Using these large polyhedra, the crystal structure of Sc0.83–xB10.0–yC0.17+ySi0.083–z can be described as shown in figure 25. Owing to the crystal symmetry, the tetrahedral coordination between these superstructure units is again a key factor. The supertetrahedron T(1) lies at the body center and at the edge center of the unit cell. The superoctahedra O(1) locate at the body center (0.25, 0.25, 0.25) of the quarter of the unit cell. They coordinate tetrahedrally around T(1) forming a giant tetrahedron. The supertetrahedra T(2) are located at the symmetry-related positions (0.25, 0.25, 0.75); they also form a giant tetrahedron surrounding T(1). Edges of both giant tetrahedra orthogonally cross each other at their centers; at those edge centers, each B10 polyhedron bridges all the super-structure clusters T(1), T(2) and O(1). The superoctahedron built of B10 polyhedra is located at each cubic face center. Scandium atoms reside in the voids of the boron framework. Four Sc1 atoms form a tetrahedral arrangement inside the B10 polyhedron-based superoctahedron. Sc2 atoms sit between the B10 polyhedron-based superoctahedron and the O(1) superoctahedron. Three Sc3 atoms form a triangle and are surrounded by three B10 polyhedra, a supertetrahedron T(1) and a superoctahedron O(1). ===ScB14–xCx (x = 1.1) and ScB15C1.6=== ScB14–xCx has an orthorhombic crystal structure with space group
Imma (No. 74) and lattice constants of
a = 0.56829(2),
b = 0.80375(3) and
c = 1.00488(4) nm. The crystal structure of ScB14–xCx is isotypic to that of MgAlB14 where Sc occupies the Mg site, the Al site is empty and the boron bridge site is a B/C mixed-occupancy site with the occupancy of B/C = 0.45/0.55. The occupancy of the Sc site in flux-grown single crystals is 0.964(4), i.e. almost 1. Solid-state powder-reaction growth resulted in lower Sc site occupancy and in the resulting chemical composition ScB15C1.6. The B-C bonding distance 0.1796(3) nm between the B/C bridge sites is rather long as compared with that (0.15–0.16 nm) of an ordinary B-C covalent bond, that suggests weak bonding between the B/C bridge sites.
Sc4.5–xB57–y+zC3.5–z Sc4.5–xB57–y+zC3.5–z (x = 0.27, y = 1.1, z = 0.2) has an orthorhombic crystal structure with space group
Pbam (No. 55) and lattice constants of
a = 1.73040(6),
b = 1.60738(6) and
c = 1.44829(6) nm. This phase is indicated as ScB12.5C0.8 (phase IV) in the phase diagram of figure 17. This rare orthorhombic structure has 78 atomic positions in the unit cell: seven partially occupied Sc sites, four C sites, 66 B sites including three partially occupied sites and one B/C mixed-occupancy site. Atomic coordinates, site occupancies and isotropic displacement factors are listed in
table IX. More than 500 atoms are available in the unit cell. In the crystal structure, there are six structurally independent icosahedra I1–I6, which are constructed from B1–B12, B13–B24, B25–B32, B33–B40, B41–B44 and B45–B56 sites, respectively; B57–B62 sites form a B8 polyhedron. The Sc4.5–xB57–y+zC3.5–z crystal structure is layered, as shown in figure 26. This structure has been described in terms of two kinds of boron icosahedron layers, L1 and L2. L1 consists of the icosahedra I3, I4 and I5 and the C65 "dimer", and L2 consists of the icosahedra I2 and I6. I1 is sandwiched by L1 and L2 and the B8 polyhedron is sandwiched by L2. An alternative description is based on the same B12(B12)12supericosahedron as in the YB66 structure. In the YB66 crystal structure, the supericosahedra form 3-dimensional boron framework as shown in figure 5. In this framework, the neighboring supericosahedra are rotated 90° with respect to each other. On the contrary, in Sc4.5–xB57–y+zC3.5–z the supericosahedra form a 2-dimensional network where the 90° rotation relation is broken because of the orthorhombic symmetry. The planar projections of the supericosahedron connection in Sc4.5–xB57–y+zC3.5–z and YB66 are shown in figures 27a and b, respectively. In the YB66 crystal structure, the neighboring 2-dimensional supericosahedron connections are out-of-phase for the rotational relation of the supericosahedron. This allows 3-dimensional stacking of the 2-dimensional supericosahedron connection while maintaining the cubic symmetry. The B80 boron cluster occupies the large space between four supericosahedra as described in the REB66 section. On the other hand, the 2-dimensional supericosahedron networks in the Sc4.5–xB57–y+zC3.5–z crystal structure stack in-phase along the
z-axis. Instead of the B80 cluster, a pair of the I2 icosahedra fills the open space staying within the supericosahedron network, as shown in figure 28 where the icosahedron I2 is colored in yellow. All Sc atoms except for Sc3 reside in large spaces between the supericosahedron networks, and the Sc3 atom occupies a void in the network as shown in figure 26. Because of the small size of Sc atom, the occupancies of the Sc1–Sc5 sites exceed 95%, and those of Sc6 and Sc7 sites are approximately 90% and 61%, respectively (see
table IX).
