Bragg–von Laue diffraction generalized to twisted X-rays

A pervasive limitation of nearly all practical X-ray methods for the determination of the atomic scale structure of matter is the need to crystallize the molecule, compound or alloy in a sufficiently large (∼10 × 10 × 10 µm) periodic array. In this paper an X-ray method applicable to structure determination of some important noncrystalline structures is proposed. It is designed according to a strict mathematical analog of von Laue's method, but replacing the translation group by another symmetry group, and simultaneously replacing plane waves by different exact closed-form solutions of Maxwell's equations. Details are presented for helical structures like carbon nanotubes or filamentous viruses. In computer simulations the accuracy of the determination of structure is shown to be comparable to the periodic case.