Adsorption and migration of carbon adatoms on zigzag carbon nanotubes
Introduction
The outstanding mechanical and electronic properties of single-walled carbon nanotubes (SWNTs) have stimulated much research on their mass production techniques. However, despite a considerable effort, further progress is hampered by the lack of the control over SWNT chiralities and diameters at the growth stage. This is in part due to the insufficient understanding of SWNT growth mechanisms.
A number of microscopic SWNT growth models have been developed [1], [2], [3], [4], [5], [6] with growth taking place either at the nanotube edge [1], [2], [3] (capped or open) or its root [4], [5], [6]. Depending on the temperature range and catalyst used, any of the mechanisms may work. However, whatever the mechanism is, the quantitative understanding of the synthesis process is not possible without knowing how the “building blocks”––carbon atoms and clusters––are supplied to the place where the SWNT growth occurs.
Carbon atoms coming from the feedstock (plasma, gas, etc.) can be captured directly at the end of the SWNT [3], especially if dangling covalent bonds are present. However, it seems to be more plausible that the atoms are first absorbed on the SWNT surface and then they migrate to the SWNT growing end [1], [2]. The adsorbed atoms (adatoms) can also aggregate and form clusters (amorphous carbon) and detach from nanotube surface. Thus, knowing the adatom migration mechanism and such key quantities like adsorption and migration energies is indispensable for the comprehensive theory of SWNT synthesis.
At the same time, there exists very little knowledge about how carbon adatoms migrate over the SWNT surface. There have been studies on the migration of carbon adatoms on a graphite (flat) surface [1], [7] but effects of SWNT surface curvature on the carbon adatom diffusion have not yet been studied by the proper methods.1 Moreover, the reported values of the adatom migration barrier (about 0.1 eV) [1], [7] seem to be much lower than the value (∼0.8 eV) obtained in experiments on the annealing of the irradiation-induced damage in SWNTs [11]. Annealing, similar to the SWNT growth, is governed by the migration of adatoms which play the role of interstitials in SWNTs [12].
In this paper we study the adsorption and diffusion of carbon adatoms on SWNTs. By using two different computational techniques we evaluate the adatom adsorption energy Ea and migration barrier Em for zigzag SWNTs with various chiralities.
Section snippets
Calculation details
In our simulations, we employed density-functional theory (DFT) implemented in the non-orthogonal real-space tight-binding (DFTB) code [13] and the plane wave (PW) basis set VASP [14] code. Although the PW DFT method has very well been established as the leading edge in electronic structure calculations, we were unable to carry out all calculations using this method because of computational limitations. However, as shown below, the DFTB approach in which the parameters of the Hamiltonian are
Carbon adatom on a graphene sheet
To check the applicability of DFTB to the problem of adatom migration, we started by calculating Ea and Em for the adatom on small graphene flakes consisting of 60–216 atoms. We found that the equilibrium position of the adatom was a bridge-like structure (the adatom is above the middle of the carbon-carbon bond) with the perpendicular distance to the graphite surface being 1.9 Å. Our recent DFT PW calculations gave exactly the same configuration with a distance of 1.87 Å [10]. Ea (with account
Carbon adatoms on zigzag nanotubes
In this work we dwell upon zigzag (n,0) SWNTs which, depending on the SWNT chiral index n, can be metals or narrow-band semiconductors. This made it possible to study effects of not only nanotube curvature, but also electronic structure on the diffusion and adsorption.
In the DFTB calculations, finite SWNTs (having a length of 12.7 Å and composed of up to 200 atoms) with periodical boundary conditions were considered. The same systems were used for the DFT PW simulations. To check how the
Conclusion
To conclude, using density-functional tight-binding and ab initio methods we studied the adsorption and migration of carbon adatoms on zigzag nanotubes. We found that the adatoms form strong covalent bonds with the nanotubes and that the migration is strongly anisotropic. The adatom adsorption energy and migration barrier depend on the nanotube diameter and chirality, which should be taken into account in models of nanotube growth and radiation damage annealing. The migration barriers, being in
Acknowledgments
We would like to thank F. Banhart for useful discussions and Th. Frauen-heim for the permission to use the DFTB code. The research was supported by the Academy of Finland under project nos. 48751 and 50578. Grants of computer time from the Center for Scientific Computing in Espoo, Finland, are gratefully acknowledged.
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