Metal borides
In metal borides, the bonding of boron varies depending on the atomic ratio B/M. Diborides have B/M = 2, as in the well-known superconductor MgB2; they crystallize in aREAlB14 and REB25
Compounds that were historically given the formulae REAlB14 and REB25 have the MgAlB14 structure with anREB66-type borides
In addition to yttrium, a wide range of rare-earth elements from Nd to Lu, except for Eu, can form REB66 compounds. Seybolt discovered the compound YB66 in 1960 and its structure was solved by Richards and Kasper in 1969. They reported that YB66 has a face-centered cubic structure with space group ''Fmc'' (No. 226) and lattice constant ''a'' = 2.3440(6) nm. There are 13 boron sites B1–B13 and one yttrium site. The B1 sites form one icosahedron and the B2–B9 sites make up another icosahedron. These icosahedra arrange in a thirteen-icosahedron unit (B12)12B12 which is shown in figure 4a and is called supericosahedron. The icosahedron formed by the B1 site atoms is located at the center of the supericosahedron. The supericosahedron is one of the basic units of the boron framework of YB66. There are two types of supericosahedra: one occupies the cubic face centers and another, which is rotated by 90°, is located at the center of the cell and at the cell edges. Thus, there are eight supericosahedra (1248 boron atoms) in the unit cell.REB41Si1.2
Similar to yttrium, rare-earth metals from Gd to Lu can form REB41Si1.2-type boride. The first such compound was synthesized by solid-state reaction and its structure was deduced as YB50. X-ray powder diffraction (XRD) andHomologous icosahedron-based rare-earth borides
Rare-earth borides REB15.5CN, REB22C2N and REB28.5C4 are homologous, i.e. have a similar crystal structure, to B4C. The latter has a structure typical of icosahedron-based borides, as shown in figure 11a. There, B12 icosahedra form a rhombohedral lattice unit (space group: ''Rm'' (No. 166), lattice constants: ''a'' = 0.56 nm and ''c'' = 1.212 nm) surrounding a C-B-C chain that resides at the center of the lattice unit, and both C atoms bridge the neighboring three icosahedra. This structure is layered: as shown in figure 11b, B12 icosahedra and bridgingRExB12C0.33Si3.0
Initially these were described as ternary RE-B-Si compounds, but later carbon was included to improve the structure description that resulted in a quaternary RE-B-C-Si composition. RExB12C0.33Si3.0 (RE=Y and Gd–Lu) have a unique crystal structure with two units – a cluster of B12 icosahedra and a Si8 ethane-like complex – and one bonding configuration (B12)3≡Si-C≡(B12)3. A representative compound of this group is YxB12C0.33Si3.0 (x=0.68). It has a trigonal crystal structure with space group ''Rm'' (No. 166) and lattice constants ''a'' = ''b'' = 1.00841(4) nm, ''c'' = 1.64714(5) nm, α = β = 90° and γ = 120°. The crystal has layered structure. Figure 15 shows a network of boron icosahedra that spreads parallel to the (001) plane, connecting with four neighbors through B1–B1 bonds. The C3 and Si3 site atoms strengthen the network by bridging the boron icosahedra. Contrary to other boron-rich icosahedral compounds, the boron icosahedra from different layers are not directly bonded. The icosahedra within one layer are linked through Si8 ethane-like clusters with (B12)3≡Si-C≡(B12)3 bonds, as shown in figures 16a and b. There are eight atomic sites in the unit cell: one yttrium Y, four boron B1–B4, one carbon C3 and three silicon sites Si1–Si3. Atomic coordinates, site occupancy and isotropic displacement factors are listed in table Va; 68% of the Y sites are randomly occupied and remaining Y sites are vacant. All boron sites and Si1 and Si2 sites are fully occupied. The C3 and Si3 sites can be occupied by either carbon or silicon atoms (mixed occupancy) with a probability of about 50%. Their separation is only 0.413 Å, and thus either the C3 or Si3 sites, but not both, are occupied. These sites form Si-C pairs, but not Si-Si or C-C pairs. The distances between the C3 and Si3 sites and the surrounding sites for YxB12C0.33Si3.0 are summarized in table Vb and the overall crystal structure is shown in figure 14. Salvador ''et al.'' reported