Direkte Methoden für Strukturen mit Überstruktureffekten

If ρ(x) describes the electron density distribution of a structure with pseudotranslation t of index p, the 'strong' reflexions H (H.t integer) determine the structure (x) of the subcell and the superstructure reflexions U (U.t not integer) the complement structure (x) = ρ(x) - (x) . But the weak reflexions U are also defined by the structure ρ^s(x) = ρ(x) - min {ρ(x + t), ..., ρ(x + pt)}. ρ^s(x) is always positive and direct methods are available for the main and superstructure reflexions separately. The shape of the maxima in ρ^s(x) depends on the type of the pseudotranslation t and is often not known a priori, but separate normalization of main and superstructure reflexions is the first approximation for normalizing structures with unknown 〈F²_abs〉. If the index p of t is greater than 2 the phase estimation of triplets and quartets is less reliable than in normal cases depending on the degree of rational dependency among the coordinates of the maxima in ρ^s(x), under specific conditions triplets with high value of κ are more reliably π than 0. Estimating triplets or quartets of 'mixed' type - containing weak and strong reflexions - has less theoretical foundation because of different functional forms of the E values of strong and weak reflexions.