Introduction

Boron (B) is a element belonging to group 13 in the perodic table (Figure 2). At the moment, there are total of five allotropes, including three that are classified as members of the boron allotropes: α- and β-rhombohedral (R), and γ-orthorhombic (O). However, there is currently debate going on regarding the classification of the remaining two allotropes, α- and β-tetragonal (T) and their properties are less known. Despite significant efforts in both experimental and theoretical research to understand the structure and characteristics of boron allotropes, their exact allotropes are yet to be determined. This is due to the fact that many boron allotropes possess complicated structures, and some are slightly distinct from others or stabilized by trace amounts of impurities, making them impure boron allotropes. In the table 2 below list of allotropes is given which are discussed further in detail. Stability of these structures varies, at normal conditions, β-rhombohedral boron remains stable over a wide range of temperatures. α-rhombohedral boron, and β-tetragonal boron, are stable at different temperatures but only at high pressure. As pressure increases further, γ-orthorhombic boron becomes stable. Boron also exist in various 1D (one-dimension) like nano tubes and 2D (two-dimensional) forms such as layer structure known as boraphenes.[1, p.1-160]

The study of boron and its compounds have been studied by both theoretical and computational methods. Through molecular orbital calculations, scientists have been able to discover important concepts in boron chemistry, such as the peculiar molecular structure of diborane and the charge state of [B12H12]2–. These concepts rely on the formation of three-center, two-electron (3c-2e) bonds and slightly electron deficient boron icosahedra, respectively. By understanding these concepts, we can better understand the different allotropes boron shows.[2]

Figure 1. Boron 99.7% purity (Figure: W. Oelen, via Wikimedia Commons. License: CC BY-SA)


Figure. 2 Boron is considered a metalloid and it is also the lightest element among other elements of group 13. It has different behaviour as compare to the neighbouring elements, as it has very high ionisation potential.[3] (Figure: Shadab Ishtiaq)

Table 1. Basic properties of boron [4][5]

Electron configuration 1s22s22p1
Atomic number5
Atomic weight

10.81

Melting Point

2200 °C 

Boiling point2550 °C
Typical oxidation state+3 

Table 2. Allotropes of Boron [6]

Type of Allotropes Space group
1. α-Boron (Rhombohedral)R-3m
2. β-Boron (Rhombohedral)R-3m
3. γ-Boron (Orthorhombic)Pnnm
4. α-Boron (Tetragonal)P42/nnm
5. β-Boron (Tetragonal)P43

Type of Allotropes 

α-Boron (Rhombohedral)

It is a surprising fact that scientists found α-rhombohedral phase after they discovered the β-rhombohedral phase.[2] Boron atoms have a tendency to form icosahedral B12 clusters and prefer this type of arrangement in its elemental crystals. These clusters are made up of boron atoms that are connected to five neighboring boron atoms through intra-B12 B-B bonds. In the case of α-boron, these icosahedral B12 clusters are connected to 12 equivalent neighboring clusters through inter-B12 B-B bonds.[7]

The rhombohedral crystal structure has one B12 icosahedron at the vertex, and its threefold symmetry axis faces the direction of the rhombohedral body diagonal. The B12 icosahedron is slightly distorted and is linked by a B-B bond between the B atoms at the vertex, but the direction of the B-B bond between B12 is slightly shifted from the edge of the rhombohedron. The lattice constant of this crystal is a = 5.074 Å and α = 58.0 degree, and the unit cell contains twelve B atoms. There is one polar atom that connects B12 with a two-center covalent bond, and the remaining B atoms form a zigzag regular hexagon in the plane perpendicular to the threefold symmetry axis, called equatorial atoms. The average length of the B-B bond in B12 is 1.79 Å, while the B-B bond length between B12 is shorter at 1.64 Å, making it difficult to consider it just as a B12 icosahedron bond. This crystal also has a large void in the center of the rhombohedron.[1] α-boron has band gap of 2.0eV and it is semi-conductor.[8]

Figure 3. a) & b) Rhombohedral crystal structure of α-boron. Figure created with VESTA[1]. Structural information from ICSD[9].(Figure: Shadab Ishtiaq)

β-Boron (Rhombohedral)

Scientists have thought for a long time that the β rhombohedral boron structure (β-B105) is the most stable form of boron at low pressures, but recent studies in quantum mechanics have shown that when certain specific partial occupation sites are chosen for β-B105, and taking into account zero point motion, it could lead to a more stable energy level for β-B105 than the α-B12 structure, even under normal conditions[10].The original β-B structure (called β-B105) was proposed in 1970 by Hoard.[11, p.268-277]

