Cluster self-organization of silicate and germanate systems: Suprapolyhedral precursor clusters and self-assembly of orthotetrahedral structures in Na,TR-germanates (silicates)

The geometrical and topological analysis of all known types of the orthotetrahedral structures of Na,TR-germanates and their silicon analogues has been carried out using computer methods (TOPOS 4.0 program package). The full 3D reconstruction of the self-assembly mechanism of crystal structures has been performed as follows: precursor cluster-primary chain-microlayer-microframework (supraprecursor). For Na₂HLaSiO₅, NaHo₄(GeO₄)₂O₂OH, NaScGeO₄, and NaSm₃Ge₂O₈(OH)₂, the same type of 2D TR, T-network has been recognized: 433334 + T 4433. For Na₂HScGeO₅, network TR 44444 + T 444 has been recognized. The coordination number (CN) of a precursor cluster in 2D networks is six. In all structures, the invariant type of cyclic four-polyhedral precursor clusters built of tetrahedron-linked TR-polyhedra has been identified with CNs being eight, seven, or six. In the Na₅Y₄Si₄O₁₆F structure, a tubular-type primary chain in which precursor clusters are tetrahedron-linked TR polyhedra with CN = 8 has been recognized. Their stacking in a layer is characterized by the network TR 8 8 4 + T 8 4 8, where 8 corresponds to the cross section of the primary chain. In a 3D network, the total number of neighboring tubular primary chains linked to the main chain is four. In the structures with TR: T = 1: 1 or 1.5: 1, the positions above and below the center of the precursor cluster are occupied by Na atoms; in NaHo₄(GeO₄)₂O₂(OH), where TR: T = 2: 1, these positions are occupied by an Na atom and a TR atom.