an isotypic terbium compound Tb3–xC2Si8(B12)3. Most parts of the crystal structure are the same as those described above; however, its bonding configuration is deduced as (B12)3≡C-C≡(B12)3 instead of (B12)3≡Si-C≡(B12)3. The authors intentionally added carbon to grow single crystals whereas the previous crystals were accidentally contaminated by carbon during their growth. Thus, higher carbon concentration was achieved. Existence of both bonding schemes of (B12)3≡Si-C≡(B12)3 and (B12)3≡C-C≡(B12)3 suggests the occupancy of the carbon sites of 50–100%. On the other hand, (B12)3≡Si-Si≡(B12)3 bonding scheme is unlikely because of too short Si-Si distance, suggesting that the minimum carbon occupancy at the site is 50%. Some B atoms may replace C atoms at the C3 site, as previously assigned to the B site. However, the carbon occupation is more likely because the site is tetrahedrally coordinated whereas the B occupation of the site needs an extra electron to complete tetrahedral bonding. Thus, carbon is indispensable for this group of compounds.Scandium compounds
Scandium has the smallest atomic and ionic (3+) radii (1.62 and 0.885 Å, respectively) among the rare-earth elements. It forms several icosahedron-based borides which are not found for other rare-earth elements; however, most of them are ternary Sc-B-C compounds. There are many boron-rich phases in the boron-rich corner of Sc-B-C phase diagram, as shown in figure 17. A slight variation of the composition can produce ScB19, ScB17C0.25, ScB15C0.8 and ScB15C1.6; their crystal structures are unusual for borides and are very different from each other.ScB19+xSiy
ScB19+xSiy has a tetragonal crystal structure with space group ''P''41212 (No. 92) or ''P''43212 and lattice constants of ''a'', ''b'' = 1.03081(2) and ''c'' = 1.42589(3) nm; it is isotypic to the α-AlB12 structure type. There are 28 atomic sites in the unit cell, which are assigned to 3 scandium atoms, 24 boron atoms and one silicon atom. Atomic coordinates, site occupancies and isotropic displacement factors are listed in table VI. The boron framework of ScB19+xSiy is based on one B12 icosahedron and one B22 unit. This unit can be observed in β-tetragonal boron and is a modification of the B20 unit of α-AlB12 (or B19 unit in early reports). The B20 unit is a twinned icosahedron made from B13 to B22 sites with two vacant sites and one B atom (B23) bridging both sides of the unit. The twinned icosahedron is shown in figure 18a. B23 was treated as an isolated atom in the early reports; it is bonded to each twinned icosahedra through B18 and to another icosahedron through B5 site. If the twinned icosahedra were independent without twinning then B23 would be a bridge site linking three icosahedra. However, because of twinning, B23 shifts closer to the twinned icosahedra than another icosahedron; thus B23 is currently treated as a member of the twinned icosahedra. In ScB19+xSiy, the two B24 sites which correspond to the vacant sites in the B20 unit are partially occupied; thus, the unit should be referred to as a B22 cluster which is occupied by about 20.6 boron atoms. Scandium atoms occupy 3 of 5 Al sites of α-AlB12, that is Sc1, Sc2 and Sc3 correspond to Al4, Al1 and Al2 sites of α-AlB12, respectively. The Al3 and Al5 sites are empty for ScB19+xSiy, and the Si site links two B22 units. This phase also exists without silicon. Figure 19a shows the network of boron icosahedra in the boron framework of ScB19+xSiy. In this network, 4 icosahedra form a superScB17C0.25
Very small amount of carbon is sufficient to stabilize "ScB17C0.25". This compound has a broad composition range, namely ScB16.5+xC0.2+y with x ≤ 2.2 and y ≤ 0.44. ScB17C0.25 has a hexagonal crystal structure with space group ''P6mmm'' (No. 199) and lattice constants ''a, b'' = 1.45501(15) nm and ''c'' = 0.84543(16) nm. There are 19 atomic sites in the unit cell, which are assigned to one scandium site Sc, 14 boron sites B1–B14 having 100% occupancy, two boron-carbon mixed-occupancy sites B/C15 and B/C16, and two partial-occupancy boron sites B17 and B18. Atomic coordinates, site occupancies and isotropic displacement factors are listed in