Threshold displacement energies in graphene and single-walled carbon nanotubes

Andrew Merrill, Cory D. Cress, Jamie E. Rossi, Nathanael D. Cox, and Brian J. Landi

Phys. Rev. B 92, 075404 – Published 3 August 2015

Abstract

The threshold displacement energy $E_{d}$ has been determined for graphene and 216 different ( $n, m$ ) single-walled carbon nanotube chiralities, with $5 \leq n \leq 20$ and $0 \leq m \leq n$ , under several model conditions using classical molecular dynamics. The model conditions vary by particle (electron or carbon ion), empirical potential (two parametrizations of Tersoff [J. Tersoff, Phys. Rev. B 39, 5566 (1989); L. Lindsay and D. A. Broido, Phys. Rev. B 81, 205441 (2010)] and one of Brenner et al. [D. W. Brenner, O. A. Shenderova, J. A. Harrison, S. J. Stuart, B. Ni, and S. B. Sinnott, J. Phys.: Condens. Matter 14, 783 (2002)]), and momentum transfer direction (towards or away from the nanotube axis). For electron irradiation simulations, $E_{d}$ exhibits a smoothly varying chirality dependence and a characteristic curvature influenced by the momentum transfer direction. Changing the empirical potential shifts the magnitude of $E_{d}$ , but the trend is preserved for electron simulations. However, the perturbation in the knock-on dynamics introduced by the carbon ion leads to $E_{d}$ trends that diverge from the equivalent electron simulation. Thus, the ion interaction has a non-negligible effect on the dynamics of the collision and leads to $E_{d}$ values that can distinctly vary depending on the selected carbon nanostructure.

Received 23 May 2014
Revised 19 June 2015

DOI:https://doi.org/10.1103/PhysRevB.92.075404

Authors & Affiliations

Andrew Merrill¹, Cory D. Cress^2,*, Jamie E. Rossi¹, Nathanael D. Cox^1,3, and Brian J. Landi^1,4,†

¹NanoPower Research Laboratory, Rochester Institute of Technology, Rochester, New York 14623
²Electronics Science and Technology Division, United States Naval Research Laboratory, Washington, DC 20375
³Department of Microsystems Engineering, Rochester Institute of Technology, Rochester, New York 14623
⁴Department of Chemical Engineering, Rochester Institute of Technology, Rochester, New York 14623

^*carbon.nanoelectronics@nrl.navy.mil
^†brian.landi@rit.edu

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Vol. 92, Iss. 7 — 15 August 2015

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Images

Figure 1
(a) Perspective view and top view schematic of the simulation setup. The black regions of the SWCNT are held fixed during the simulation, the red regions are thermostatted, and the gray and blue regions evolve freely over the course of the simulation. The target PKA is selected randomly from the atoms in the blue region. Arrows branching out from the target PKA region point to snapshots of the three variations under model conditions (axial view) involving different irradiation particles (electron or carbon ion) and the direction of momentum transfer [radially inward ( $-$ ) vs outward ( $+$ )] along with its corresponding symbolic representation for the model: $Φ_{e}^{+}, Φ_{e}^{-}$ , and $Φ_{C}^{-}$ . (b) Chirality-mapped, threshold displacement energies across nine different combinations of irradiation particle, direction, and empirical potential. The rows correspond to the combination of particle and direction as indicated by the axial view snapshot and symbolic notation (defined in the text). Constant diameter contours are shown to highlight the diameter dependence. The right-handed chiralities have been mapped to the left-handed chiralities to effect a full chirality map.
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Figure 2
Threshold displacement energy $E_{d}$ as a function of nanotube diameter for nine combinations of irradiation particles, direction, and empirical potentials. The $E_{d}$ for electron irradiation with PKA momentum transfer directed radially (a) outward, away from the nanotube axis, and (b) inward, towards the nanotube axis. (c) Carbon ion irradiation with ion-PKA momentum transfer directed radially inward. The symbolic notation ( $Φ_{e}^{+}, Φ_{e}^{-}, Φ_{C}^{-}$ ) is defined in the text. The zigzag chirality markers are filled in with black and the armchair markers with gray. The dashed lines show the mean $E_{d}$ ( ${\bar{E}}_{d}$ ) values for each set of conditions. The solid lines are the $E_{d}$ values obtained for graphene at each simulated irradiation condition.
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Figure 3
(a) Threshold displacement energy $E_{d}$ and snapshots of the time-dependent changes in the median PKA nearest-neighbor bond length 5 fs following simulated knock-on for electron irradiation simulations. The zigzag chirality markers are filled in with black and the armchair markers with gray. (b) Schematic diagram showing two-dimensional (2D) projections of the PKA and its nearest-neighbors onto the tangent plane of the PKA, highlighting the change in the orientation of the PKA's three nearest-neighbor bond vectors with respect to the SWCNT chiral vector $C_{h}$ and the translation vector $T$ , as the chiral angle increases from $0^{\circ}$ ( $m = 0$ ) to $30^{\circ}$ ( $m = n$ ) for a given chiral series $n$ . The bond vectors of the PKA's three nearest-neighbor atoms are shown in red. The projection of the bond 2 vector onto the translation vector is represented by the dashed red line in each orientation.
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