text: Compounds that were historically given the formulae REAlB and REB have the MgAlB 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 REB. Both metal sites of REAlB structure have partial occupancies of about 60–70%, which shows that the compounds are actually non-stoichiometric. The REB formula merely reflects the average atomic ratio [B]/[RE] = 25. Yttrium borides form both YAlB and YB structures. Experiments have confirmed that the borides based on rare-earth elements from Tb to Lu can have the REAlB structure. A subset of these borides, which contains rare-earth elements from Gd to Er, can also crystallize in the REB structure.
  Korsukova et al. analyzed the YAlB 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 YAlB 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; B clusters are depicted as the green icosahedra. Boron framework of YAlB 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 B 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 B 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 YAlB needs donation of four electrons from metal elements: two electrons for a B icosahedron and one electron for each of the two bridging boron atoms – to support their tetrahedral coordination. The actual chemical composition of YAlB, determined by the structure analysis, is YAlB 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 YAlB phase stabilization.