Quantitative theory of diffraction by ordered coaxial nanotubes: reciprocal-lattice and diffraction pattern indexing.

A quantitative theory of diffraction by right- and left-handed coaxial nanotubes with an ordered structure is developed. Their reciprocal lattices, including pseudo-orthogonal nodes, are studied. The explicit formulas that govern relations between direct and reciprocal lattices of a nanotube are achieved and a simple descriptive tool for diffraction pattern indexing is proposed.

Structure of ordered coaxial and scroll nanotubes: general approach.

The explicit formulas for atomic coordinates of multiwalled coaxial and cylindrical scroll nanotubes with ordered structure are developed on the basis of a common oblique lattice. According to this approach, a nanotube is formed by transfer of its bulk analogue structure onto a cylindrical surface (with a circular or spiral cross section) and the chirality indexes of the tube are expressed in the number of unit cells. The monoclinic polytypic modifications of ordered coaxial and scroll nanotubes are also discussed and geometrical conditions of their formation are analysed. It is shown that tube radii of ordered multiwalled coaxial nanotubes are multiples of the layer thickness, and the initial turn radius of the orthogonal scroll nanotube is a multiple of the same parameter or its half.