Metals, and specifically rare-earth elements, form numerous chemical complexes with boron. Their crystal structure and chemical bonding depend strongly on the metal element M and on its atomic ratio to boron. When B/M ratio exceeds 12, boron atoms form B12 icosahedra which are linked into a three-dimensional boron framework, and the metal atoms reside in the voids of this framework. Those icosahedra are basic structural units of most allotropes of boron and boron-rich rare-earth borides. In such borides, metal atoms donate electrons to the boron polyhedra, and thus these compounds are regarded as electron-deficient solids.
The crystal structures of many boron-rich borides can be attributed to certain types including MgAlB14, YB66, REB41Si1.2, B4C and other, more complex types such as RExB12C0.33Si3.0. Some of these formulas, for example B4C, YB66 and MgAlB14, historically reflect the idealistic structures, whereas the experimentally determined composition is nonstoichiometric and corresponds to fractional indexes. Boron-rich borides are usually characterized by large and complex unit cells, which can contain more than 1500 atomic sites and feature extended structures shaped as "tubes" and large modular polyhedra ("superpolyhedra"). Many of those sites have partial occupancy, meaning that the probability to find them occupied with a certain atom is smaller than one and thus that only some of them are filled with atoms. Scandium is distinguished among the rare-earth elements by that it forms numerous borides with uncommon structure types; this property of scandium is attributed to its relatively small atomic and ionic radii.
Crystals of the specific rare-earth boride YB66 are used as X-ray monochromators for selecting X-rays with certain energies (in the 1–2 keV range) out of synchrotron radiation. Other rare-earth borides may find application as thermoelectric materials, owing to their low thermal conductivity; the latter originates from their complex, "amorphous-like", crystal structure.
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 a hexagonal AlB2-type layered structure. Hexaborides have B/M = 6 and form a three-dimensional boron framework based on a boron octahedron (Fig. 1a). Tetraborides, i.e. B/M = 4, are mixtures of diboride and hexaboride structures. Cuboctahedron (Fig. 1b) is the structural unit of dodecaborides, which have a cubic lattice and B/M = 12. When the composition ratio exceeds 12, boron forms B12 icosahedra (Fig. 1c) which are linked into a three-dimensional boron framework, and the metal atoms reside in the voids of this framework.
This complex bonding behavior originates from the fact that boron has only three valence electrons; this hinders tetrahedral bonding as in diamond or hexagonal bonding as in graphite. Instead, boron atoms form polyhedra. For example, three boron atoms make up a triangle where they share two electrons to complete the so-called three-center bonding. Boron polyhedra, such as B6 octahedron, B12 cuboctahedron and B12 icosahedron, lack two valence electrons per polyhedron to complete the polyhedron-based framework structure. Metal atoms need to donate two electrons per boron polyhedron to form boron-rich metal borides. Thus, boron compounds are often regarded as electron-deficient solids. The covalent bonding nature of metal boride compounds also give them their hardness and inert chemical reactivity property.
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 and SiB6.
YB25 and YB50 decompose without melting that hinders their growth as single crystals by the floating zone method. However, addition of a small amount of Si solves this problem and results in single crystals with the stoichiometry of YB41Si1.2. This stabilization technique allowed the synthesis of some other boron-rich rare-earth borides.
Albert and Hillebrecht reviewed binary and selected ternary boron compounds containing main-group elements, namely, borides of the alkali and alkaline-earth metals, aluminum borides and compounds of boron and the nonmetals C, Si, Ge, N, P, As, O, S and Se. They, however, excluded the described here icosahedron-based rare-earth borides. Note that rare-earth elements have d- and f-electrons that complicates chemical and physical properties of their borides. Werheit et al. reviewed Raman spectra of numerous icosahedron-based boron compounds.
Figure 2 shows a relationship between the ionic radius of trivalent rare-earth ions and the composition of some rare-earth borides. Note that scandium has many unique boron compounds, as shown in figure 2, because of the much smaller ionic radius compared with other rare-earth elements.
In understanding the crystal structures of rare-earth borides, it is important to keep in mind the concept of partial site occupancy, that is, some atoms in the described below unit cells can take several possible positions with a given statistical probability. Thus, with the given statistical probability, some of the partial-occupancy sites in such a unit cell are empty, and the remained sites are occupied.
REAlB14 and REB25 Compounds that were historically given the formulae REAlB14 and REB25 have the MgAlB14 structure with an orthorhombic symmetry and space group Imma (No. 74). In this structure, rare-earth atoms enter the Mg site. Aluminium sites are empty for REB25. Both metal sites of REAlB14 structure have partial occupancies of about 60–70%, which shows that the compounds are actually non-stoichiometric. The REB25 formula merely reflects the average atomic ratio [B]/[RE] = 25. Yttrium borides form both YAlB14 and YB25 structures. Experiments have confirmed that the borides based on rare-earth elements from Tb to Lu can have the REAlB14 structure. A subset of these borides, which contains rare-earth elements from Gd to Er, can also crystallize in the REB25 structure.
