Diffraction by the ideal paracrystal

A detailed analysis is made of the statistics and diffraction by a general, finite, two-dimensional ideal paracrystal. The statistics of the diagonal chain through the ideal paracrystal are derived, and the special cases of square and hexagonal ideal paracrystals are considered. Expressions for the diffraction are derived and characteristics of diffraction patterns are discussed in terms of the different parameters of the model for square and hexagonal ideal paracrystals. The variation of peak widths with scattering angle along different directions in reciprocal space is examined.