Cluster Self-Organization of Intermetallic Systems: Clusters-Precursors K3, K4, K6, K12 for the Self-Assembly of La₈Ni₄₀As₂₄–oP72 and Ca₁₂Fe₃₂Pd₄As₂₄-oP72 Crystal Structures

Using computer methods (ToposPro software package), a combinatorial-topological analysis and modeling of the self-assembly of crystal structures of the La₈Ni₄₀As₂₄–oP72 (V = 1069.3 ų, etc., Pnma group) and Ca₁₂Fe₃₂Pd₄As₂₄-oP72 (V = 1155.89 ų, etc., Pnma group) families are carried out. For the crystal structure of La₈Ni₄₀As₂₄–oP72, 79 variants are established for identifying cluster structures with the number of clusters N = 2 (1 variant), 3 (18 variants), 4 (30 variants), and 6 (30 variants). A variant of the self-assembly of a crystal structure with the participation of clusters-precursors forming the packing is considered: double tetrahedra-dimers K6(4a) = 0@6(La₂Ni₂As₂) and K6(4b) = (Ni₂As₂Ni₂) with symmetry g = –1, tetrahedra K4 = 0@4 (LaNi₂As), rings K3 = 0@3(Ni₂As), and spacer atoms Ni7 and As5. For the crystal structure of Ca₁₂Fe₃₂Pd₄As₂₄-oP72 93 variants are established of the cluster representation of a 3D atomic grid with the number of structural units equal to 2 (2 variants), 3 (15 variants), 4 (49 variants), and 6 (29 variants). A variant of self-assembly of the crystal structure of Ca₁₂Fe₃₂Pd₄As₂₄-oP72 with the participation of the clusters-precursors forming the packing is considered: double tetrahedra-dimers K6(4a) = 0@6(Ca₂Fe₂As₂) with symmetry g = –1, tetramers K12(4b) = 0@12 (CaFeFe₂As₂)2 with symmetry g = –1, tetrahedra K4 = 0@4(CaFe₂As), rings K3 = 0@3(Fe₂As), and Pd and As spacer atoms. The symmetry and topological code of the self-assembly processes of the 3D La₈Ni₄₀As₂₄–oP72 and Ca₁₂Fe₃₂Pd₄As₂₄-oP72 structures is reconstructed from clusters-precursors in the following form: primary chain → layer → framework.