A calculation model for X-ray diffraction by curved-graphene nanoparticles

An approximation of the positions of carbon atoms in a curved graphene sheet is suggested for calculation of X-ray diffraction (XRD) patterns of curved-graphene nanoparticles. The model is tested for carbon nanotubes and newly calculated carbon nanotoroids consisting of several hundreds of atoms. It is shown that the random distribution of carbon atoms with graphene surface-averaged density and the local graphene-like rearrangement of atoms in a curved lattice are sufficient for describing the XRD patterns of an ensemble of respective exact carbon nanoparticles of random isotropic orientation in the range of scattering wave vector's modulus q from several units to several tens of inverse nanometers. The model is of interest to a fast-routine identification of curved-graphene nanoparticles in carbonaceous materials.