Adatoms and nanoengineering of carbon

We present a new and general mechanism for inter-conversion of carbon structures via a catalytic exchange process, which operates under conditions of Frenkel pair generation. The mechanism typically lowers reaction barriers by a factor of four compared to equivilent uncatalysed reactions. We examine the relevance of this mechanism for fullerene growth, carbon onions and nanotubes, and dislocations in irradiated graphite. Corresponding author. e-mail: [email protected] fax: +44-1273-677196 Nanotechnology with carbon is made possible by the myriad metastable structures afforded by three fold coordinated carbon. The quintessential fullerene structure: hexagonal rings with 12 pentagons, comprises but a small subset of possible metastable structures of different ring statistics and properties[1]. Any arbitrary shape of surface may be engineered from a hexagonal net modified to include rings of different sizes [2]. Quasi-spherical carbon onions[3,4] are observed after > 100 keV electron irradiation of polyhedral carbon particles[5] and under some CVD conditions[6]. They shrink under sustained irradiation[7], suffer self-compression and, through surface tension, adopt nearly spherical shape. The phenomenon arises from Frenkel pair creation, migration and annihilation[8] and it appears to be a radial analogue of the c axis expansion (or “plating out”), observed in graphites under neutron irradiation [9]. One of the structural models which appears to mimic well experimental HRTEM onion images, achieves spherical shape through insertion of pentagon/heptagon pairs or pentagon-pentagon-octagon triads into the ground state, icosahedral, faceted fullerene shell[10]. In order to discuss shape changes, it is instructive to map a flat graphite sheet to a general shape by the introduction of topological defects. Pentagons and heptagons are, respectively, positive and negative 60 wedge disclinations. Their disposition is the main determinant of shape. They can be moved by the Preprint submitted to Elsevier Preprint 1 February 2008 absorption and emission of edge dislocations, which themselves are identified as wedge disclination dipoles and appear as pentagon-heptagon pairs. If such processes occur in even-numbered systems through the Stone-Wales (SW) route[11], high barriers must be overcome (> 6 eV)[12]. This may be theoretically possible within the thermal spike of an irradiation event or under the extreme conditions of a carbon arc, but is unlikely to contribute as strongly as a mechanism which operates more homogeneously and is modestly thermally activated at typical substrate and annealing temperatures. Carbon dimers afford an intuitively simple basis for interpretation of growth and attrition of fullerenes (observed as stable, even n clusters Cn). Addition of a C2 dimer to a fullerene or a graphite sheet followed by bond reconstruction (as invoked in the “Pentagon Road” of fullerene growth) leads to replacement of a hexagon by a pair of pentagons. Removal of such a pair (as might be invoked in onion formation) yields, in the case of graphite, two pentagons and an octagon. Each such addition/removal step must be accompanied by rearrangement to lower energy and stabilise the growth or shrinkage process. Carbon dimers are known to be ejected during thermal decomposition of fullerenes[13] and C2 is a substantial component of a carbon gas[14]. However, odd numbered species principally C and C3 also exist in the gas phase and may be ejected under irradiation above the displacement threshold. These observations led to the proposal that the SW transformations occurring during growth be auto-catalysed — catalysed by the presence of additional carbon atoms i.e. in locally odd-numbered systems. Here we explore further this possibility, first discussed by Eggen et al.[12] in the case of the last in the sequence of transformations [15] which convert an arbitrary C60 fullerene into icosahedral C60 or buckminsterfullerene (BF). In that first study, a carbon adatom was shown to reduce the barrier for this last transformation step (from a C2v isomer to BF) from 4.7 to 2.9 eV. Whereas there has been much work on the topology and sequence of transformations, including a detailed study of the energy landscape[16], there is still a need to establish energetically viable transformation paths of the kind we propose here. As before, we apply Local Spin Density Functional Theory code AIMPRO [17], using the Ceperley-Alder functional[18] and norm-conserving pseudopotentials[19]. A real-space sp basis of 16 Gaussians per atom is used for the wavefunction and 4 Gaussians per atom for the valence charge density. Analytic atomic forces are used within the conjugate gradient method to optimise structures until forces were negligible. In this way we have examined the final annealing transformation in C60 when the adatom is not in the lowest energy state and we have considered generalised transformations that create and move dislocations and disclinations