Radiation diffraction in a hollow of a nanotube

I.K.Nasyrov, E.A.Semyonov, Z.Ya.Khalitov

Russia

 

Spectral dependences and distributions of intensity of short-wave radiation diffraction (X-ray quanta, particles of corresponding energies) on circular, helical, spiral and radial lattices into an internal hollow of a nanotube were calculated. Differences and abnormal character of a nanotube internal hollow passage by radiation, possessing the characteristic wavelength, were revealed.

The cylindrical crystals, called nanotubes, possess a number of unique properties distinguishing them from crystals with rectilinear lattice. One of such properties is their internal cylindrical hollow which has no crystal lattice but is an integral part of cylindrical crystal. The problem of diffraction behavior of radiation of a corresponding wave range into such a hollow on the surrounding cylindrical structure is of fundamental interest and can enable new applied developments.

Note, analysis of intensity distribution of short-wave radiation's Fresnel's diffraction in various nanotubes hollow in case of a lattice, performed by direct computer calculation, showed that at longitudinal passage of radiation and diffraction condition fulfillment the radiation concentrates forming a standing wave: in case of a radial lattice - on nanotube axis, in case of circular and spiral nanotubes - on nanotube axis and around its average radius, in case of a helical nanotube - around the h-threaded helical line with radius equal to average radius of a lattice and with step equal to longitudinal parameter of a lattice a, where h - is a characteristic wave mode number. The degree of diffraction intensity concentration on tube axis is maximal for radial lattices, minimal for helical lattices, and for circular and spiral lattices has intermediate behavior. In case of a radial lattice almost full concentration of scattered radiation in an internal hollow of a nanotube takes place.

This phenomenon can have various areas of practical application. Concentration of X-ray radiation in certain area of a cylindrical crystal can be used for determination of chemical composition of a given area by secondary X-ray spectrum. Special properties of circular, spiral and radial lattices allow realizing so-called in X-ray range. Estimation of angular selectivity of such a system gives value of ~10^-8 radians, and detector can be rather compact and have higher aperture ratio if natural parallel blocks of chrysotile are used.

One can approve that in case of longitudinal passage of charged particles (e.g. electrons) through a nanotube, the discussed phenomena will take place along with the effects, connected with behavior of electron in a cylindrical potential well. In this case an electron with the wavelength, scattered in an internal hollow of a circular, spiral or radial nanotube, should form a longitudinal standing wave in vacuum of a hollow. This effect can explain the known phenomenon of quantum conductivity observed for carbon nanotubes.

Discussed phenomena have obvious analogy with area of waveguide effects. Not concerning the terminological side of a question, authors on the basis of obtained results assume that in nanotubes (non-helical) it is possible to realize longitudinal passage of radiation with characteristic wavelength regardless of physical nature of particles (X-ray quanta, fundamental particles with nonzero rest mass, atoms).