inside the GB loop generally shrinks the amorphous area. Thus, the V2 reconstruction can be viewed as the competition between This journal is © The Royal Society of Chemistry [year]
80
85
Pin ( Et > ∆Er ) , Pout ( Et > ∆E )
(5)
For such CG amorphous model, ∆E and ∆Er may be estimated by averaging the barriers for the expansion from V2(r6) to V2(r666), as shown in Figs. 1 and 2, which gives ∆E = 7.7 eV. For the shrinkage from V2(r666) to V2(r6), the average of the three reverse barriers gives ∆Er = 5.6 eV. The difference between ∆E and ∆Er, i.e., 2.1 V, is reasonable as the formation energy of a pentagon-heptagon pair in graphene is of the similar level.35 Eq. (5) may be estimated via Eq. (S1) in the computational methods section, which gives ξ = 1.79 and ξ = 2.27, respectively, under 80 keV and 60 keV EI. Therefore, the radius, r, of the average amorphous area is 1.81 Å and 1.12 Å for 80 keV and 60 keV EI from Eq. (4). Further coarse graining r6 as a circle of r = 1.42 Å, the level of amorphization, which gives the number of r6 enclosed by the GB loop, may be estimated to be L = 1.6 and L = Journal Name, [year], [vol], 00–00 | 3
Nanoscale Accepted Manuscript
DOI: 10.1039/C3NR05215J
Nanoscale
Page 4 of 6 View Article Online
5
Published on 14 November 2013. Downloaded by University of Virginia on 16/11/2013 16:53:39.
10
15
0.6, respectively, under 80 keV and 60 keV EI. The above two L’s agree well with the level of amorphization, i.e., L = 1.1 and L = 0.8, respectively, from the simulation in quality. Thus, the kinetic model is validated, from which the level of the amorphization may be understood for the competition between expansion and shrinkage of the amorphous structure. It is important to note that the discrepancy between the kinetic model and the simulation may be stemmed from the following factors: (i) the rough estimation of the threshold barrier that triggers a GSWT, which should be higher than the exact barrier of bond rotation because of the lattice vibrations at finite temperature and energy dissipation in real experiments and simulations; 24, 42, 43 (ii) the rough estimation of the loop width; (iii) the CG kinetic model may not well applicable for a very system like r6; and (iv) the inaccuracy of the empirical REBO2 potential.34
60
65
70
Conclusion
20
25
30
In summary, we have simulated the real-time reconstruction of a divacancy from point defect to various amorphous structures in graphene under EI via NEMD simulation. The reconstruction is found through a series of generalized Stone-Wales transformation (GSWT). During such evolution, although under stochastic EI of high intensity, the GSWT that leads to less energy rising occurs more frequently and can be described by the Boltzmann distribution. In addition, the level of amorphization, i.e., the number of r6’s that are enclosed by the GB loop, can be understood by a coarse grained kinetic model, which accounts for the competition between expansion and shrinkage of the amorphous structure. Thus, the route of amorphous structure is predictable, with the structure following MEP, and the level of amorphization within the framework of a kinetic model. This finding greatly improved our understanding on the reconstruction of amorphous structure in point defective graphene under EI, and provides a model to estimate the amorphous area in quantity
75
80
85
90
Acknowledgements 35
40
This work done in Nankai is supported by NSFC (21373118, 21073097), Natural Science Foundation of Tianjin (12JCYBJC13900), NCET-10-0512, and National Innovative Research Program for Undergraduates (201210055035). The work done in Hong Kong Polytechnic University is supported by
Hong Kong GRF research grant (B-Q35N, B-Q26K), Hong Kong PolyU Internal grants (G-YM60, G-UC49 G-UB57, APM35, A-PK89, A-PJ50) and NSFC grant (21273189) The simulations were performed on TianHe-1A Supercomputer Center in Tianjin, China.
