REB66-type borides Crystal structure of boron-rich metal borides

in addition yttrium, wide range of rare-earth elements nd lu, except eu, can form reb66 compounds. seybolt discovered compound yb66 in 1960 , structure solved richards , kasper in 1969. reported yb66 has face-centered cubic structure space group fm3c (no. 226) , lattice constant = 2.3440(6) nm. there 13 boron sites b1–b13 , 1 yttrium site. b1 sites form 1 icosahedron , b2–b9 sites make icosahedron. these icosahedra arrange in thirteen-icosahedron unit (b12)12b12 shown in figure 4a , called supericosahedron. icosahedron formed b1 site atoms located @ center of supericosahedron. supericosahedron 1 of basic units of boron framework of yb66. there 2 types of supericosahedra: 1 occupies cubic face centers , another, rotated 90°, located @ center of cell , @ cell edges. thus, there 8 supericosahedra (1248 boron atoms) in unit cell.

fig. 5a boron framework of yb66 viewed along z-axis.

another structure unit of yb66, shown in figure 4b, b80 cluster of 80 boron sites formed b10 b13 sites. 80 sites partially occupied , in total contain 42 boron atoms. b80 cluster located @ body center of octant of unit cell, i.e., @ 8a position (1/4, 1/4, 1/4); thus, there 8 such clusters (336 boron atoms) per unit cell. 2 independent structure analyses came same conclusion total number of boron atoms in unit cell 1584. boron framework structure of yb66 shown in figure 5a. indicate relative orientations of supericosahedra, schematic drawing shown in figure 5b, supericosahedra , b80 clusters depicted light green , dark green spheres, respectively; @ top surface of unit cell, relative orientations of supericosahedra indicated arrows. there 48 yttrium sites ((0.0563, 1/4, 1/4) yb62) in unit cell. richards , kasper fixed y site occupancy 0.5 resulted in 24 y atoms in unit cell , chemical composition of yb66. shown in figure 6, y sites form pair separated 0.264 nm in yb62. pair aligned normal plane formed 4 supericosahedra. y site occupancy 0.5 implies pair has 1 y atom 1 empty site.

slack et al. reported total number of boron atoms in unit cell, calculated measured values of density, chemical composition , lattice constant, 1628 ± 4, larger value 1584 obtained structural analysis. number of b atoms in unit cell remains constant when chemical composition changes yb56 yb66. on other hand, total number of yttrium atoms per unit cell varies, , is, example, ~26.3 yb62 (see right table). if total number of y atoms stays below or equal 24 possible 1 y atom accommodates in each y pair (partial occupancy). however, experimental value of 26.3 exceeds 24, , both pair sites might occupied. in case, because of small separation between 2 y atoms, must repelled coulomb force. clarify point, split y sites introduced in structure analysis resulting in better agreement experiment. y site distances , occupancies presented in left table.

there twenty y pair sites 1 y atom , 3 pairs 2 y atoms; there 1 empty y pair (partial occupancy = 0). separation 0.340 nm y2 pair site (two y atoms in pair site) larger separation 0.254 nm y1 pair site (one y atom in pair site), expected. total number of y atoms in unit cell 26.3, measured. both cases compared in figure 7. larger separation y2 pair site clear compared y1 pair site. in case of y2 pair, neighboring boron sites belong b80 cluster must unoccupied because close y2 site.

splitting y site yields right number of y atoms in unit cell, not b atoms. not occupation of b sites in b80 cluster must dependent on whether or not y site y1 state or y2 state, position of occupied b sites must affected state of y site. atomic coordinates , site occupancies summarized in table ii.