Cluster Self-Organization of Intermetallic Systems: Cluster-Precursors K13, K11, K4, and K3 for the Self-Assembly of Crystal Structures Ce56Ni24Si44-mS124 and Ba10La2Si12-oP48

Using computer methods (the ToposPro software package), a combinatorial topological analysis and modeling of the self-assembly of crystal structures of Ce₅₆Ni₂₄Si₄₄-mS124 (a = 34.08 Å, b = 4.245 Å, c = 21.37 Å, β = 113.52(3)°, V = 2835.14 ų, C12/m1) and Ba₁₀La₂Si₁₂-oP48 (a = 17.144 Å, b = 4.876 Å, c = 17.910 Å, V = 1497.46 ų, Pnma) are carried out. For the crystal structure of Ce₅₆Ni₂₄Si₄₄-mS124, 5511 variants of the cluster representation of the 3D atomic network are established with the number of structural units 5 (28 variants), 6 (943 variants), 7 (2316 variants), 8 (1704), and 9 (520 variants). The variant of the self-assembly of a crystal structure from the packing components of three types of cluster-precursors K13 = 0@13(Ce₆CeNi₂Si₄), K4 = 0@4(Ce₂NiSi), and K3 = 0@3(CeNiSi), as well as Si spacer atoms, is considered. For the crystal structure of Ba₁₀La₂Si₁₂-oP48, 21 variants of the cluster representation of the 3D atomic network with the number of structural units of 2 and 3 are established. The variant of self-assembly of the crystal structure with the participation of cluster-precursors forming the packing K11 = 0@11(Ba5LaSi5) and Si spacer atoms is considered. The symmetry and topological code of the processes of self-assembly of 3D structures from cluster-precursors is reconstructed in the following form: primary chain → layer → framework.