Quantitative theory of diffraction on polytypic modifications of coaxial nanotubes

Introduction. Research into the electronic properties of field-effect transistor prototypes and other nanotube-based elements has highlighted their potential for use in nanoelectronic devices, boosting experimental design and industrial development. However, these studies also reveal a significant sensitivity of electronic parameters to the nanotube structure, compounded by the fact that synthesis methods rarely produce strictly monophase products with the desired structural characteristics, primarily influenced by their polytypic modifications. Consequently, there is an increasing need for technology that can select conditioned nanotubes from synthesis outputs to ensure consistent production.

This study aims at enhancing a quantitative theory of diffraction applicable to the full range of shear, chiral, and radial polytypic modifications of ordered coaxial nanotubes of various chemical compositions. There were addressed several key problems, including analyzing basal, diffuse, and clear nodes of reciprocal lattices, which led to the derivation of X-ray crystallography formulas linking diffraction patterns of polytypes to their structural parameters. The performed mathematical analysis revealed distinct diffraction phenomena for shear, chiral, and radial polytypes in ordered coaxial nanotubes. The following findings were obtained: 1) Shear polytypes cause the rotation of reciprocal lattice rosettes within their planes; clear rosettes rotate uniformly while diffuse rosettes rotate at varying angles, resulting in shifts along layer lines in diffraction patterns. 2) Chiral polytypes influence both the positions of layer planes and lines, as well as angular splittings of diffuse reflections, with shifts and rotations in repeating layers affecting reflection intensities. We shall note that the chiral indices defined in this study characterize chirality even in nanotubes lacking structural hexagons. The radial polytype is indicated by specific high-frequency oscillations in intensity profiles due to intra-tube interference.

Conclusions: The proposed mathematical framework for analyzing diffraction from polytype modifications of coaxial nanotubes facilitates structural analysis and identification within synthesis products. This technology is applicable not only in the experimental design phase of nanoelectronic elements but also in the production of nanoelectronic devices using tailored nanotube materials. Furthermore, our calibration technology for coaxial nanotubes can enhance process control in related industries.