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

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.