Cluster self-organization of Na-TR-Ge-O-H (TR = La-Lu, Y, and Sc) germanate systems: Suprapolyhedral precursor clusters and self-assembly of Na2Pr6Ge8O26, Na4Sc2Ge4O13, and Na5ScGe4O12 crystal structures

In an M-T-O model system (M is a polyvalent metal; T = Ge or Si), we consider initial stages of formation of cyclic MT clusters and the mechanism of their modification by T tetrahedra. The polyhedron ratio T/M in clusters increases progressively during modeling from one in M 2 T 2 to two (M 2 T 2 + 2T = M 2 T 4 ), three (M 2 T 2 + 2T 2 = M 2 T 6 ), and four (M 2 T 2 + 2T + 2T 2 = M 2 T 8 ). These types of clusters were used to find precursor clusters for T-condensed structures of Na 2 Pr 6 Ge 8 O 26 , Na 4 Sc 2 Ge 4 O 13 , and Na 5 ScGe 4 O 12 . The TOPOS program package was used to carry out the complete 3D reconstruction of the self-assembly of Na,TR germanates: precursor cluster → primary chain → microlayer → microframework (supraprecursor) → ... framework. In all structures, as previously in six orthotetrahedral Na,TR germanate structures, the basic invariant type of four-polyhedral cyclic precursor cluster M 2 T 2 was identified; this cluster is built of TR polyhedra, with CN = 6 or 7, linked via orthotetrahedra. The features of the generation of a Ge radical were considered in the form of a Ge 2 O 7 chain and a Ge 4 O 12 ring in various layers of the Na 2 Pr 6 Ge 8 O 26 composite structure, a Ge 4 O 13 chain in Na 4 Sc 2 Ge 4 O 13 , and a Ge 12 O 36 ring in the Na 5 ScGe 4 O 12 superionic conductor.