Cluster self-organization of germanate systems:: Suprapolyhedral precursor clusters and self-assembly of K2Nd4Ge4O13(OH)4, K2YbGe4O10(OH), K2Sc2Ge2O7(OH)2, and KScGe2O6(PYR)

Geometric and topological analysis of all known types of K,TR germanates (TR = La-Lu, Y, Sc, In) is carried out with the use of computer techniques (the TOPOS 4.0 program package). Framework structures are represented as three-dimensional (3D) K,TR,Ge networks (graphs) with oxygen atoms removed. The following crystal-forming 2D TR,Ge networks are determined: for K2Nd4Ge4O13(OH)(4), this is TR 4 3 3 4 3 3 + T 4 3 4 3; for K2YbGe4O10(OH), this is TR 6 6 3 6 + T 1 6 8 6 + T 2 3 6 8; for K2Sc2Ge2O7(OH)(2), this is TR 6 4 6 4 + T 6 4 6; and for KScGe2O6, TR 6 6 3 6 3 4 + T 1 6 3 6 + T 2 6 4 3. The full 3D reconstruction of the self-assembly mechanism of crystal structures is performed as follows: precursor cluster-primary chain-microlayer-microframework (supraprecursor). In K2Nd4Ge4O13(OH)(4), K2Sc2Ge2O7(OH)(2), and KScGe2O6, an invariant type of cyclic six-polyhedral precursor cluster is identified; this precursor clusters is built of TR octahedra, which are stabilized by atoms K. For K2Nd4Ge4O13(OH)(4), the type of cyclic four-polyhedral precursor cluster of tetrahedron-linked TR octatopes is identified. The cluster coordination number in a layer is six (the maximum possible value) only for anhydrous germanate KScGe2O6 (an analogue of pyroxene, PYR); in the other OH-containing germanates, this number is four. The mechanism of formation of Ge radicals in the form of groups Ge2O7 and Ge4O13, a chain GeO3, and a tubular assembly of linked cyclic groups Ge8O20 is considered.