Cluster Self-Organization of Intermetallic Systems: Precursor Clusters K3, K4, K5, and K6 for the Self-Assembly of Crystal Structures (Ce4Mg7Ge6)2-mS34, (Eu4Li7Bi6)2-mS34, and Li13Ba8GaSb12-mS34

Using computational methods (ToposPro software package), a combinatorial-topological analysis and modeling of self-assembly of crystalline structures are carried out for (Ce4Mg7Ge6)2-mS34, (Eu4Li7Bi6)2-mS34, and Li13Ba8GaSb12-mS34. For (Ce4Mg7Ge6)2-mS34, ten variants for identifying cluster structures are established. The self-assembly of a crystal structure involving trimers formed from cluster K6 = 0@6(Ce2Mg2Ge2) with symmetry g = –1, two clusters K3 = 0@3 (CeMgGe), and spacers Mg and Ge is considered. For (Eu4Li7Bi6)2-mS34, eight variants for identifying cluster structures are established. The self-assembly of a crystal structure involving tetramers formed from clusters K6 = 0@6(Eu4Bi2), cluster K5 = Li @ 4(Li2Bi2), and two clusters K3 = 0@3(Li2Bi) is considered. For Li13Ba8GaSb12-mS34, 11 variants of identifying cluster structures are established. The self-assembly of a crystal structure involving tetramers formed from clusters K6 = 0@6(Ba2Li2Sb2) in the form of double tetrahedra with symmetry g = –1, clusters K4 = 0@4(Ba2Sb2) in the form of a tetrahedron, two clusters K3 = 0@3 (Li2Sb) in the form of three rings, and Li spacer atoms is considered. The symmetry and topological code of the self-assembly processes of 3D structures from precursor clusters is reconstructed in the following form: primary chain → layer → framework.