Symmetry and Models of Single-Wall BN and TiO₂ Nanotubes with Hexagonal Morphology

Abstract

For ab initio simulations on hexagonal single-wall BN and TiO2 nanotubes (SW NTs), we have applied the formalism of line symmetry groups describing one-periodic (1D) nanostructures with rotohelical symmetry. Both types of NTs can be formed by rolling up the stoichiometric nanosheets of either (i) a (0001) monolayer of BN hexagonal phase or (ii) a three-layer (111) slab of fluorite-type TiO2 phase. Optimized parameters of the atomic and electronic structure of corresponding slabs and nanotubes have been calculated using hybrid LCAO method as implemented in CRYSTAL code. Their band gaps (Δεgap) and strain energies (Estrain) have been analyzed as functions of NT diameter (DNT). For hexagonal BN and TiO2 nanotubes, certain qualitative similarities between the Δεgap(DNT) or Estrain(DNT) functions exist despite the different chemical nature.