45
95
at
National
100
Notes and References a
50
55
Tianjin Key Laboratory of Metal- and Molecule-Based Material Chemistry, Synergetic Innovation Center of Chemical Science and Engineering (Tianjin), Key Laboratory of Advanced Energy Materials Chemistry (Ministry of Education), Institute of New Energy Material Chemistry, College of Chemistry, Nankai University, Tianjin 300071, China. Email: [email protected] b Institute of Textiles and Clothing, Hong Kong Polytechnic University, Hung Hom, Hong Kong, China. Email: [email protected] † Electronic supplementary information (ESI) available: Computational methods
4 | Journal Name, [year], [vol], 00–00
105
110
1. A. Hashimoto, K. Suenaga, A. Gloter, K. Urita and S. Iijima, Nature, 2004, 430, 870-873. 2. A. V. Krasheninnikov and F. Banhart, Nat. Mater., 2007, 6, 723-733. 3. F. Banhart, J. Kotakoski and A. V. Krasheninnikov, ACS Nano, 2010, 5, 26-41. 4. A. V. Krasheninnikov and K. Nordlund, J. Appl. Phys., 2010, 107, 071301-071370. 5. Ç. Ö. Girit, J. C. Meyer, R. Erni, M. D. Rossell, C. Kisielowski, L. Yang, C.-H. Park, M. F. Crommie, M. L. Cohen, S. G. Louie and A. Zettl, Science, 2009, 323, 1705-1708. 6. J. H. Warner, E. R. Margine, M. Mukai, A. W. Robertson, F. Giustino and A. I. Kirkland, Science, 2012, 337, 209-212. 7. S. Kurasch, J. Kotakoski, O. Lehtinen, V. Skákalová, J. Smet, C. E. Krill, A. V. Krasheninnikov and U. Kaiser, Nano Lett., 2012, 12, 3168-3173. 8. O. Lehtinen, S. Kurasch, A. V. Krasheninnikov and U. Kaiser, Nat Commun, 2013, 4, 2098. doi:2010.1038/ncomms3098. 9. R. Khare, S. L. Mielke, J. T. Paci, S. Zhang, R. Ballarini, G. C. Schatz and T. Belytschko, Phys. Rev. B, 2007, 75, 075412. 10. O. V. Yazyev and L. Helm, Phys. Rev. B, 2007, 75, 125408. 11. M. T. Lusk and L. D. Carr, Phys. Rev. Lett., 2008, 100, 175503. 12. A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov and A. K. Geim, Rev. Mod. Phys., 2009, 81, 109-162. 13. O. Cretu, A. V. Krasheninnikov, J. A. Rodríguez-Manzo, L. Sun, R. M. Nieminen and F. Banhart, Phys. Rev. Lett., 2010, 105, 196102. 14. J. Lahiri, Y. Lin, P. Bozkurt, I. I. Oleynik and M. Batzill, Nat. Nanotech., 2010, 5, 326-329. 15. D. J. Appelhans, Z. Lin and M. T. Lusk, Phys. Rev. B, 2010, 82, 073410. 16. J. Li and F. Banhart, Nano Lett., 2004, 4, 1143-1146. 17. F. Banhart, J. Li and M. Terrones, Small, 2005, 1, 953-956. 18. F. Banhart, J. X. Li and A. V. Krasheninnikov, Phys. Rev. B, 2005, 71, 241408. 19. J. C. Meyer, C. Kisielowski, R. Erni, M. D. Rossell, M. F. Crommie and A. Zettl, Nano Lett., 2008, 8, 3582-3586. 20. J. A. Rodriguez-Manzo and F. Banhart, Nano Lett., 2009, 9, 22852289. 21. J. Kotakoski, A. V. Krasheninnikov, U. Kaiser and J. C. Meyer, Phys. Rev. Lett., 2011, 106, 105505. 22. A. W. Robertson, C. S. Allen, Y. A. Wu, K. He, J. Olivier, J. Neethling, A. I. Kirkland and J. H. Warner, Nat. Commun., 2012, 3, 1144. 23. A. Zobelli, A. Gloter, C. P. Ewels and C. Colliex, Phys. Rev. B, 2008, 77, 045410. 24. G.-D. Lee, C. Z. Wang, E. Yoon, N.-M. Hwang, D.-Y. Kim and K. M. Ho, Phys. Rev. Lett., 2005, 95, 205501. 25. G.-D. Lee, C. Z. Wang, E. Yoon, N.-M. Hwang and K. M. Ho, Phys. Rev. B, 2006, 74, 245411. 26. J. Kotakoski, J. C. Meyer, S. Kurasch, D. Santos-Cottin, U. Kaiser and A. V. Krasheninnikov, Phys. Rev. B, 2011, 83, 245420. 27. Z. Wang, Y. G. Zhou, J. Bang, M. P. Prange, S. B. Zhang and F. Gao, J. Phys. Chem. C, 2012, 116, 16070-16079. 28. A. J. Stone and D. J. Wales, Chem. Phys. Lett., 1986, 128, 501-503. 29. L. Li, S. Reich and J. Robertson, Phys. Rev. B, 2005, 72, 184109. 30. J. Ma, D. Alfé, A. Michaelides and E. Wang, Phys. Rev. B, 2009, 80, 033407.
