Frequency distribution and selection of space groups in inorganic crystal chemistry

Abstract

Statistical analysis of modern structural databases on inorganic crystals and minerals is carried out to elucidate the classification of crystal structure distributions over space groups. The known fact about extremely uneven occupation of space groups is confirmed; the relative abundance of all and, in particular, 24 most frequent groups (>1%) is derived, and the latter are noted to belong to holohedral and centrosymmetric classes. The data on occupation of extremely rare and empty space groups are analyzed and refined separately, which allows the reduction of a number of unreliable structural data. The theoretical analysis of empirical regularities is performed from the standpoint of filling rules for special structural positions (Wyckoff positions) and the symmetry of lattice complexes. It is shown that only combined consideration of different symmetry rules and restrictions provides an explanation for most regularities observed in occupation of symmetry point groups.