Modeling Self-Organization Processes in Crystal-Forming Systems: Suprapolyedic Na18Hg157 Precursor Clusters for the Self-Assembly of the Na99Hg468–hP567 Crystal Structure

Abstract

Using computer methods (the ToposPro software package), the combinatorial-topological analysis and modeling of the self-assembly of the Na₉₉Hg₄₆₈–hP567 crystal structure are carried out with the following parameters of the hexagonal cell: a = b = 39.703 Å, c = 9.681 Å, V = 13216 ų, space group P-6, and 132 crystallographically independent atoms. Three supracluster precursors K175-A, K175-B, and K175-C composed of Na₁₈Hg₁₅₇ are identified in the form of three connected gear rings of Na-polyhedra with symmetry g = –6. The symmetry and topological code for the self-assembly of the 3D structures from the precursor nanoclusters is reconstructed. In the [001] direction, the K175 supracluster precursors are linked by Hg₆ gear rings and Na spacers to form columns. In the columns, the distance between supraclusters K175 determines the value of the translational vector modulus c = 9.681 Å. When a skeleton is formed in the local environment of a column of K175-C supraclusters (centered at a height of z = 0), six columns of alternating K175-A and K175-B supraclusters are located with an offset of 1/2 in the [001] direction. The distance between equivalent columns from K175 clusters corresponds to the value of the translation vector modules a and b.