This journal is © The Royal Society of Chemistry [year]
Nanoscale Accepted Manuscript
DOI: 10.1039/C3NR05215J
Page 5 of 6
Nanoscale View Article Online
DOI: 10.1039/C3NR05215J
10
15
20
25
This journal is © The Royal Society of Chemistry [year]
Nanoscale Accepted Manuscript
Published on 14 November 2013. Downloaded by University of Virginia on 16/11/2013 16:53:39.
5
31. B. Song, G. g. F. Schneider, Q. Xu, G. g. Pandraud, C. Dekker and H. Zandbergen, Nano Lett., 2011, 11, 2247-2250. 32. F. Börrnert, L. Fu, S. Gorantla, M. Knupfer, B. Büchner and M. H. Rümmeli, ACS Nano, 2012, 6, 10327-10334. 33. C. J. Russo and J. A. Golovchenko, Proc. Natl. Acad. Sci. USA, 2012, 109, 5953-5957. 34. D. W. Brenner, O. A. Shenderova, J. A. Harrison, S. J. Stuart, B. Ni and S. B. Sinnott, J. Phys.: Condens. Matter, 2002, 14, 783-802. 35. Y. Kim, J. Ihm, E. Yoon and G.-D. Lee, Phys. Rev. B, 2011, 84, 075445. 36. A. A. El-Barbary, R. H. Telling, C. P. Ewels, M. I. Heggie and P. R. Briddon, Phys. Rev. B, 2003, 68, 144107. 37. A. V. Krasheninnikov, P. O. Lehtinen, A. S. Foster and R. M. Nieminen, Chem. Phys. Lett., 2006, 418, 132-136. 38. T. Dumitrica and B. I. Yakobson, Appl. Phys. Lett., 2004, 84, 27752777. 39. F. Ding, K. Jiao, M. Wu and B. I. Yakobson, Phys. Rev. Lett., 2007, 98, 075503. 40. Y. Liu and B. I. Yakobson, Nano Lett., 2010, 10, 2178-2183. 41. B. I. Yakobson and F. Ding, ACS Nano, 2011, 5, 1569-1574. 42. J. C. Meyer, F. Eder, S. Kurasch, V. Skakalova, J. Kotakoski, H. J. Park, S. Roth, A. Chuvilin, S. Eyhusen, G. Benner, A. V. Krasheninnikov and U. Kaiser, Phys. Rev. Lett., 2012, 108, 196102. 43. J. C. Meyer, F. Eder, S. Kurasch, V. Skakalova, J. Kotakoski, H. J. Park, S. Roth, A. Chuvilin, S. Eyhusen, G. Benner, A. V. Krasheninnikov and U. Kaiser, Phys. Rev. Lett., 2013, 110, 239902.
Journal Name, [year], [vol], 00–00 | 5
Nanoscale Accepted Manuscript
Published on 14 November 2013. Downloaded by University of Virginia on 16/11/2013 16:53:39.
Nanoscale View Article Online
Page 6 of 6
DOI: 10.1039/C3NR05215J
Table of Contents (TOC) Graphic
