Symmetry and Topology Code of the Cluster Self-Assembly of Intermetallic Compounds A 2 [16] B 4 [12] of the Friauf Families Mg2Cu4 and Mg2Zn4

Abstract

A geometrical and topological analysis of intermetallic compounds A 2 [16] B 4 [12] of the Friauf families Mg2Cu4 (formed in 273 binary and 775 ternary systems) and Mg2Zn4 (formed in 67 binary and 121 ternary systems) has been performed. Basic 3D nets are determined in the form of a graph, whose sites correspond to the centers of tetrahedral cluster precursors В4: Cu-type net with a coordination number (CN) of 12 for Mg2Cu4 and a BN-type net with a CN of 8 for Mg2Zn4. The symmetry and topology code is determined for the crystal structure self-assembly in the following form: primary chain S 3 1 → microlayer S 3 2 → microframework S 3 3 . An identical mechanism of primary chain S 3 1 self-assembly from B4 clusters with participation of large template atoms A[16] for both families and a mechanism of S 3 2 microlayer self-assembly from parallel S 3 1 chains in Mg2Cu4 (basic 2D net 44) and shifted chains in Mg2Zn4 (basic 2D net 36) have been determined for the first time. The constant chemical composition of intermetallic compounds A 2 [16] B 4 [12] is related to the functional difference between the B atoms forming 3D frameworks and template atoms А. The numbers of chemically different В4 clusters for the Mg2Cu4 and Mg2Zn4 families are found to be 25 and 19, respectively.