Geometric Model for Boron Nitride Nanotubes Incorporating Curvature

Abstract

The conventional rolled-up model of nanotubes does not apply to the very small radii tubes, for which curvature effects become significant. Here, an existing geometric model for carbon nanotubes that has been proposed by the authors, which accommodates this deficiency and 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 generalization 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. Working from five simple geometric assumptions, expressions are derived for the various structural parameters such as radii and bond angles for the two species for specific values of the chiral vector numbers (n, m). The new model incorporates an additional constant of proportionality (τ), which we assume applies to all nanotubes comprising the same elements a...