Modeling the Processes of Self-Organization in Crystal-Forming Systems: New Two-Layer Clusters–Precursors 0@(Na₂Cd₆)@(Na₁₂Cd₂₆) and 0@(Na₃Cd₆)@(Na₆Cd₃₅) for the Self-Assembly of the Na₂₆Cd₁₄₁–hP168 Crystal Structure

Abstract—The combinatoric and topological analysis and modeling of the self-assembly of the Na₂₆Cd₁₄₁–hP168 crystal structure (space group Pbcm; a = 5.483 Å, b = 24.519 Å, and c = 14.573 Å; and V = 1895 ų) are performed using computational methods (the ToposPro software package). Ninety-eight versions of the cluster representation of the 3D atomic network with the number of structural units ranging from four to seven are found. It is determined that polyhedral clusters–precursors C8 = 0@Na₂Cd₆ and C9 = 0@Na₃Cd₆ are templates, on the surface of which atomic shells consisting of 38 and 41 atoms are formed. The composition of the two-layer clusters is C46 = 0@(Na₂Cd₆)@(Na₁₂Cd₂₆) and C50 = 0@(Na₃Cd₆)@(Na₆Cd₃₅). The centers of clusters C46 and C50 are occupied by positions 1a with the symmetry 6/mmm and 2c with the symmetry −6m2. The symmetry and topology codes of the processes of self-assembly of 3D structures from nanoclusters–precursors C46 and C50 are reconstructed.