350 rub
Journal Nonlinear World №5 for 2010 г.
Article in number:
Features of Diffraction by Spiral Nanotubes
Keywords: nanotube diffraction spiral coordinates of atoms intensity of diffraction layered line
Authors:
I.K. Nasyrov, D.N. Valeeva, Z.J. Khalitov
Abstract:
The purpose of consideration is to obtain the cylindrical coordinates of spiral nanotube-s atoms, based on an Archimedes spiral, and development of the quantitative theory of diffraction by spiral nanotubes. The crystallographic description of monoclinic and orthogonal polytype modifications of a multilayer multiple spiral lattice is ad-vanced, the expressions for cylindrical coordinates of sites and of number of sites on the coils of spiral are obtained. Is shown, that, as well as in case of circular lattices, at transition from a layer to a layer the number of sites changes on the value of generator. The linear approximation for coordinates of a lattice sites, simplifying the analysis of strong reflexes of a diffractional pattern, is offered. The disposition of the unit cell of spiral structure differs from a case of circular structure only by small turns around of an axis, parallel nanotube-s axis, and axis, perpendicular layer. Then as a first approximation the coordinates of atoms of spiral structure can be written down as the sum of coordinates of sites of a spiral lattice and coordinates of atoms in unit cell of circular nanotube. The quantitative theory of diffraction by spiral nanotubes is developed, the expressions for intensity of strong and diffuse reflexes, and also for coordinates of their layered lines are received. Is shown, that the layered lines of strong reflexes are not split, but the value and direction of displacement of diffuse reflex from a layered line depends on an index k. Both the profiles of diffraction along the layered lines of plan section of the spiral nanotube-s reciprocal space, and the distribution of intensity in plan section, perpendicular to the nanotube-s axis, are calculated. In spiral nanotubes, as well as in circular, the effect of pseudoorthogonality takes place. The effect means the presence in diffraction pattern of monoclinic polytype alongside with its reflexes h00 also of reflexes h00 of orthogonal polytype at complete absence of its other reflexes. The pseudo-orthogonal reflexes are designated by two-place indexes h0, and their intensity in case of spiral structures is much less, than from the circular nanotubes.
Pages: 269-276
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