The diffraction space of circular and polygonized multishell nanotubules

The diffraction space of circular multishell graphite nanotubules consists of loci corresponding to the various reciprocal lattice nodes characteristic of graphitic structures. These loci are in general evolutes of circles; for certain nodes they become circles. The geometrical properties of diffraction space are discussed analytically and simulated numerically by using the kinematical diffraction theory. It is shown that the diffraction pattern will in general not exhibit 2 mm planar symmetry, as is often assumed, but will have a centre of symmetry only. This is confirmed by observations. In tubules having a polygonal cross section the diffraction space becomes a curvilinear lattice of discrete nodes.