Modeling Self-Organization Processes in Crystal-Forming Systems: New Two-Layer Cluster–Precursor K44 = 0@8(Na2In6)@36(In6Cd6K6)2 for the Self-Assembly of the K23Na8Cd12In48–hP91 Crystal Structure

Abstract

Using computer methods (the ToposPro software package), the combinatorial-topological analysis and modeling of the self-assembly of the K₂₃Na₈Cd₁₂In₄₈–hP91(a = b = 17.114 Å, c = 10.442 Å, group P6/mmm) crystal structure are carried out. The chemically different precursor clusters 0@8(Na₂In₆) and 0@K₂In₆ in the form of hexagonal bipyramids are established. The centers of Na₂In₆ clusters occupy positions 1a with a symmetry of 6/mmm. The centers of the K₂In₆–A and K₂In₆–B clusters occupy positions 2c with symmetry –6m2, and 3g positions with mmm symmetry. The Na₂In₆ clusters are the templates on the surface of which atomic shells of 36 atoms are formed. The composition of the two-layer cluster is K44 = 0@8(Na₂In₆)@36(In₆Cd₆K₆)₂. Layer formation occurs upon the K44 clusters binding to the K₂Cd₆–A clusters. The symmetry and topological code of the self-assembly of the 3D structures from the K44 suprapolyhedral precursors with the participation of the K₂Cd₆ polyhedral clusters, as well as Na and K spacer atoms, are reconstructed.