Demonstrating structural deformation in an inorganic nanotube

There is much current interest in nanostructured materials (nanotubes, nanobelts, nanospheres, etc.). Their crystal structures can differ from those of the equivalent bulk materials. Determining these differences is important in understanding how the properties of nanomaterials differ from those of the bulk. Established methods of X-ray structure determination become increasingly difficult or impossible to apply on reducing the dimensions to a few nanometers. Here we show that, by combining the Debye equation for X-ray scattering (which relates an ensemble of atoms to-their diffraction pattern without recourse to symmetry) with a model of the crystal structure, generated by folding the ideal crystal structure into a nanotube, the severely broadened/distored powder diffraction pattern may be described. This procedure reveals the significant structural deformations necessary to accommodate the nanotube shape. The importance of knowing the (deformed) crystal structure is discussed.