table VII. Although a very small amount of carbon (less than 2 wt%!) plays an important role in the phase stability, carbon does not have its own sites but shares with boron two interstitial sites B/C15 and B/C16. There are two inequivalent B12 icosahedra, I1 and I2, which are constructed by the B1–B5 and B8–B12 sites, respectively. A "tube" is another characteristic structure unit of ScB17C0.25. It extends along the ''c''-axis and consists of B13, B14, B17 and B18 sites where B13 and B14 form 6-membered rings. B17 and B18 sites also form 6-membered rings; however, their mutual distances (0.985 Å for B17 and 0.955 Å for B18) are too short for a simultaneous occupation of the neighboring sites. Therefore, boron atoms occupy 2nd neighbor site forming a triangle. The occupancies of B17 and B18 sites should be 50%, but the structure analysis suggests larger values. The crystal structure viewed along the ''a''-axis is shown in figure 20, which suggests that the ScB17C0.25 is a layered material. Two layers, respectively constructed by the icosahedra I1 and I2, alternatively stack along the ''c''-axis. However, the ScB17C0.25 crystal is not layered. For example, during arc-melting, ScB17C0.25 needle crystals violently grow along the ''c''-axis – this never happens in layered compounds. The crystal structure viewed along the ''c''-axis is shown in figure 21a. The icosahedra I1 and I2 form a ring centered by the "tube" shown in figure 21b, which probably governs the properties of the ScB17C0.25 crystal. B/C15 and B/C16 mixed-occupancy sites interconnect the rings. A structural similarity can be seen between ScB17C0.25 and BeB3. Figures 22a and b present HRTEM lattice images and electron diffraction patterns taken along theSc0.83–xB10.0–yC0.17+ySi0.083–z
Sc0.83–xB10.0–yC0.17+ySi0.083–z (''x'' = 0.030, ''y'' = 0.36 and ''z'' = 0.026) has a cubic crystal structure with space group ''F3m'' (No. 216) and lattice constant ''a'' = 2.03085(5) nm. This compound was initially identified as ScB15C0.8 (phase I in the Sc-B-C phase diagram of figure 17). A small amount of Si was added into the floating zone crystal growth and thus this phase is a quaternary compound. Its rare cubic structure has 26 sites in the unit cell: three Sc sites, two Si sites, one C site and 20 B sites; 4 out of 20 B sites are boron-carbon mixed-occupancy sites. Atomic coordinates, site occupancies and isotropic displacement factors are listed in table VIII. In the unit cell, there are three independent icosahedra, I1, I2 and I3, and a B10 polyhedron which are formed by the B1–B4, B5–B8, B9–B13 and B14–B17 sites, respectively.There are more than 4 sites in total among, say, B5–B8 sites, but many of them are equivalent by symmetry and thus do not have an individual label. The B10 polyhedron has not been observed previously and it is shown in figure 23. The icosahedron I2 has a boron-carbon mixed-occupancy site B,C6 whose occupancy is B/C=0.58/0.42. Remaining 3 boron-carbon mixed-occupancy sites are bridge sites; C and Si sites are also bridge sites. More than 1000 atoms are available in the unit cell, which is built up by large structure units such as two supertetrahedra T(1) and T(2) and one superoctahedron O(1). As shown in figure 24a, T(1) consists of 4 icosahedra I(1) which have no direct bonding but are bridged by four B and C20 atoms. These atoms also form tetrahedron centered by the Si2 sites. The supertetrahedron T(2) that consists of 4 icosahedra I(2) is the same as shown in figure 18b; its mixed-occupancy sites B and C6 directly bond with each other. The superoctahedron O(1) consists of 6 icosahedra I(3) and bridge sites B, C18, C1 and Si1; here Si1 and C1 exhibit a tetrahedral arrangement at the center of O(1). The B10 polyhedra also arrange octahedrally, without the central atom, as shown in figure 24c where the B and C19 atoms bridge the B10 polyhedra to form the octahedral supercluster of the B10 polyhedra. 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
The diversity of the crystal structures of rare-earth borides results in unusual physical properties and potential applications inNotes
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