Cluster Self-Organization of Crystal-Forming Systems: New Three-Layer (K155 = Al@Al6Pd8@Pd12Al30@Pd8Сo18Al72) and Double-Layer (K55 = Co@Al12@Co12Al30) Precursor Clusters for the Self-Assembly of the Pd112Co204Al684-cP1000 Crystal Structure

Geometric and topological analysis of the Pd 112 Co 204 Al 684 -cP1000 crystal structure with the sp. gr. Pa -3, a = 24.433 Å, and V = 14587.24 Å 3 is performed using the ToposPro software package. Metal precursor clusters of crystalline structures are determined using an algorithm for decomposing structural graphs into cluster structures and by constructing a basic grid of the structure in the form of a graph whose nodes correspond to the position of the centers of precursor clusters A total of 26 906 variants of the cluster representation of a 3D atomic mesh with the number of structural units ranging from 3 to 12 are established. The self-assembly of the crystal structure from new three-layer K 155(4a) = Al@Al 6 Pd 8 )@Pd 12 Al 30 @Pd 8 Co 18 Al 72 and bilayer precursor clusters K 55(4b) = Co@Al 12 @Co 12 A l30 with symmetry g = –3 is considered. In the unit cell, positions 4a are occupied by Al atoms, which are the central atoms of the 15-atom polyhedron K 15(4a) = Al@Al 8 Pd 6 , and positions 4b are occupied by Co atoms, which are the central atoms of the 13-atom icosahedron K 13(4b) = Co@Al 12 . The symmetric and topological code of the processes of self-assembly of 3D structures from precursor clusters K 155 and K 55 is reconstructed as follows: primary chain → microlayer → microframework. Al atoms are established as spacers occupying voids in the 3D framework of the K 155 and K 55 nanoclusters.