Cluster Self-Organization of Intermetallic Systems: 124-Icosahedral Three-Layered Cluster 0@12(Ga12)@32(Ga12Na20)@80(Ga60Na6K14) for the Self-Assembly of the Crystalline Framework of Na26K8Ga104 (R\(\bar {3}\)m, R414)

Abstract

A combinational-topological analysis and simulation of the crystal structure of Na₂₆K₈Ga₁₀₄-hR414, R\(\bar {3}\)m, V = 8109 ų are performed by computer methods (the TOPOS software package). The framework-forming 124-atom three-layered icosahedral nanocluster ico-K124 = 0@12(Ga₁₂)@32(Ga₁₂Na₂₀)@80(Ga₆₀Na₆K₁₄) with a diameter of 17 Å and the symmetry g = \(\bar {3}\) is established by the method of the complete decomposition of a 3D atomic lattice into cluster structures. The second shell corresponds to the Bergman cluster with 32, 90, and 60 peaks, edges, and faces, respectively. The chemical composition of the shell is Ga₁₂Na₂₀. The third shell consisting of 80 atoms is characterized by 80, 210, and 132 peaks, edges, and faces, respectively. The chemical composition of the shell is made up of Ga₆₀Na₆K₁₄. Sixty atoms of Ga in the shell are located in the same manner as 60 carbon C atoms in the fullerene С₆₀. All 20 positions above the Ga₆ hexagons are occupied by 6 Na atoms and 14 K atoms. The symmetry and topological code of the self-assembly of 3D structures from iсo-K143 nanoclusters-precursors are simulated in the following form: primary chain → layer → framework. iсo-K124 nanoclusters form densely packed 2D layers 3⁶. The large voids in the 3D framework are occupied by 10-atom GaGa₉ clusters with the symmetry g = 3m.