Sc4.5.E2.80.93xB57.E2.80.93y.2BzC3.5.E2.80.93z Crystal structure of boron-rich metal borides

an alternative description based on same b12(b12)12supericosahedron in yb66 structure. in yb66 crystal structure, the　supericosahedra form 3-dimensional boron framework shown in figure 5. in framework, neighboring supericosahedra rotated 90° respect each other. on contrary, in sc4.5–xb57–y+zc3.5–z supericosahedra form 2-dimensional network 90° rotation relation broken because of orthorhombic symmetry. planar projections of supericosahedron connection in sc4.5–xb57–y+zc3.5–z , yb66 shown in figures 27a , b, respectively. in yb66 crystal structure, neighboring 2-dimensional supericosahedron connections out-of-phase rotational relation of supericosahedron. allows 3-dimensional stacking of 2-dimensional supericosahedron connection while maintaining cubic symmetry.

the b80 boron cluster occupies large space between 4 supericosahedra described in reb66 section. on other hand, 2-dimensional supericosahedron networks in sc4.5–xb57–y+zc3.5–z crystal structure stack in-phase along z-axis. instead of b80 cluster, pair of i2 icosahedra fills open space staying within supericosahedron network, shown in figure 28 icosahedron i2 colored in yellow.

all sc atoms except sc3 reside in large spaces between supericosahedron networks, , sc3 atom occupies void in network shown in figure 26. because of small size of sc atom, occupancies of sc1–sc5 sites exceed 95%, , of sc6 , sc7 sites approximately 90% , 61%, respectively (see table ix).