Crystal structure of boron-rich metal borides

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.^[1] 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, REB₄₁Si_1.2, B₄C and other, more complex types such as RE_xB₁₂C_0.33Si_3.0. 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.