Cluster Self-Organization of Intermetallic Systems: Cluster Precursors K4, K5, and K9 for the Self-Assembly of Zr72P36-oS108, Zr18Ni22-tI40, and Zr4Ni4-oS8 Crystal Structures

Abstract

Using computer methods (ToposPro software package), a combinatorial topological analysis and modeling of the self-assembly of Zr72P36-oS108 (a = 29.509 Å, b = 19.063 Å, c = 3.607 Å, V = 2029.49 Å3, Cmmm), Zr18Ni22-tI40 (a = b = 9.880 Å, c = 6.610 Å, V = 645.23 Å3, I4/m, and Zr4Ni4-oS8 (a = 3.271 Å, b = 9.931 Å, c = 4.107 Å, V = 133.43 Å3, Cmcm) crystal structures are carried out. For the crystal structure of Zr72P36-oS108, 40 variants of the cluster representation of the 3D atomic net with the number of structural units 5, 6, and 7 are established. Structural units in the form of a pyramid K5 = 0@PZr4, tetrahedron K4 = 0@Zr4, and supratetrahedron K9 = Zr(Zr4P4) of four connected tetrahedra. For the crystal structure of Zr18Ni22-tI40 also defined supratetrahedra K9 = Ni(Zr4Ni4) are defined. For the crystal structure of Zr4Ni4-oS8, the tetrahedral cluster precursor K4 = Zr2Ni2 is defined. The symmetry and topological code of the processes of self-assembly of 3D structures from cluster precursors is reconstructed in the following form: primary chain → layer → framework.