Structural Chemistry of Intermetallic Compounds: Geometric and Topological Analysis, Icosahedral Cluster Precursors K45 = Hg@Hg₁₂@Cs₁₂Hg₂₀ and K81 = Hg@Hg₁₂@Hg₃₂@Hg₃₆, as Well as the Self-Assembly of Crystal Structures Cs₆Hg₄₀–cP46 and Cs₁₂Hg₁₆₂–cI174

Abstract

With the help of computer methods (software package ToposPro), geometric and topological analysis and modeling of the self-assembly of crystal structures of intermetallic compounds Cs₆Hg₄₀-cP46, a = 10.913 Å, Pm-3n and Cs₁₂Hg₁₆₂-cI174, a = 16.557 Å, and Im-3 are carried out. The precursor metal clusters are determined using an algorithm for decomposing structural graphs into cluster structures and by constructing a basic grid of the structure in the form of a graph whose nodes correspond to the position of the centers of the precursor clusters ${\text{S}}_{3}^{0}$_{. In} the crystal structure Cs₆Hg₄₀-cP46, two-layer icosahedral clusters K45 = Hg@Hg₁₂@Cs₁₂Hg₂₀ are established, and for the crystal structure Cs₁₂Hg₁₆₂-cI174, three-layer icosahedral clusters K81 = Hg@Hg₁₂@Hg₃₂@Hg₃₆ are defined with symmetry g = m-3 and Cs-spacers. The symmetry and topological code of the processes of self-assembly of crystal structures of intermetallic compounds from precursors ${\text{S}}_{3}^{0}$ is reconstructed in the following form: chain ${\text{S}}_{3}^{1}$ → microlayer ${\text{S}}_{3}^{2}$ → microframework ${\text{S}}_{3}^{3}$.