The Symmetric and Topological Code of the Cluster Self-Assembly of the Icosahedral Structure of (Rb₁₃)(Rb₂O)₃ (Fm-3c, cF184) Metal Oxide

Abstract—A search for crystal structures of A_nO_m metal oxides containing icosahedral i–A@A₁₂ cluster precursors is performed (TOPOS program package, ICSD and CRYSTMET databases). Among 1802 metal oxides, the local region represented by i–Cs@Cs₁₂ is determined in the Cs₇O (P-6m2) metal oxide. In the case of the (Rb₁₃)(Rb₂O)₃ (Fm-3c, cF184, V = 12 409.8 ų) metal oxide, the i–Rb@Rb₁₂ cluster precursor with the symmetry m-3 and cluster spacers in the form of Rb–O–Rb chains, which occupy the pores in the three-dimensional framework, are identified. Cluster i–Rb@Rb₁₂ occupies position 8b with the highest possible crystallographic symmetry m-3 for icosahedron. The topological type of the basic 3D network, which characterizes the packing of cluster precursors Rb₁₃, corresponds to a simple cubic 3D network P_c (Pm-3m, cP1) with CN = 6. The symmetric and topological codes of the self-assembly processes of the crystal structure from the ${\text{S}}_{3}^{0}$ nanocluster precursors is fully reconstructed in the following form: primary chain ${\text{S}}_{3}^{1}$ → microlayer ${\text{S}}_{3}^{2}$ → microframework ${\text{S}}_{3}^{3}.$ Cluster precursors in the primary chain are flipped through 90° and are characterized by the maximum possible number of Rb–Rb bonds corresponding to 8 and this mechanism of local binding is realized at all stages of the self-assembly of the 3D framework structure. During the assembly of the primary chain and microlayer, there is additional binding of the Rb@Rb₁₂ icosahedra via the Rb atoms of three-atomic cluster spacers Rb–O–Rb. In the 3D framework structure, in the local environment of Rb@ Rb₁₂, there are 12 Rb–O–Rb cluster spacers.