Single-parameter model for multi-walled geometry of nanotubular boron

•A reliable geometrical model for boron multi-walled nanotubes is constructed.•It is a model with single structural parameter – the average B–B bonds length.•This model will be useful for purposeful application of nanotubular boron.•Density of bundles of boron nanotubes exceeds that of amorphous boron.

For designing devices based on nanotubular elemental boron with predetermined properties, it is important to have a reliable geometrical model of boron multi-walled nanotubes. We propose a model taking into account the following attributes of boron nanotubes: (i) defectiveness of tubular surfaces (buckling/puckering, presence of hexagonal vacancies), (ii) covalent bonding between the neighboring walls in multi-walled nanotubes and nanotubular bundles, and (iii) differences in the wall structures of single- and multi-walled nanotubes. This is a geometric model with a single structural parameter d – the average length of B–B bonds – which is based on the interpolation formulas for a nanotube radius and the 1D lattice constant. Within this model, boron nanotubes are not classified in the widely accepted fashion, i.e., in the same way as carbon nanotubes, but according to results of initial search for the boron nanotubes of reciprocal geometry of carbon nanotubes. The proposed model is tested for the value d ≈ 1.78 Å which corresponds to the equilibrium bond length according to the quasi-classical B–B pair potential. Estimates made for various bundle structures show that typically the concentrations of boron atoms are expected in the narrow range (1.6–1.8)·1023 cm−3.

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