Polyhedral model for boron nitride nanotubes

Abstract

The conventional rolled‐up model for nanotubes does not apply to very small radii tubes, for which curvature effects become significant. An existing geometric model for carbon nanotubes proposed by the authors, which accommodates this deficiency and which is based on the exact polyhedral cylindrical structure, is extended to a nanotube structure involving two species of atoms in equal proportion, and in particular boron nitride nanotubes. This generalisation allows the principle features to be included as the fundamental assumptions of the model, such as equal bond length but distinct bond angles and radii between the two species. The polyhedral model is based on the five simple geometric assumptions: (i) all bonds are of equal length; (ii) all bond angles for the boron atoms are equal; (iii) all boron atoms lie at an equal distance from the nanotube axis; (iv) all nitrogen atoms lie at an equal distance from the nanotube axis; and (v) there exists a fixed ratio of pyramidal height τ, between the boron species compared with the corresponding height in a symmetric single species nanotube. Working from these postulates, expressions are derived for the various structural parameters such as radii and bond angles for the two species for general values of the chiral vector numbers (n, m). The new model incorporates the additional constant of proportionality τ, which we assume applies to all nanotubes comprising the same elements and is such that τ = 1 for a single species nanotube. Comparison with ab initio studies suggest that this assumption is entirely reasonable, and in particular we determine the value τ = 0.56±0.04 for boron nitride.