Cluster Self-Organization of Intermetallic Systems: Role of K5 = 0@5, K9 = 1@8 and K11 = 0@11 Clusters in the Self-Assembly of Crystal Structures

The combinatorial-topological analysis and simulation of self-assembly of the Na96Hg36-hR132 (space group R-3c, a = b = 9.228 A, c = 52.6380 A, V = 3881.91 A3) and Na12Hg8-tP20 (space group P42/mnm, a = b = 8.520, c = 7.800 A, V = 566.2 A3) crystal structures are conducted by computer-based methods (ToposPro program package). Polyhedral cluster precursors K11 = 0@11(Na8Hg3) and K9 = Hg@Na8 are first determined for the intermetallic compound Na96Hg36-hR132, while polyhedral cluster precursors K5 = 0@Na3Hg2 are determined for the intermetallic compound Na12Hg8-tP20. The symmetry and topology code of the self-assembly processes of the 3D structure Na96Hg36-hR132 from the nanocluster precursors K11 and K9, and of the 3D structure Na12Hg8-tP20 from the K5 clusters are reconstructed as the primary chain $$S_{{\text{3}}}^{1}$$ → layer $$S_{{\text{3}}}^{2}$$ → frame $$S_{{\text{3}}}^{3}.$$ The structural analysis of all known intermetallic compounds is conducted, and numerous examples of the assembly of their structures from the K5, K9, and K11 clusters are found.