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

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 angstrom, c = 10.442 angstrom, 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.