Electron diffraction patterns from scroll nanotubes: interpretation peculiarities

Abstract

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.

Quantitative theory of diffraction by cylindrical scroll nanotubes

“…If condition (25) is satisfied, then exponents will become trivial phase factors and the positions and shape of the reciprocallattice nodes will be defined by other factors in (22)-(24). It should be noted that for k = 0 expression (25) becomes similar to expression (5) from our already published work (Khalitov et al, 2015). Maxima conditions of sums over m are listed in the third column of Table 2, where l ¼ 0; AE1; AE2; .…”

“…It follows that basal reflections do not have any conditions for the formation of distinct reflections that were found for other reflections: basal reflections are observable in the diffraction pattern from all scroll nanotubes independently of their structural parameters. From equation (27) it is also seen that the basal reflection intensity of scroll tubes, contrary to coaxial tubes (Khalitov et al, 2015(Khalitov et al, , 2016a, depends on '* with period equal to /l. Fig.…”

“…The observable dependence of the diffraction intensity of basal reflections on '* proves our above-mentioned conclusions. This dependence can be used as a diffraction criterion for separation of scroll nanotubes from coaxial ones (Khalitov et al, 2015).…”

“…Transmission electron microscopy (TEM) is one of the most suitable methods for structural analysis of individual nanotubes; moreover, almost all studies of different nanotubes are accompanied by TEM images. An electron diffraction technique that can be realized on the basis of conventional TEM allows researchers to investigate structural parameters of an individual tube (Deniz et al, 2010;Deniz & Qin, 2012;Khalitov et al, 2015;Chen et al, 2017) and recent developments in nanomanipulator systems have made it possible to simultaneously analyse the structure and properties of an individual nanotube directly in a TEM column (Kociak et al, 2002;Rodríguez-Manzo et al, 2009;Schaper, Hou et al, 2011;. Therefore, further development of an electron diffraction technique for structural analysis of scroll nanotubes is very important for fundamental and applied research.…”

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

“…The proposed qualitative approach has allowed scientists to describe the geometry of nanotube reciprocal space and explain several observed diffraction phenomena. In some cases, for example, in describing the fine structure of diffuse reflections, in addition to qualitative considerations of nanotube structure (Bernaerts & Amelinckx, 1996) authors have performed numerical simulations of intensity distribution in diffraction space (DeVouard & Baronnet, 1995;Bernaerts et al, 1998;Khalitov et al, 2015).…”