Cluster Self-Organization of Intermetallic Systems: New Two-Layer Cluster-Precursors K57 = Li@15(Ga6Cu9)@41(Cu15Mg26) and K41 = 0@8(Mg2Ga6)@33(Li6Mg3Ga24) in the Li10Mg34Cu24Ga71-hP139 Crystal Structure and K5 = 0@Ca2LiInGe in the Ca2LiInGe2-oP24 Crystal Structure

Abstract

A geometric and topological analysis of the crystal structure of the Li10Mg34Cu24Ga71-hP139 (a = 14.080 Å, c = 13.625 Å, V = 2339.36 Å3, P-6m2) and Ca2LiInGe2-oP24 (a = 7.251, 4.940 Å, b = 4.438 Å, c = 16.902 Å, V = 543.9 Å3, Pnma) intermetallic compounds is carried out. For the Li10Mg34Cu24Ga71-hP139 intermetallic compound, using the method of the complete decomposition of the 3D factor graph into cluster structures, 1319 variants of the cluster representation of the 3D atomic grid with three to nine structural units are found. Two frame-forming nanoclusters K57 = Li@15(Ga6Cu9)@41(Cu15Mg26) with the internal Frank–Kasper polyhedron Li@15(Ga6Cu9) and K41 = 0@8(Mg2Ga6) @ 33(Li6Mg3Ga24) with an internal polyhedron in the form of a hexagonal bipyramid 0@8(Mg2Ga6) are established. The center of the K57 and K41 cluster-precursor is in positions 1f and 1c with symmetry g = –6m2. The large frame cavity contains double LiGa13, which are polyhedra centered at position 1b. For the Ca2LiInGe2-oP24 intermetallic compound, the K5 = 0@Ca2LiInGe cluster-precursor is found in the form of a triangular bipyramid with Li, In, and Ge atoms lying at the base of the bipyramid and Ca atoms, which are the vertices of the bipyramid. The symmetry and topological code of the processes of self-assembly of the Li10Mg34Cu24Ga71-hP139 and Ca2LiInGe2-oP24 crystal structures of the cluster-precursors is reconstructed in the following form: primary chain → layer → framework.