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 Å3, Pu20Os12-tI32: a = 10.882 Å, c = 5.665 Å, V = 670.8 Å3. (Pu4Co)2 (Pu4)-tI28: a = 10.475 Å, c = 5.340 Å, V = 585.9Å3. (Ti4Ni)2(Bi4)-tI28: a = 10.554 Å, c = 4.814 Å, V = 536.2Å3, Bi4-tI8: a = 8.518 Å, c = 4.164 Å, V = 302.15 Å3. 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.