Symmetry and Topology Code of the Cluster Self-Assembly of Intermetallic Compounds A2[16]B4[12] of the Friauf Families Mg2Cu4 and Mg2Zn4

Abstract

A geometrical and topological analysis of intermetallic compounds A₂^[16]B₄^[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 S₃¹ → microlayer S₃² → microframework S₃³. An identical mechanism of primary chain S₃¹ self-assembly from B₄ clusters with participation of large template atoms A^[16] for both families and a mechanism of S₃² microlayer self-assembly from parallel S₃¹ 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 A₂^[16]B₄^[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.