Allotropes of boron

Elemental boron can exist in several allotropes, the most common of which are crystalline boron and brown amorphous boron. Crystalline boron has four major polymorphs: α, β, γ and T. Whereas the β phase is most stable and others are metastable, the transformation rate is negligible at room temperature, and thus all those phases can exist at ambient conditions.

Crystalline boron is a very hard (Vickers hardness comparable to that of cubic boron nitride), black, diamagnetic material with a melting point of 2080 °C.^[1] Pure elemental boron is difficult to extract. The earliest methods involved reduction of boric oxide with metals such as magnesium or aluminum. However the product is almost always contaminated with metal borides. Pure boron can be prepared by reducing volatile boron halides with hydrogen at high temperatures.^[2][3] Very pure boron, for the use in semiconductor industry, is produced by the decomposition of diborane at high temperatures and then further purified with the zone melting or Czochralski processes.^[4] Even more difficult is to prepare pure single crystals of pure boron phases, because of polymorphism, reactivity of boron with impurities, etc.; typical crystal size is ~0.1 mm.^[5]

Contents 1 Summary of properties 2 α-rhombohedral boron 3 β-rhombohedral boron 4 γ-boron 5 Tetragonal boron phases 6 High-pressure superconducting phase 7 Amorphous boron 8 References

Summary of properties

Boron phase	α	β	γ	T
Symmetry	Rhombohedral	Rhombohedral	Orthorhombic	Tetragonal
Atoms/unit cell[6]	12	~105	28	192
Density (g/cm3)[7][8][5][9]	2.46	2.35	2.52	2.36
Vickers hardness (GPa)[10][11]	42	45	50–58
Bulk modulus (GPa)[11][12]	224	184	227
Bandgap (eV)[11][13]	2	1.6	2.1

α-rhombohedral boron

α-rhombohedral boron has a unit cell of twelve boron atoms. The structure consists of B₁₂ icosahedra in which each boron atom has five nearest neighbors within the icosahedron. If the bonding were the conventional covalent type then each boron would have donated 5 electrons. However, boron has only 3 valence electrons, and it is thought that the bonding in the B₁₂ icosahedra is achieved by the so-called 3-center electron-deficient bonds where the electron charge is accumulated at the center of a triangle formed by 3 adjacent atoms.^[12]

The isolated B₁₂ icosahedra are not stable; thus boron is not a molecular solid, but the icosahedra in it are connected by strong covalent bonds.

β-rhombohedral boron

β-rhombohedral boron has a subcell containing 105–108 atoms — or a unit cell of 320 atoms. Many atoms form B₁₂ icosahedra, but there are also a large number of non-icosahedral atoms as well. For long time, it was unclear whether the α or β phase is most stable at ambient conditions; however, gradually a consensus was reached that β phase as the thermodynamically stable allotrope.^[6][14][15]

γ-boron

The γ-phase can be described as a NaCl-type arrangement of two types of clusters, B₁₂ icosahedra and B₂ pairs.^[6] It can be produced by compressing other boron phases to 12–20 GPa, heating to 1500–1800 ⁰C and is quenchable to ambient conditions.^[6][7][11] There is evidence of significant charge transfer from B₂ pairs to the B₁₂ icosahedra in this structure;^[6] in particular, lattice dynamics suggests the presence of significant long-range electrostatic interactions.

This phase was reported by Wentorf in 1965,^[7][16] however neither structure nor chemical composition were established. The structure was solved using ab initio crystal structure prediction calculations^[6] and confirmed using single crystal X-ray diffraction.^[11]

Tetragonal boron phases

Two tetragonal phases have been reported, T-50 (or α-tetragonal boron)^[17] and T-192 (or ß-tetragonal boron) with 50 and 192 atoms in the unit cell, respectively. Whereas T-50 has been assigned to a compound (nitride (B₅₀N₂) or carbide (B₅₀C₂)),^[8] T-192 is a genuine pure boron phase. It was produced in 1960 by hydrogen reduction of BBr₃ on hot tungsten, rhenium or tantalum filaments at temperatures 1270–1550 °C (i.e. chemical vapor deposition).^[9] Further studies have reproduced the synthesis and confirmed the absence of impurities in this phase.^{[18][19][20][21]}

High-pressure superconducting phase

Compressing boron above 160 GPa produces a boron phase with an as yet unknown structure. Contrary to other phases, which are semiconductors, this phase is a metal and becomes a superconductor with a critical temperature increasing from 4 K at 160 GPa to 11 K at 250 GPa.^[22] This structural transformation occurs at pressures at which theory predicts the icosahedra to dissociate.^[23]

Amorphous boron

Amorphous boron contains B₁₂ regular icosahedra that are randomly bonded to each other without long range order.^[24][25] Pure amorphous boron can be produced by thermal decomposition of diborane at temperatures below 1000 °C. Annealing at 1000 °C converts amorphous boron to β-rhombohedral boron.^[26] Amorphous boron nanowires (30–60 nm thick)^[27] or fibers^[28] can be produced by magnetron sputtering and laser-assisted chemical vapor deposition, respectively; and they also convert to β-rhombohedral boron nanowires upon annealing at 1000 °C.^[27]

References