Modeling of self-organization of silicate systems: Precursor nanoclusters and self-assembly of Na3MSi3O9 (M = Y, Eu-Lu; oP256) crystal structures producing two interpenetrating diamond-type frameworks

In the M-T-O model system (M is a polyvalent metal with CN ≥ 4; T is Si), cyclic clusters have been deduced as graphs in the T/M range from one to three. The case is considered when monocyclic cluster M2T2 is modified by T-tetrahedra that form diortho groups T2. The M sites of the cluster have either topologically different local MT structures (four types) or identical local MT structures (two types). The cluster types for T/M = 3 obtained by modeling were used in analysis of one of the most complicated types of silicate crystal structures Na3MSi3O9 (M = Y; Eu-Lu; T/M = 3) with the Pearson index oP256 and 64 independent atoms. The TOPOS program package was used to carry out the complete 3D reconstruction of the self-assembly of the crystal structure: suprapolyhedral precursor nanocluster → primary chain → microlayer → microframework (supraprecursor) → ... three-dimensional framework. The calculation of the coordination sequences of site atoms in the 3D network of the MT framework MT3O9 revealed topological symmetry related to a three-dimensional separation of the framework into two interpenetrating frameworks. Each framework structure is generated by topologically equivalent cyclic precursor clusters Na2M2T6 consisting of two YO6 octahedra comprising three diortho groups Si2O7 and two Na atoms located above and below the ring center. The 3D graphs characterizing the connectivity of the centers of crystallographically equivalent clusters in the frameworks correspond to diamond-type networks.