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 A, c = 10.442 A, 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.