Korsukova et al. analyzed the YAlB14 crystal structure using a single crystal grown by the high-temperature solution-growth method. The lattice constants were deduced as a = 0.58212(3), b = 1.04130(8) and c = 0.81947(6) nm, and the atomic coordinates and site occupancies are summarized in table I.
Figure 3 shows the crystal structure of YAlB14 viewed along the x-axis. The large black spheres are Y atoms, the small blue spheres are Al atoms and the small green spheres are the bridging boron sites; B12 clusters are depicted as the green icosahedra. Boron framework of YAlB14 is one of the simplest among icosahedron-based borides – it consists of only one kind of icosahedra and one bridging boron site. The bridging boron site is tetrahedrally coordinated by four boron atoms. Those atoms are another boron atom in the counter bridge site and three equatorial boron atoms of one of three B12 icosahedra. Aluminium atoms are separated by 0.2911 nm and are arranged in lines parallel to the x-axis, whereas yttrium atoms are separated by 0.3405 nm. Both the Y atoms and B12 icosahedra form zigzags along the x-axis. The bridging boron atoms connect three equatorial boron atoms of three icosahedra and those icosahedra make up a network parallel to the (101) crystal plane (x-z plane in the figure). The bonding distance between the bridging boron and the equatorial boron atoms is 0.1755 nm, which is typical for the strong covalent B-B bond (bond length 0.17–0.18 nm); thus, the bridging boron atoms strengthen the individual network planes. On the other hand, the large distance between the boron atoms within the bridge (0.2041 nm) suggests weaker interaction, and thus the bridging sites contribute little to the bonding between the network planes.
The boron framework of YAlB14 needs donation of four electrons from metal elements: two electrons for a B12 icosahedron and one electron for each of the two bridging boron atoms – to support their tetrahedral coordination. The actual chemical composition of YAlB14, determined by the structure analysis, is Y0.62Al0.71B14 as described in table I. If both metal elements are trivalent ions then 3.99 electrons can be transferred to the boron framework, which is very close to the required value of 4. However, because the bonding between the bridging boron atoms is weaker than in a typical B-B covalent bond, less than 2 electrons are donated to this bond, and metal atoms need not be trivalent. On the other hand, the electron transfer from metal atoms to the boron framework implies that not only strong covalent B-B bonding within the framework but also ionic interaction between metal atoms and the framework contribute to the YAlB14 phase stabilization.
REB66-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.
+ Number of B, Y and Mo or Pt atoms in the unit cell deduced from chemical composition, lattice constant and density (experiment).Composition a(nm) ρ(g/cm3) NB Ny NMo/Pt YB66 2.3440 2.52 1610 24.4 – YB61.754 2.3445 2.5687 1628 26.4 – YB62 2.34364 2.5662 1624 26.2 – YB56 2.34600 2.5927 1626 29.0 – YMo0.20B62.4 2.34258 2.64 1628 26.1 5.3 YPt0.091B63.5 2.34300 2.6344 1634 25.7 2.4 YPt0.096B63.3 2.34223 2.6355 1630 25.7 2.5 YPt0.14B62.0 2.34055 2.6762 1629 26.3 3.7
Another structure unit of YB66, shown in figure 4b, is B80 cluster of 80 boron sites formed by the B10 to B13 sites. All those 80 sites are partially occupied and in total contain only about 42 boron atoms. The B80 cluster is located at the body center of the octant of the unit cell, i.e., at the 8a position (1/4, 1/4, 1/4); thus, there are eight such clusters (336 boron atoms) per unit cell. Two independent structure analyses came to the same conclusion that the total number of boron atoms in the unit cell is 1584. The boron framework structure of YB66 is shown in figure 5a. To indicate relative orientations of the supericosahedra, a schematic drawing is shown in figure 5b, where the supericosahedra and the B80 clusters are depicted by light green and dark green spheres, respectively; at the top surface of the unit cell, the relative orientations of the supericosahedra are indicated by arrows. There are 48 yttrium sites ((0.0563, 1/4, 1/4) for YB62) in the unit cell. Richards and Kasper fixed the Y site occupancy to 0.5 that resulted in 24 Y atoms in the unit cell and the chemical composition of YB66. As shown in figure 6, Y sites form a pair separated by only 0.264 nm in YB62. This pair is aligned normal to the plane formed by four supericosahedra. The Y site occupancy 0.5 implies that the pair has always one Y atom with one empty site.
+x-coordinates and occupancies of the Y1 and Y2 sites.Atom x Occupancy Y1 0.0542(3) 0.437(9) Y2 0.0725(11) 0.110(12)