Cluster self-organization of TR-containing silicate and germanate systems: Suprapolyhedral precursors and self-assembly of A2HMTO5 (A = Li, Na; M = Sc, Lu, Yb) crystal structures with MTO5 frameworks

The combinatorial topological analysis is carried out using the coordination sequences method (the TOPOS 4.0 program package) and the matrix self-assembly is modeled for silicates Li2HTRSiO5 (TR = Lu, Yb; space group ) and germanate Na2HScGeO5 (space group P21ab). These compounds, having identical formulas, have different MT frameworks built of M octahedra (TRO6) and T tetrahedra (SiO4, GeO4). New types of crystal-forming binodal nets are discovered: 4 4 6 6 + 4 4 6 for lutetium silicate and 44444(45) + Ge 444(43) for scandium germanate; the atom-site ratio in the nets is M: T = 1: 1. A ring invariant suprapolyhedral precursor cluster composed of four polyhedra is identified, with two (A = Li, Na) atoms lying one above and one below the center of the cluster. A2M2T2 precursor clusters control the evolution of high-level crystal-forming clusters by means of the matrix assembly mechanism. The evolution routes of the suprapolyhedral precursor clusters bifurcate at the stage where topologically dissimilar layers are formed of equivalent chains. The cluster coordination numbers (CCNs) in a layer for the precursor clusters are four for lutetium silicate and six for scandium germanate.