Cluster Self-Organization of Intermetallic Systems: New Cluster-Precursors K12 = 1Zn@11(Mg₅Zn₆), K5 = 0@5(LiZn₄), K4 = 0@4(Li₂Al₂) in the Li₁₂Mg₂₀Al₈Zn₆₀-oC100 Crystal Structure and K3 = 0@3(CaMgGe), K4 = 0@4(LiCaMgGe), K4 = 0@4(Ca₂Ge₂) in the Li₄Ca₃₂Mg₈Ge₃₂-oP76 Crystal Structure

Abstract—Geometrical and topological analysis of the crystal structures Li₁₂Mg₂₀Al₈Zn₆₀-oC100 (a = 5.102 Å, b = 23.477 Å, c = 13.691 Å, V = 1639.90 ų, space group Cmcm) and Li₄Ca₃₂Mg₈Ge₃₂-oP76 (a = 21.98 Å, c = 18.560 Å, V = 1826.58 ų, space group Pnma) are performed using computer methods (ToposPro software package). For the Li₁₂Mg₂₀Al₈Zn₆₀-oC100 three cluster precursors K12, K5, and K4 have been established. The cluster K12 = 1Zn@11(Mg₅Zn₆) in the form of coupled planar 5th rings Mg₅ and Zn₅, with Zn atoms located above their centers with symmetry m2m. The cluster K5 = 0@5(LiZn₄) is in the form of a triangular bipyramid LiZn₄ with symmetry 2. The cluster K4 = 0@4(Li₂Al₂) is in the form of a tetrahedra Li₂Al₂ with symmetry 2. For the Li₄Ca₃₂Mg₈Ge₃₂-oP76 two topological types of clusters have been established: triple ring K3 = 0@3(CaMgGe), tetrahedra K4 = 0@4(LiCaMgGe), and tetrahedra K4 = 0@4(Ca₂Ge₂). Clusters K3 = 0@3(CaMgGe) and K4 = 0@4(LiCaMgGe) form a suprapolyhedral ensemble (the tetramer) of four linked clusters 2(K3 + K4) with symmetry –1 centered at position 4a. Tetrahedra K4 = 0@ 4(Ca₂Ge₂) form a suprapolyhedral ensemble (the hexamer) of 6 linked clusters with symmetry –1. The symmetry and topological code of the processes of self-assembly of crystal structures Li₁₂Mg₂₀Al₈Zn₆₀-oC100 and Li₄Ca₃₂Mg₈Ge₃₂-oP76 from cluster precursors has been reconstructed in the form: primary chain → layer → framework.