The intensities and Fourier transforms of difference reflections

The intensities of `difference reflections' of crystals with supercells or of crystals with a modulated structure are formulated using `generalized atomic scattering factors'. The Fourier transform of the structure factors of a single set of difference reflections is the sum of the convolutions of the point functions representing average atomic positions, with the transforms of the generalized atomic scattering factors. The Patterson function of one set of difference reflections is the sum of the convolutions of the point functions representing average interatomic vectors, with the convolutions of the transforms of the generalized atomic scattering factors. These results are applied in a subsequent paper to Patterson maps based on the satellite reflections of a plagioclase feldspar.