Modeling of the self-organization processes in crystal-forming systems. Tetrahedral metal clusters and the self-assembly of crystal structures of intermetallic compounds

Abstract

A combinatorial and topological modeling of 1D, 2D, and 3D packings of symmetrically linked A₄ tetrahedra has been performed. Three types of 1D chains with tetrahedra connectivities of 4, 6, and 8 were used to model 2D layers L-1, L-2, and L-3 and 3D frameworks FR-1, FR-2, FR-3, and FR-4. A family of tetrahedral structures with FR-1, FR-2, and FR-3 frameworks has been selected among the intermetallic compounds with chemical compositions of A₃B, A₂B₂, AB₃, A₂BC, AB₂C, and ABCD; this family includes more than 1900 compounds (TOPOS program package). It is found that the topological models of tetrahedral 3D frameworks are in correspondence with all types of the crystal structures formed in Au–Cu binary systems (FR-1 for Cu₃Au (auricupride), Cu₂Au₂ (tetraauricupride), and CuAu₃ (bogdanovite)), in the Mg–Cd system (FR-3 for Mg₃Cd, Mg₂Cd₂, and MgCd₃), in the Li–Hg system (FR-2 for Li₃Hg and Li₂Hg₂ and FR-3 for LiHg₃), in the Li–Ag–Al ternary system (FR-2 for LiAg₂Al and Li₂AgAl), and in the Li–Mg–Pd–Sn quaternary system (FR-2 for LiMgPdSn). Framework FR-4 has been established in ternary intermetallic compounds A(Li₂Sn₂); A = Cu, Ag, Au.