Direct methods and structures showing superstructure effects. III. A general mathematical model

A general mathematical model is presented which can describe a large variety of structures showing superstructure effects. In particular the model can take into account deviations, both of displacive and of replacive type, of the substructural part from ideal pseudotranslational symmetry. The formulation is used to predict statistical effects of deviations on diffraction data. It is shown that the scattering power of the substructural part may be estimated via a statistical analysis of diffraction data for ideal pseudotranslational symmetry or for displacive deviation from it, while it is not estimable in the case of replacive deviation.