Sc3.67–xB41.4–y–zC0.67+zSi0.33–w Sc3.67–xB41.4–y–zC0.67+zSi0.33–w (x = 0.52, y = 1.42, z = 1.17 and w = 0.02) has a hexagonal crystal structure with space group
Pm2 (No. 187) and lattice constants
a =
b = 1.43055(8) and
c = 2.37477(13) nm. Single crystals of this compound were obtained as an intergrowth phase in a float-zoned single crystal of Sc0.83–xB10.0–yC0.17+ySi0.083–z. This phase is not described in the phase diagram of figure 17 because it is a quaternary compound. Its hexagonal structure is rare and has 79 atomic positions in the unit cell: eight partially occupied Sc sites, 62 B sites, two C sites, two Si sites and six B/C sites. Six B sites and one of the two Si sites have partial occupancies. The associated atomic coordinates, site occupancies and isotropic displacement factors are listed in
table X. There are seven structurally independent icosahedra I1–I7 which are formed by B1–B8, B9–B12, B13–B20, B/C21–B24, B/C25–B29, B30–B37 and B/C38–B42 sites, respectively; B43–B46 sites form the B9 polyhedron and B47–B53 sites construct the B10 polyhedron. B54–B59 sites form the irregularly shaped B16 polyhedron in which only 10.7 boron atoms are available because most of sites are too close to each other to be occupied simultaneously. Ten bridging sites C60–B69 interconnect polyhedron units or other bridging sites to form a 3D boron framework structure. One description of the crystal structure uses three pillar-like units that extend along the
c-axis that however results in undesired overlaps between those three pillar-like units. An alternative is to define two pillar-like structure units. Figure 29 shows the boron framework structure of Sc3.67–xB41.4–y–zC0.67+zSi0.33–w viewed along the
c-axis, where the pillar-like units P1 and P2 are colored in dark green and light green respectively and are bridged by yellow icosahedra I4 and I7. These pillar-like units P1 and P2 are shown in figures 30a and b, respectively. P1 consists of icosahedra I1 and I3, an irregularly shaped B16 polyhedron and other bridge site atoms where two supericosahedra can be seen above and below the B16 polyhedron. Each supericosahedron is formed by three icosahedra I1 and three icosahedra I3 and is the same as the supericosahedron O(1) shown in figure 24a.The P2 unit consists of icosahedra I2, I5 and I6, B10 polyhedron and other bridge site atoms. Eight Sc sites with occupancies between 0.49 (Sc8) and 0.98 (Sc1) spread over the boron framework. As described above, this hexagonal phase originates from a cubic phase, and thus one may expect a similar structural element in these phases. There is an obvious relation between the hexagonal
ab-plane and the cubic (111) plane. Figures 31a and b show the hexagonal (001) and the cubic (111) planes, respectively. Both network structures are almost the same that allows intergrowth of the hexagonal phase in the cubic phase. ==Applications==