Cluster Self-Organization
of Li- and TR-Containing Germanate Systems:
Suprapolyhedral Precursors and Self-Assembly
of LiScGeO₄ and LiHo₃(GeO₄)₂F₂ Crystal Structures

G. D. Ilyushin and L. N. Dem’yanets

Shubnikov Institute of Crystallography, Russian Academy of Sciences, Leninskii pr. 59, Moscow, 119991 Russia

e-mail: ilyushin@ns.crys.ras.ru

Received March 1, 2005

Abstract—The combinatorial and topologic analysis (the TOPOS 4.0 program package, the coordination
sequences method) is carried out for the crystal structures of the orthogermanates Li^[6]Sc^[6]Ge^[4]O₄ (the olivine
type, space group Pnma) and Li^[6]Ho^[8](GeO₄)₂F₂ (space group I2/c). The same type of 2D TR,Ge-net
with the Schläfli index of 3⁴4² + 3²4² and the site ratio of TR : Ge = 1 : 1 is discovered for both structures. Four-
polyhedral ring precursor clusters (TR)₂T₂ are identified using the two-color decomposition of structural
graphs. All the clusters have a symmetry center; they differ in the types of TR polyhedra (ScO₆ and HoO₆F),
which are linked through GeO₄ orthotetrahedra into a ring. The Li atoms reside above and under the centers of
the clusters. The Li₂(TR)₂T₂ clusters determine the formation of crystal-forming clusters of a higher level by
means of matrix self-assembly. The coordination number of the precursor clusters in the 2D net is six, which is
the highest possible value.

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