Metal borides Crystal structure of boron-rich metal borides

fig. 1. (a) b6 octahedron, (b) b12 cuboctahedron , (c) b12 icosahedron.

in metal borides, bonding of boron varies depending on atomic ratio b/m. diborides have b/m = 2, in well-known superconductor mgb2; crystallize in hexagonal alb2-type layered structure. hexaborides have b/m = 6 , form three-dimensional boron framework based on boron octahedron (fig. 1a). tetraborides, i.e. b/m = 4, mixtures of diboride , hexaboride structures. cuboctahedron (fig. 1b) structural unit of dodecaborides, have cubic lattice , b/m = 12. when composition ratio exceeds 12, boron forms b12 icosahedra (fig. 1c) linked three-dimensional boron framework, , metal atoms reside in voids of framework.

this complex bonding behavior originates fact boron has 3 valence electrons; hinders tetrahedral bonding in diamond or hexagonal bonding in graphite. instead, boron atoms form polyhedra. example, 3 boron atoms make triangle share 2 electrons complete so-called three-center bonding. boron polyhedra, such b6 octahedron, b12 cuboctahedron , b12 icosahedron, lack 2 valence electrons per polyhedron complete polyhedron-based framework structure. metal atoms need donate 2 electrons per boron polyhedron form boron-rich metal borides. thus, boron compounds regarded electron-deficient solids.

icosahedral b12 compounds include α-rhombohedral boron (b13c2), β-rhombohedral boron (mebx, 23≤x), α-tetragonal boron (b48b2c2), β-tetragonal boron (β-alb12), alb10 or alc4b24, yb25, yb50, yb66, nab15 or mgalb14, γ-alb12, beb3 , sib6.

fig. 2. relationship between ionic radius of trivalent rare-earth ion , chemical composition of icosahedron-based rare-earth borides.

yb25 , yb50 decompose without melting hinders growth single crystals floating zone method. however, addition of small amount of si solves problem , results in single crystals stoichiometry of yb41si1.2. stabilization technique allowed synthesis of other boron-rich rare-earth (re) borides.

albert , hillebrecht reviewed binary , selected ternary boron compounds containing main-group elements, namely, borides of alkali , alkaline-earth metals, aluminum borides , compounds of boron , nonmetals c, si, ge, n, p, as, o, s , se. they, however, excluded described here icosahedron-based rare-earth borides. note rare-earth elements have d- , f-electrons complicates chemical , physical properties of borides. werheit et al. reviewed raman spectra of numerous icosahedron-based boron compounds.

figure 2 shows relationship between ionic radius of trivalent rare-earth ions , composition of rare-earth borides. note scandium has many unique boron compounds, shown in figure 2, because of smaller ionic radius compared other rare-earth elements.

in understanding crystal structures of rare-earth borides, important keep in mind concept of partial site occupancy, is, atoms in described below unit cells can take several possible positions given statistical probability. thus, given statistical probability, of partial-occupancy sites in such unit cell empty, , remained sites occupied.