New Cluster Precursors K7 and K9 for Self-Assembly of Crystal Structures of the Fe3(PFe3)P2-hP9, Zr3(NiAl3)Ni2-hP9, Y3(NiAl3)Ge2 -hP9, Pr3(CoAl3)Co3(CoPr3)Ge-hP15, and Mg(Y2Cu2Mg4)Y3(CuMg3)Cu2-oP36 Families

Abstract

A geometrical and topological analysis has been performed and the self-assembly of crystal structures of the Fe₃(PFe₃)P₂-hP9, Zr₃(NiAl₃)Ni₂-hP9, and Y₃(NiAl₃)Ge₂ -hP9 (sp. gr. P \(\bar {6}\)2m, no. 189), Pr₃(CoAl₃)Co₃(CoPr₃)Ge-hP15 (sp. gr. P \(\bar {6}\)2m, no.189), and Mg(Y₂Cu₂Mg₄)Y₃(CuMg₃)Cu₂-oP36 (sp. gr. Pmma, no 51) families has been simulated using computer methods (ToposPro software). The precursor metal clusters of the crystal structures are determined based on the algorithms of structural-graph decomposition in cluster structures. For the topological set of binary, ternary, and quaternary intermetallic compounds Fe₃(PFe₃)P₂-hP9, Zr₃(NiAl₃)Ni₂-hP9, and Y₃(NiAl₃)Ge₂ -hP9, which constitute 15, 580, and 64 compounds, a version of their self-assembly from templated precursor clusters Fe₃(PFe₃), Zr₃(NiAl₃)Ni₂, and Y₃(NiAl₃)Ge₂ with participation of spacer atoms P, Ni, and Ge is considered. Two chemically different seven-atom precursor clusters are established for quaternary intermetallic compounds of the Pr₃(CoAl₃)Co₃(CoPr₃)Ge-hP15 family: K7 = Pr₃(CoAl₃) and K7 = Co₃(CoPr₃), as well as Ge spacer atoms. Seven-atom precursor cluster K7 = 0@Y₃(CuMg₃), new-type nine-atom cluster K9 = Mg(Y₂Cu₂Mg₄), and Cu spacer atom are established for the ternary intermetallic compound Mg(Y₂Cu₂Mg₄)Y₃(CuMg₃)Cu₂-oP36, which has no analogues. The symmetry and topology code of the self-assembly of crystal structures of intermetallic compounds from precursor clusters K7 and K9 is reconstructed in the following form: chain \(S_{3}^{1}\) → microlayer \(S_{3}^{2}\) → microframework \(S_{3}^{3}\).