The quantitative theory of diffraction by azimuthally ordered circular nanotubes of any chemical composition is offered. The pseudoorthogonality effect, earlier found out experimentally, is considered. The obtained results are compared with X-ray diffraction patterns of oriented preparations of chrysotile nanotubes.
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.
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.
This article describes the structure of scroll nanotubes and associated diffraction effects in the context of electron diffraction from a single nanotube. It is suggested that the effect of multiple equidistant splitting of diffuse reflections into cone series be used as a diffraction criterion for conical scroll structure identification. For cylindrical scroll structure determination, the effect of the azimuthal dependence of the intensity of basal diffraction spots is proposed as a characteristic sign. Good agreement between specific oscillations in both theoretical and experimental profiles of basal diffraction spots was achieved. It was also established that there are special values of chiral angles in cylindrical scroll nanotubes that lead to order enhancement in their structure along the tube axis, whereas even a small deviation from these angles results in degradation of diffraction conditions for some diffraction spots in the diffraction pattern.
The quantitative theory of diffraction by separate chiral nanotubes of arbitrary chemical composition is offered. The pseudoorthogonality effect and dependence of diffraction on the azimuthal ordering are considered. The calculated diffraction patterns for the case of electron microdiffraction by separate chrysotile nanotubes are adduced.
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