Cluster Self-Organization of Intermetallic Systems: New Clusters-Precursors K3, K4, K6, and K11 for the Self-Assembly of Crystal Structures of the Li₄₀P₄Ge₂₀-oP64 and Ti₄₀P₂₄-oP64 Families

Using computer methods (ToposPro software package), a combinatorial-topological analysis and modeling of the self-assembly of Li₄₀P₄Ge₂₀-oP64 (V = 1082.85 ų, Pnma) and Ti₄₀P₂₄-oP64 (V = 955.14 ų, Pnma) crystalline structures is carried out. For the crystal structure of Li₄₀P₄Ge₂₀-oP64, 36 variants of the identification of cluster structures with the number of clusters N = 2, 3, and 4 are established. The self-assembly of a crystal structure with the participation of clusters-precursors K11 = 0@11(Li₅(LiGe₅)) is considered in the form of pentagonal pyramids LiGe₅ with five Li atoms located on five faces of the pyramid, rings K3 = @3(Li₂P), and Li spacer atoms. For the crystal structure of Ti₄₀P₂₄-oP64, 55 variants of the identification of cluster structures with the number of clusters N = 2, 3, 4, and 6 are established. The self-assembly of a crystal structure involving clusters-precursors in the form of six-atom double tetrahedra, K6(4a) = 0@6(Ti₄P₂), K6(4b) = 0@6 (Ti₄P₂), three-atom rings K3 = 0@3(TiP₂) and K3 = 0@3(Ti₂P), and tetrahedrons K4 = 0@4 (Ti₃P) is considered. The symmetric and topological code of the self-assembly processes of 3D Li₄₀P₄Ge₂₀-oP64 and Ti₄₀P₂₄-oP64 structures from clusters-precursors is reconstructed in the following form: primary chain → layer → framework.