Cluster Self-Organization of Intermetallic Systems: K3, K4, and K6 Clusters-Precursors for the Self-Assembly of Crystal Structures of the Ce4Pt14Si8-oP52 and Ce6Pd8Sn12-oP52 Family

Using computer methods (ToposPro software package), a combinatorial-topological analysis and modeling of the self-assembly of crystalline structures of the Ce₄Pt₁₄Si₈-oP52 (a = 19.633 Å, b = 4.036 Å, c = 11.224 Å, V = 889.4 ų) and Ce₆Pd₈Sn₁₂-oP52 (a = 27.701 Å, b = 4.614 Å, c = 9.371 Å, V = 1198.02 ų) family are carried out. For the crystal structure of Ce₄Pt₁₄Si₈-oP52, 21 variants of the allocation of cluster structures with the number of clusters N = 2 (6 variants) and 3 (9 variants), and 3 (6 variants) are established. A variant of the self-assembly of a crystal structure with the participation of clusters-precursors forming the following packing is considered: double tetrahedra K6 = 0@6 (Ce₂Pt₂Si₂) with symmetry g = –1, tetrahedra K4 = 0@4 (CePt₂Si), and rings K3 = 0@3 (Pt₂Si). For the crystal structure of Ce₆Pd₈Sn₁₂-oP52, 27 variants of the allocation of cluster structures with the number of clusters N = 2 (6 variants), 3 (11 variants), and 4 (10 variants) are established. A variant of the self-assembly of a crystal structure with the participation of clusters-precursors forming the following packing is considered: double tetrahedra K6 = 0@6 (Ce₂Pd₂Sn₂) with symmetry g = –1, rings K3 = 0@3 (CePdSn), rings K3 = 0@3 (PdSn₂), and spacer atoms Sn. The symmetry and topology code of the self-assembly processes of 3D Ce₄Pt₁₄Si₈-oP52 and Ce₆Pd₈Sn₁₂-oP52 structures are reconstructed from clusters-precursors in the following form: primary chain → layer → framework.