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The superspace concept is currently applied with success for the determination and description of incommensurately modulated crystal structures (IMSs). The number of IMSs is increasing similar to the increase of the number of 3dimensional (3D) structures starting from the sixties of last century. With the number and complexity of the determined 3D structures, crystal chemistry started to evolve in order to bring some better understanding in the manifold of structures. Three well known examples of the results of this development can be cited: (i) experimentally determined interatomic distances essentially improved, corrected and sometimes reversed both the chemical bond and the molecular structure concepts; (ii) the determination of the symmetry of crystal structures induced the development of the phase transition theory based on the group-subgroup relationships; (iii) the large manifold of crystal structure determinations generated the need to classify them. For instance, the concept of structure type (ST) was introduced for the investigation and prediction of both physical and chemical properties of compounds. It appears that the (3+d)D IMSs can be used for further development of the field of crystal chemistry. The basis of this development refers to the improvement and generalisation of fundamental crystal chemical approaches considering (3+d)D symmetry. The generalisation of the concepts relies on additional atomic characteristics varying in terms of additional internal dimensions. Experimentally determined interatomic distance variations allow to reveal both the interatomic interactions and the origin of the modulation in an IMS [1,2,3]. A single IMS of a compound with complex chemical composition presents a unique new opportunity to estimate the relative flexibility and rigidity of chemical bonds appearing between atoms [1,2,3]. The role of atomic interactions in the series of phase transitions can be also better understood if one of the phases is an IMS [4]. The experimentally determined variation of the atomic site occupancy in an IMS opens a new way for the description and prediction of order-disorder phase transitions [5]. With the example of scheelite-like family, it is shown that the concept of ST can be generalized in the frame of (3+d)D superspace groups of symmetry. A family of compounds can be represented as a family of 3D sections of a single (3+d)D IMS. This family can be defined as a (3+d) ST. The (3+d) ST definition encompasses the traditional ST but extends it in order to include also ST-like, ST-relative and IMSs. The determination of one IMS allows to fully describe the (3+d)D corresponding ST and to predict its members. The extension of crystal chemistry into (3+d)D superspace opens new perspectives in the field of condensed matter physics and other material sciences.

acta crystallographica. section a, foundations of crystallography/acta crystallographica. section a

New aspects in the analysis of compositionally flexible systems in the superspace: Fe1−xS and Sb1−xTex