Symmetry of incommensurate crystal phases. II. Incommensurate basic structure

In this second part [part I: Acta Cryst. (1980), A36, 399-408] the superspace-group approach is formulated for a class of crystals (called composite crystals) which involve a basic structure composed of subsystems, each one having three-dimensional space-group symmetry, but being mutually incommensurate. By taking into account the interaction among these subsystems, or other second-order effects, one is led to the actual structure, which very often is modulated, and in any case incommensurate. Neither the basic structure nor the actual one has a three-dimensional space-group symmetry but both allow a superspace-group characterization of their symmetry properties. The aim of the present paper is to show how these concepts apply in practice. Accordingly, two composite crystals, extensively studied in the literature, are considered from the present point of view: the organic compound (TTF)₇I_{5 - x}, i.e. C₄₂H₂₈S₂₈.I_{5 - x}, and the polymercury cation compound Hg_{3 - δ}AsF₆. The regularities found in these two compounds are interpreted and fit naturally with the corresponding superspace-symmetry groups.