Structures of the ZrZn22 family: suprapolyhedral nanoclusters, methods of self-assembly and superstructural ordering

A combinatorial topological analysis is carried out by means of the program package TOPOS4.0 [Blatov (2006), IUCr Comput. Commun. Newsl. 7, 4–38] and the matrix self-assembly is modeled for crystal structures of the ZrZn22 family (space group Fd\bar 3m, Pearson code cF184), including the compounds with superstructural ordering. A number of strict rules are proposed to model the crystal structures of intermetallics as a network of cluster precursors. According to these rules the self-assembly of the ZrZn22-like structures was considered within the hierarchical scheme: primary polyhedral cluster → zero-dimensional nanocluster precursor → one-dimensional primary chain → two-dimensional microlayer → three-dimensional microframework (three-dimensional supraprecursor). The suprapolyhedral cluster precursor AB 2 X 37 of diameter ∼ 12 Å and volume ∼ 350 Å3 consists of three polyhedra (one AX 16 of the \bar 43m point symmetry and two regular icosahedra BX 12 of the \bar 3m point symmetry); the packing of the clusters determines the translations in the resulting crystal structure. A novel topological type of the two-dimensional crystal-forming 4,4-coordinated binodal net AB 2, with the Schläfli symbols 3636 and 3366 for nodes A and B, is discovered. It is shown that the ZrZn22 superstructures are formed by substituting some atoms in the cluster precursors. Computer analysis of the CRYSTMET and ICSD databases shows that the cluster AB 2 X 37 occurs in 111 intermetallics belonging to 28 structure types.