We determine properties of the vacancy in graphite from first principles calculations. The ground-state structure is associated with a formation energy of 7.4 eV and arises through a combination of symmetric relaxation and symmetry-breaking Jahn-Teller distortion to one of three degenerate, symmetry-related structures. The distortion results in a weak reconstructed bond and small out-of-plane atomic displacements. Dynamic switching between degenerate structures is activated by a barrier of 0.1 eV and we interpret scanning tunneling microscopy observations on the basis of thermal averaging between structures. The calculated migration energy of 1.7 eV is lower than that widely accepted from experiment, and we propose that the discrepancy is explained by a revised picture of trapping during vacancy transport, dependent on concentration. We discuss the significance of these findings in understanding defect behavior in irradiated graphite and related graphitic materials, in particular single-walled nanotubes.

Nitrogen doping of single and multi-walled carbon nanotubes is of great interest both fundamentally, to explore the effect of dopants on quasi-1D electrical conductors, and for applications such as field emission tips, lithium storage, composites and nanoelectronic devices. We present an extensive review of the current state of the art in nitrogen doping of carbon nanotubes, including synthe- sis techniques, and comparison with nitrogen doped carbon thin films and azofullerenes. Nitrogen doping significantly alters nanotube morphology, leading to compartmentalised 'bamboo' nanotube structures. We review spectroscopic studies of nitrogen dopants using techniques such as X-ray photoemission spectroscopy, electron energy loss spectroscopy and Raman studies, and associated theoretical models. We discuss the role of nanotube curvature and chirality (notably whether the nanotubes are metallic or semiconducting), and the effect of doping on nanotube surface chemistry. Finally we review the effect of nitrogen on the transport properties of carbon nanotubes, notably its ability to induce negative differential resistance in semiconducting tubes.

We present a theoretical description of electron irradiation of single-walled carbon and boron nitride nanotubes. In a first step, the anisotropy of the atomic emission energy threshold is obtained within extended molecular-dynamics simulations based on the density-functional tight-binding method. In a second step, we numerically derive the total Mott cross section for different emission sites as a function of the incident electron energy. Two regimes are then described: at low irradiation energies (below $300\mathrm{keV}$), the atoms are preferentially ejected from the upper and lower parts of the tube, while at high energies (above $300\mathrm{keV}$), the atoms are preferentially ejected from the side walls. Typical values from a fraction of barn (at side wall for $150\mathrm{keV}$ electron) up to around $20\text{barn}$ (for $1\mathrm{MeV}$ electrons) are obtained for the total cross section of knock-on processes for both C and BN nanotubes. These values are smaller than those previously reported using isotropic models and the main reasons for the discrepancies are discussed. Finally, in boron nitride nanotubes, we report that the emission energy threshold maps show boron sputtering to be more favorable for low irradiation energies, while nitrogen sputtering is more favorable at high energies. These calculations of the total knock-on cross section for various nanotubes can be used as a guideline for transmission electron microscopy experimentalists using high energy focused beams to shape nanotubes, and also more generally if electron irradiation is to be used to change nanotube properties such as their optical behavior or conductivity.

Activation energies and reaction paths for diffusion and nucleation of mono- and divacancy defects in hexagonal boron nitride layers are theoretically investigated. Migration paths are derived using the nudged elastic band method combined with density-functional-based techniques. We find a different behavior for migration of single boron and nitrogen vacancies with the existence of intermediate metastable states along the migration paths. The temperature dependence of entropic and vibrational contributions to the free Gibbs energies is explicitly taken in account. A rich phase diagram for vacancy migration is then obtained. Boron vacancies are first thermally activated and can migrate to form more stable BN divacancies. At high temperatures, the divacancies can further be activated. In the contrary, nitrogen vacancy migration is energetically unfavorable within all the temperature range below the melting point of h-BN.