Cluster self-organization of germanate systems: Suprapolyhedral nanocluster precursors and self-assembly of the Li8GeO6, Li4GeO4, and Li6Ge2O7 crystal structures

Nanoparticles (An clusters of atoms or Kn polyhedra, where n is the number of atoms or polyhedra) corresponding to the initial stage of evolution of a chemical system have been modeled. Four series of cluster isomers K3 and K4 formed by different T tetrahedra are selected. The clusters are topologically represented by two-colored graphs. A change in their symmetry, depending on the composition and mutual arrangement of L and G tetrahedra in the chemical isomers, is established. Our model is used to search for cluster precursors in Li germanates Li8GeO6 (P63mc, hP30), Li4GeO4(Cmcm, mC36), and Li6Ge2O7 (P21/n, mP60). Three types of nanocluster precursors are identified: (A) polycyclic, with a tetrahedral arrangement of 3L + GG polyhedra (L and G are LiO4 and GeO4, respectively) in the Li8GeO6 structure; (B) monocyclic, with a sequence of L-G-L-G polyhedra in the Li4GeO4 structure; and (C) polycyclic, in the form of two bound monocyclic clusters with a sequence of L-L-G-G polyhedra in the Li6Ge2O7 structure. Lithium atoms are found to play three different roles during structural self-assembly: they participate in the formation of nanocluster precursors, they serve as templates stabilizing the local structure of nanocluster precursors, and they act like spacers filling the voids between nanocluster precursors.