Symmetry and topology codes of cluster self-assembly for icosahedral structures of the NaZn13-cF112 and TRB66-cF1944 family

Abstract

Algorithms for combinatorial topology analysis have been developed that allow restoring symmetry and topology codes (program) of crystal structure cluster self-assembly for intermetallic systems. The analysis method is based on the determination of the chemical composition and structure of an intermetallic cluster-precursor and the construction of a basic 3D net of the structure in the form of a graph with the nodes corresponding to the positions of the centers of gravity of the cluster-precursors. The cluster self-assembly of icosahedral structures was modeled for the family of NaZn13-cF112 and TRB66-cF1944 structures, in which the unit cubic cF-cells contain 112 atoms (8 · NaZn13, V = 1849 A3) and 1608 atoms (24 · YB66, V = 23440 A3), respectively. The topological type of the basic 3D net in the NaZn13 and TRB66 structures (with space group Fm-3c) corresponds to the primitive 3D net P c (Pm–3m, cP1) with c.n. = 6. The cluster-precursor of the NaZn13 structure is an icosahedral cluster Zn@Zn12. The cluster-precursor of the TRB66 structure containing 156 B atoms comprises 13 icosahedrons (B12)13, with the icosahedron B12 in the center of the supracluster linked to the 12 icosahedrons forming an icosahedral shell. The Zn13 and (B12)13B cluster-precursors occupy positions 8b in the crystal structures with the highest crystallographically possible symmetry of m3. The symmetry and topology code of the processes of self-assembly of 3D structures from the nanocluster-precursors—primary chain → microlayer → micronetwork—has been completely reconstructed. The large metal atoms A (with c.n. = 24) are spacers in the AZn13 structures, which occupy voids in the 3D nets from the Be13, Co13, Cu13, Zn13, and Cd13 icosahedrons. The atoms spacers in the TRB66 structures (3 TR and 39 B, TR = Y, Sm, Gd–Lu) statistically occupy the large voids in the 3D nets. The TRB66 crystal structure can be obtained from the NaZn13 by the replacement (decoration) of all 13 Zn atoms with 13 icosahedral B12 clusters; and the system of bonds between the structural units is completely conserved in the process.