Intermetallic Compounds KnMm (М = Ag, Au, As, Sb, Bi, Ge, Sn, Pb): Geometrical and Topological Analysis, Cluster Precursors, and Self-Assembly of Crystal Structures

Abstract

A geometrical and topological analysis and simulation of the self-assembly of the crystal structures of intermetallic compounds formed in the K–M (M = Ag, Au, As, Sb, Bi, Ge, Sn, Pb) systems have been performed using computation methods (the ToposPro software). The precursor metal clusters of KnMm crystal structures are determined based on the algorithms of structure-graph decomposition in cluster structures and construction of the basic net of structure in the form of a graph with nodes corresponding to cluster centers. Tetrahedral metal clusters, forming packings in the K3Bi-cF16, K3Bi-hP8, K2As2-oP16, K2Sb2-mP16, and K2Sb2-mP32 crystal structures; tetrahedral metal clusters and spacers for the K(K2As2)2-mC18, K4(Pb4)-tI64, and K2(Au4)-hP12 structures; polyhedral metal clusters KK4Pb12 and spacers for the Pb12K(K4Pb12)-cI58 structure; and dodecahedral metal clusters KGe20 and spacers for the K3Ge3(KGe20)-cP54 structure have been found. The symmetry and topology code of the self-assembly of crystal structures of intermetallic compounds KnMm has been reconstructed from precursors $$S_{3}^{0}$$ in the following form: primary chain $$S_{3}^{1}$$ → microlayer $$S_{3}^{2}$$ → microframework $$S_{3}^{3}$$ .