Direct methods and superstructures. I. Effects of the pseudotranslations on the reciprocal space

The effects on the reciprocal space of one or more pseudotranslations occurring in a crystal structure are studied. A quantitative theory is described, which gives full account of the subsets of pseudonormalized structure factors whose mean intensity significantly deviates from unity. Conversely, statistical criteria are suggested aiming at facilitating the recognition of the nature of the superstructure. The theory has been implemented into a computer program that, from 72 different pseudotranslational symmetries, chooses the most probable one, estimates the number of atoms suffering pseudosymmetry and renormalizes structure factors.