Cluster Self-Organization of Intermetallic Systems: K3, K4, K5, K6, and K13 Clusters-Precursors for the Self-Assembly of U₈Ni₁₀Al₃₆-mC54, U₂₀Ni₂₆-mC46, and U₈Co₈-cI16 Crystal Structures

Abstract—Using computer methods (the ToposPro software package), a combinatorial topological analysis and modeling of the self-assembly of U₈Ni₁₀Al₃₆-mC54 (a = 15.5470 Å, b = 4.0610 Å, c = 16.4580 Å, β = 120.00°, V = 899.89 ų, C m), U₂₀Ni₂₆-mC46 (a = 7.660 Å, b = 13.080 Å, c = 7.649 Å, β = 108.88°, V = 725.26 ų, C2/m), and U₈Co₈-cI16 (a = 6.343 Å, V = 255.20 ų, I 2₁3) are carried out. For the U₈Ni₁₀Al₃₆-mC54 crystal structure, 960 variants of the cluster representation of the 3D atomic grid with the number of structural units 5, 6, and 7 are established. Six crystallographically independent structural units in the form of a pyramid K5 = 0@Al(U₂Al₂), pyramid K6A = 0@U(NiAl₄), and pyramid K6B = 0@U(NiAl₄), as well as rings K3A = 0@NiAl₂, K3B = 0@NiAl₂, and K3C = 0@Al₃, are determined. For the U₂₀Ni₂₆-mC46 crystal structure, the structural units K5 = Ni(Ni₂U₂) and icosahedra K13= Ni@Ni₆U₆ are defined. For the crystal structure U₂Co₂-cI16, the structural units—tetrahedra K4 = U₂Co₂—are defined. The symmetry and topological code of the processes of self-assembly of 3D structures from clusters-precursors are reconstructed in the following form: primary chain → layer → framework.