Crystal structure of boron-rich metal borides

Their crystal structure and chemical bonding depend strongly on the metal element M and on its atomic ratio to boron.

In such borides, metal atoms donate electrons to the boron polyhedra, and thus these compounds are regarded as electron-deficient solids.

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.

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.

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.

The covalent bonding nature of metal boride compounds also give them their hardness and inert chemical reactivity property.

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.

[4][13] 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.

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.

[16] In addition to yttrium, a wide range of rare-earth elements from Nd to Lu, except for Eu, can form REB66 compounds.

Two independent structure analyses [19][22] came to the same conclusion that the total number of boron atoms in the unit cell is 1584.

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.

An unusual linkage is depicted in figure 8b, where two B12-I5 icosahedra connect via two B atoms of each icosahedron forming an imperfect square.

However, the bonding distances between the apex B atoms (0.1619 and 0.1674 nm) of neighboring I4 icosahedra are usual for the considered metal borides.

This structure is layered: as shown in figure 11b, B12 icosahedra and bridging carbons form a network plane that spreads parallel to the c-plane and stacks along the c-axis.

High-resolution transmission electron microscopy (HRTEM) lattice images of the latter three compounds, added to Fig.

Decreasing the number of the B6 octahedra diminishes the role of nitrogen because the C-B-C chains start bridging the icosahedra.

[33] Single-crystal structure analysis yielded trigonal symmetry for ScB15.5CN (space group P3m1 (No.164) with a = 0.5568(2) and c = 1.0756(2) nm), and the deduced atomic coordinates are summarized in table IVa.

Y, Ho, Er, Tm and Lu also form REB28.5C4 which has a trigonal crystal structure with space group R3m (No.

Initially these were described as ternary RE-B-Si compounds,[36][37][38] but later carbon was included to improve the structure description that resulted in a quaternary RE-B-C-Si composition.

Figure 15 shows a network of boron icosahedra that spreads parallel to the (001) plane, connecting with four neighbors through B1–B1 bonds.

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%.

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.

[7] Figures 22a and b present HRTEM lattice images and electron diffraction patterns taken along the [0001] and [1120] crystalline directions, respectively.

A small amount of Si was added into the floating zone crystal growth and thus this phase is a quaternary compound.

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.

[50] The diversity of the crystal structures of rare-earth borides results in unusual physical properties and potential applications in thermopower generation.

[51] Thermal conductivity of boron icosahedra based compounds is low because of their complex crystal structure; this property is favored for thermoelectric materials.

On the other hand, these compounds exhibit very low (variable range hopping type) p-type electrical conductivity.

Two single crystals of YB 66 (1 cm diameter) grown by floating zone technique using (100) oriented seeds. In the top crystal, the seed (left from the black line) has same diameter as the crystal. In the bottom crystal (sliced), the seed is much thinner and is on the right side.
Fig. 1 . (a) B 6 octahedron , (b) B 12 cuboctahedron and (c) B 12 icosahedron .
Fig. 2 . Relationship between the ionic radius of trivalent rare-earth ion and chemical composition of icosahedron-based rare-earth borides.
Fig. 3 . Crystal structure of YAlB 14 . Black and blue spheres indicate Y and Al atoms, respectively. Vacancies at the Y and Al sites are ignored. [ 17 ]
Fig. 5a The boron framework of YB 66 viewed along the z -axis. [ 22 ]
Fig. 14 . Crystal structure of RE x B 12 C 0.33 Si 3.0 (RE=Y or Dy) viewed along the direction close to [100]. Red, black and blue spheres correspond to Y/Dy, C and Si atoms, respectively. Vacancies at the Y/Dy site are ignored. [ 35 ]
Fig. 15 . A network of boron icosahedra lying in the (001) plane. Black, blue and red spheres correspond to C, Si and Y atoms, respectively. [ 39 ]
Fig. 17 . The boron-rich corner of the Sc-B-C phase diagram. [ 40 ] [ 41 ]
Fig. 20 . ScB 17 C 0.25 crystal structure viewed along the a -axis. The icosahedron layers alternatively stack along the c -axis in the order I1–I2–I1–I2–I1. [ 47 ]
Fig. 23 . B 10 polyhedron in the Sc 0.83–x B 10.0–y C 0.17+y Si 0.083–z crystal structure. [ 48 ]
Fig. 25 . Boron framework structure of Sc 0.83–x B 10.0–y C 0.17+y Si 0.083–z depicted by supertetrahedra T(1) and T(2), superoctahedron O(1) and the superoctahedron based on B 10 polyhedron. Vertexes of each superpolyhedron are adjusted to the center of the constituent icosahedra, thus the real volumes of these superpolyhedra are larger than appear in the picture. [ 48 ]
Fig. 29 . Boron framework structure of Sc 3.67–x B 41.4–y–z C 0.67+z Si 0.33–w viewed along the c -axis. [ 50 ]