Polar intermetallic crystals and quasicrystals

Two main questions guide these investigations of polar intermetallic compounds: (1) Where are the atoms, based on observed electron densities via diffraction? and (2) What gives rise to the observed structures, based on chemical bonding and electronic structure theory? At nearly equal Au: Al molar ratios, NaZn13-derivatives of Sr/Ca(AuxAl1–x)12–13 show a progression from cubic to tetragonal, to orthorhombic, and then monoclinic symmetry with subtle decreasing Au concentrations, results which reveal preferential ordering of Au and Al to maximize the number of Au–Al (or Al-rich) shortest distances. In the Au-rich region of the Ca–Au–Al system, the 1/0 crystalline approximant (CA) CaAu3+xAl1–x and icosahedral quasicrystal (i-QC) CaAu4.5–xAl1.5+x were discovered, and the i-QC is shown to irreversibly transform into the 2/1 CA Ca13Au56.79(6)Al21.20 via in-situ, high-energy, variable-temperature powder X-ray diffraction (XRD). The QC was characterized from high-energy single-crystal XRD to have icosahedral symmetry, ܲ݉3ത5ത, and a quasilattice (aQC = 5.383(4) Å) in close agreement to those calculated from the 1/0 and 2/1 CAs (aQC-Calc.1/0 = 5.336(2)–5.354(2) Å; aQC-Calc.2/1 = 5.364(6) Å). Following the polar intermetallic depiction from the calculated electronic structures, the 1/0 and 2/1 CA crystal structures show formally electronegative Au+Al sharing polyhedra and electropositive Ca in the voids or in intervening shells so that overall, the 2/1 CA can be described as interpenetrating and edge-sharing icosahedra. The origin of hexagonal ScAuAl, in which the unit cell is distorted due to long-short alternating Au–Au chains, is rationalized from a Peierls-type distortion of its calculated electronic structures. Chemical pressure effects and valence electron count variations were examined in the series CaAuAl–ScAuAl–TiAuAl. In general, the calculated electronic structures of all these (Sr/Ca/Sc)–Au–Al crystalline compounds reveal significant Sr/Ca/Sc– (Au+Al) polar-covalent interactions that contribute to structural cohesion and preferential ordering to maximize the number of Au–Al shortest distances