Cluster Self-Organization of Intermetallic Systems: Clusters-Precursors K15, K6, K5, and K4 for the Self-Assembly of Crystal Structures Pu31Rh20-tI204, Pu20Os12-tI32, (Pu4Co)2(Pu4)-tI28, (Ti4Ni)2(Bi4)-tI28, and Bi4-tI8

Using the ToposPro software package, a combinatorial-topological analysis and modeling of the self-assembly of the following crystal structures with space group I4/mcm are realized: Pu₃₁Rh₂₀-tI204: a = 11.076 Å, c = 36.933 Å, V = 4530.86 ų, Pu₂₀Os₁₂-tI32: a = 10.882 Å, c = 5.665 Å, V = 670.8 ų. (Pu₄Co)₂ (Pu₄)-tI28: a = 10.475 Å, c = 5.340 Å, V = 585.9ų. (Ti₄Ni)₂(Bi4)-tI28: a = 10.554 Å, c = 4.814 Å, V = 536.2ų, Bi₄-tI8: a = 8.518 Å, c = 4.164 Å, V = 302.15 ų. For the crystal structure of Pu₃₁Rh₂₀-tI204, 113 variants of the cluster representation of the 3D atomic network with the following number of structural units are established: 4 (14 variants), 5 (61 variants), and 6 (38 variants). A variant of the self-assembly of the crystal structure with the participation of three types of framework-forming polyhedra is considered: K15 = Pu@14(Rh₂Pu₅)₂ with symmetry –42m, double pyramids K10 = (Rh@Pu₄)₂ with symmetry 4, and octahedra K6 = 0@8(Rh₂Pu₆) with symmetry mmm and spacers Rh. For the crystal structure of Pu₂₀Os₁₂-tI32, framework-forming pyramid-shaped polyhedra K5 = 0@OsPu₄ with symmetry 4, as well as spacers Pu and Os, are defined. For the crystal structure (Ti₄Ni)₂(Bi4), frame-forming pyramids K5 = 0@Ti₄Ni and tetrahedra K4 = 0@Bi₄) are defined. For the crystal structure (Pu₄Co)₂(Pu₄)-tI28, frame-forming pyramids K5 = 0@ Pu₄Co and tetrahedra K4 = 0@Pu₄ are defined. For the crystal structure of Bi₄-tI8, frame-forming tetrahedra K4 = 0@Bi₄ are defined. The symmetric and topological code of self-assembly processes of 3D structures is reconstructed from clusters-precursors in the following form: primary chain → layer → framework.