Cluster Self-Organization of Intermetallic Systems: Clusters-Precursors K3, K4, and K6 for the Self-Assembly of RbNa8Ga3As6-oP72, Sr2Ca4In3Ge6-oP56, and Sr8Li4In4Ge8-oP24 Crystal Structures

Using computer methods (the ToposPro software package), combinatorial-topological analysis and modeling of self-assembly of the following crystal structures are carried out: RbNa 8 Ga 3 As 6 - oP 72 ( a = 22.843Å, b = 4.789 c = 16.861 Å, V = 1844.6 Å 3 , Pnma ), Sr 2 Ca 4 In 3 Ge 6 - oP 56 ( a = 13.243 Å, b = 4.460 Å, c = 23.505 Å, V = 1388.47 Å 3 , Pnma ), and Sr 8 Li 4 In4Ge 8 - oP 24 ( a = 7.503 Å, b = 4.619 Å, c = 17.473 Å, V = 605.6 Å 3 , Pnma ). For the RbNa 8 Ga 3 As 6 - oP 72 crystal structure, 93 variants of a cluster representation of a 3D atomic mesh with the number of structural units of 3, 4, and 6 are established. A variant of self-assembly involving three types of clusters-precursors is considered: double tetrahedra K6(4a) = 0@6 (Rb 2 Na 2 As 2 ) and K6(4b) = 0@6 (Na 4 As 2 ) with symmetry g = –1, tetrahedron K4(8d) = 0@4(Na 3 As), two triple rings K3-1 = 0@3(NaGaAs), and Ga and As spacer atoms. For the Sr 2 Ca 4 In 3 Ge 6 - oP 56 crystal structure, 43 variants of a cluster representation of a 3D atomic mesh with the number of structural units of 3, 4, and 6 are established. A variant of self-assembly of a crystal structure involving three types of clusters-precursors from double tetrahedra K6(4a) = 0@6 (Sr) 2 In 2 Ge 2 ) and K6(4b) = 0@6 (Ca 2 In 2 Ge 2 ) with symmetry g = –1, double tetrahedra K6(4c) = 0@6 (SrCa 2 InGe 2 ), and Ge2 and Ge4 spacer atoms is considered. For the Sr 8 Li 4 In4Ge 8 - oP 24 crystal structure, three variants of a cluster representation of a 3D atomic mesh with two structural units are established. A variant of the self-assembly of a crystal structure involving two types of clusters-precursors in the form of double tetrahedra K6 = (Sr 2 Li 2 Ge 2 ) with symmetry g = –1 and triple rings K 3 = 0@3 (SrInGe) is considered. 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.