Modeling of self-organization processes in crystal-forming systems: Templated precursor nanoclusters T48 and the self-assembly of crystal structures of 15-crown-5, Na-FAU, 18-crown-6, Na-EMT, and Ca,Ba-TSC zeolites

Abstract

The combinatorial and topological modeling of packings of symmetry-related nanoclusters T48 (diameter: ∼16 Å, symmetry $\bar 43m$) is performed. The packings are 1D claims S ¹₃ and 2D microlayers S ²₃ , which give rise to 3D structures S ³₃ . For three of the five framework structures, correspondence was established with zeolite FAU (Faujasite, Fd-3m, Z = 4 T48), EMT (P6₃/mmc, Z = 2 T48), and TSC (Tschortnerite $Fm\bar 3m$, Z = 8 T48). Combinatorial topological analysis methods (the ToposPro program package) were used to model the steps of zeolite crystal structure self-assembly. The underlying idea of these methods consists in that the basal 3D network of the zeolite structure is designed as a graph, where the nodes correspond to the centroid positions of clusters T48. For FAU, the basal 3D network corresponds to the copper cubic strucutre (CN = 12); for EMT, it corresponds to the hexagonal (H) strucutre of magnesium (CN = 12); and for TSC, to the cubic structure of polonium (CN = 6). The symmetry and topology code of zeolite strucutre formation has been restored in the form of the sequence of significant elementary events that characterize the shortest (rapidest) program of convergent cluster self-assembly. The functional role played by 15-crown-5 and 18-crown-6 template molecules has been established to consist in the stabilization of the primary chains and microlayers of FAU and EMT frameworks and the relevant network of diamond and graphite topological types. The model for 3D structure self-assembly from clusters T48 is capable of explaining the morphogenesis of single crystals to form regular octahedra in FAU, hexagonal prisms in EMT, and regular cubes in TSC.