text: In addition to yttrium, a wide range of rare-earth elements from Nd to Lu, except for Eu, can form REB compounds. Seybolt discovered the compound YB in 1960  and its structure was solved by Richards and Kasper in 1969. They reported that YB 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 (B)B 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 YB. 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.
  Another structure unit of YB, shown in figure 4b, is B 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 B 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 YB 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 B 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 YB) 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 YB. As shown in figure 6, Y sites form a pair separated by only 0.264 nm in YB. 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.
  Slack et al. reported that the total number of boron atoms in the unit cell, calculated from the measured values of density, chemical composition and lattice constant, is 1628 ± 4, which is larger than the value 1584 obtained from the structural analysis. The number of B atoms in the unit cell remains nearly constant when the chemical composition changes from YB to YB. On the other hand, the total number of yttrium atoms per unit cell varies, and it is, for example, ~26.3 for YB (see right table). If the total number of Y atoms stays below or equal to 24 then it is possible that one Y atom accommodates in each Y pair (partial occupancy). However, the experimental value of 26.3 significantly exceeds 24, and thus both pair sites might be occupied. In this case, because of the small separation between the two Y atoms, they must be repelled by the Coulomb force. To clarify this point, split Y sites were introduced in the structure analysis resulting in a better agreement with the experiment. The Y site distances and occupancies are presented in the left table.
  There are twenty Y pair sites with one Y atom and three pairs with two Y atoms; there is also one empty Y pair (partial occupancy = 0). The separation 0.340 nm for the Y2 pair site (two Y atoms in the pair site) is much larger than the separation 0.254 nm for the Y1 pair site (one Y atom in the pair site), as expected. The total number of Y atoms in the unit cell is 26.3, exactly as measured. Both cases are compared in figure 7. The larger separation for the Y2 pair site is clear as compared with that for the Y1 pair site. In case of the Y2 pair, some neighboring boron sites that belong to the B cluster must be unoccupied because they are too close to the Y2 site.
  Splitting the Y site yields right number of Y atoms in the unit cell, but not B atoms. Not only the occupation of the B sites in the B cluster must be strongly dependent on whether or not the Y site is the Y1 state or the Y2 state, but also the position of the occupied B sites must be affected by the state of the Y site. Atomic coordinates and site occupancies are summarized in table II.