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

Abstract

Using computer methods (the ToposPro software package), combinatorial-topological analysis and modeling of self-assembly of the following crystal structures are carried out: RbNa₈Ga₃As₆-oP72 (a = 22.843Å, b = 4.789 c = 16.861 Å, V = 1844.6 ų, Pnma), Sr₂Ca₄In₃Ge₆-oP56 (a = 13.243 Å, b = 4.460 Å, c = 23.505 Å, V = 1388.47 ų, Pnma), and Sr₈Li₄In4Ge₈-oP24 (a = 7.503 Å, b = 4.619 Å, c = 17.473 Å, V = 605.6 ų, Pnma). For the RbNa₈Ga₃As₆-oP72 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 (Rb₂Na₂As₂) and K6(4b) = 0@6 (Na₄As₂) with symmetry g = –1, tetrahedron K4(8d) = 0@4(Na₃As), two triple rings K3-1 = 0@3(NaGaAs), and Ga and As spacer atoms. For the Sr₂Ca₄In₃Ge₆-oP56 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) ₂In₂Ge₂) and K6(4b) = 0@6 (Ca₂In₂Ge₂) with symmetry g = –1, double tetrahedra K6(4c) = 0@6 (SrCa₂InGe₂), and Ge2 and Ge4 spacer atoms is considered. For the Sr₈Li₄In4Ge₈-oP24 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 = (Sr₂Li₂Ge₂) with symmetry g = –1 and triple rings K3 = 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.