Geometric and topological analysis of icosahedral structures of samson Mg2Zn11 (cP39) Phases, K6Na15Tl18H (cP40), and Tm3In7Co9 (cP46): Nanocluster precursors, self-assembly mechanism, and superstructure ordering

Geometric and topological analysis and 3D reconstruction of self-assembly of icosahedral structures of Samson Mg2Zn11 clusters (space group , cP39, 10 compounds) and the K6Na15Tl18H and Tm3In7Co9.29 structures were performed by computer methods (the TOPOS program package). The complete decomposition of the 3D graph of the crystal structures into cluster substructures showed the existence of the crystal-forming nanocluster precursor A comprising 45 atoms (A-45). The S-6 cluster spacers were identified in Mg2Zn11, and the S-7 cluster spacers were found in K6Na15Tl18H. In Tm3In7Co9.29, the S-6 and S-7 cluster spacers with the centers statistically occupying the same position were determined. The A-45, S-6 (octahedron), and S-7 (centered octahedron) clusters have symmetry . The A-45 nanocluster contains an inner Zn(Zn)(12) template icosahedron and an external quasi-spherical shell composed of 32 atoms (deltahedron D32). A-45 is equivalent to the Bergman cluster used as the approximant of the local structure of quasicrystals. For deltahedron D32, the existence of a hierarchical structure was identified as a result of self-assembly involving two types of cyclic clusters: K-7 with an atom in the center of the sixth ring and three-atom cyclic clusters K-3. The atoms of the K-3 and K-7 clusters occupy all possible positions over the 12 vertices and 20 faces of an icosahedron and thereby form an edge net of bonds made of triangles. For the K-6(Na14MTl18) structures (M = Mg, An, Cd, Hg), the cluster nature of superstructure ordering of three chemically different atoms (14Na, M, and 18Tl) over 33 positions of the Zn atoms in the unit cell of the basis Mg2Zn11(Mg6Zn33) structure was considered.