An idealized polyhedral model and geometric structure for silicon nanotubes.

In this paper, we introduce an idealized model of silicon nanotubes comprising an exact polyhedral geometric structure for single-walled silicon nanotubes. The silicon nanotubes considered here are assumed to be formed by sp(3) hybridization and thus the nanotube lattice is assumed to comprise only squares or skew rhombi. Beginning with the three postulates that all bond lengths are equal, all adjacent bond angles are equal, and all atoms are equidistant from a common axis of symmetry, we derive exact formulae for the geometric parameters such as radii, bond angles and unit cell length. We present asymptotic expansions for these quantities to the first two orders of magnitude. Because of the faceted nature of the polyhedral model we may determine a perceived inner radius for the nanotube, from which an expression for the wall thickness emerges. We also describe the geometric properties of some ultra-small silicon nanotubes. Finally, the values of the diameters for the polyhedral model are compared with results obtained from molecular dynamics simulations and some limited numerical calculations are undertaken to confirm the meta-stability of the proposed structures.