β rhombohedral boron has 105 atoms, with 15 boron positions (B1 to B15) in the unit cell. The structure consists of 8 clusters at the vertices and 12 clusters at the edges of an icosahedron in a rhombohedral unit cell. Additionally, there is a single B15 atom located in the cell center, which connects to two B28 units through B13 sites. The quantum mechanics predicted structure of β-B105 has lattice parameters of a = 10.11 Å and α = 65.4°, which match closely with the experimental values of a = 10.14 Å and α = 65.2° [10]. Through experiments the band gap of β-rhombohedral boron found to be approximately 1.5 eV which differes from 2.0 eV theoretical value and properties are similar to semiconductors. [8]


Figure 4. Crystal structure of β-rhombohedral boron. Figure created with VESTA[12] using data from ICSD [11]. (Figure: Shadab Ishtiaq)


γ-Boron (Orthorhombic)

 γ-Boron (O) remains in a solid form even when subjected to high pressure ranging from 19 to 89 (GPa), and it can be cooled down rapidly to normal conditions [13]. The arrangement of atoms in the material is organized into Pnnm space group, and each unit cell contains 28 atoms. The atoms are made up of icosahedral B12 clusters and B2 dumbbells, which are arranged in a pattern similar to NaCl [1]. The arrangement of atoms in the material was discovered using a technique X-ray diffraction experiment (XRD). The material is made up of two clusters, B12 and B2, which have a transfer of electrical charge between them. This means that γ-B28 can be considered as a type of boron boride, with B12 having a negative charge (δ-) and B2 having a positive charge (δ+). The phase is a type of high-pressure form of boron atoms, arranged in an ionic pattern. [13] γ-Boron has indirect band gap of 1.7 eV and at a high pressure of 200 GPa, the γ-B28 phase maintains a band gap of 1.25 eV.[14]

Figure 5. Crystal structure of γ-Boron (Orthorhombic). Figure created with VESTA[15]using data from ICSD.[16] (Figure: Shadab Ishtiaq)


α-Boron (Tetragonal)

The α-tetragonal boron's first crystal was first discovered in 1951, which was called T-50 because of its tetragonal unit cell containing 50 atoms. In 1955, it was estimated through molecular orbital theory that the B12H12 cluster's electron requirements were not met in the T-50 structure, as it was 10 electrons short of filling all bonding orbitals or valence bands. This suggests that a pure version of T-50 would not be stable.[12] So this structure is closely related to the boron, but it is not entirely pure boron. It contains four sets of B12 and two individual B atoms in each unit cell, making a total of 50 boron atoms. The lattice constants are a = 8.75 Å and c = 5.06 Å. Additionally, there are two C or N atoms situated along the c-axis, where the B atoms are arranged. The total number of atoms in a unit cell is 52. Pure boron nano-belts with the crystal structure (50 per unit cell) has a lower surface energy than other structures. [1] 


Figure 6. Crystal structure of α-boron (tetragonal). Figure created with VESTA[1] using data from ICSD.[17] (Figure: Shadab Ishtiaq)


β-Boron (Tetragonal)

β-Boron has a complex structure made up of a two-center or three-center covalent bond, where two or three B atoms share two electrons each. The unit cell contains 190 B atoms with lattice constants of a = 10.14 Å and c = 14.17 Å. The structure includes four chain structures of B12 icosahedra arranged perpendicular to the c-axis, increasing in height by 0.25c perpendicular to each other, and two single atoms per unit cell on a plane perpendicular to the c-axis. There are eight B12 icosahedra in total, with two for each chain per unit cell. The B21 structure, in which two B12 clusters are joined together by sharing a triangular surface, places its center in the void near specific coordinates.[1]


Figure 7: β-Boron (tetragonal) crystal structure. Figure created with VESTA[1] using data from ICSD.[18] (Figure: Shadab Ishtiaq)

Figure 8.  β-Boron (tetragonal) crystal structure in (001) plane. Figure created with VESTA[1] using data from ICSD.[18] (Figure: Shadab Ishtiaq)


One-Dimensional Boron Nanostructures

One-dimensional (1D) boron nanostructures have caught the interest of researchers because they could be useful in making very small electronic devices and sensors. Different kinds of 1D boron structures like nanobelts, nanotubes, and nanocones have been made using various methods, but they are still not very well understood and are difficult for researchers to study compared to other boron materials. Boron nanotubes can act as either metals or semiconductors depending on their size and shape. The type of boron nanotube, whether it has a zigzag, armchair, or chiral structure, also affects its behavior. Boron nanotubes with larger diameters, over 17 Å, always behave like metals.[1]


Two-Dimensional Boron

Scientists have found that boron crystals have many different ways of bonding, and there are many different types of boron structures. This is different from carbon, which mainly forms either graphite or diamonds through a specific type of bonding. Researchers have studied two-dimensional forms of boron using calculations and studying how boron atoms bond together. Crystal structure of β12 borophene or metal borides such as ZrB2 and MgB2, contain boron sheets, including the outermost layer, that resemble a graphitic structure. These boron sheets are referred to as "boraphene" and they are similar to graphene, which is a two-dimensional carbon material with a hexagonal lattice structure. In 2014, a 2D cluster of 36 boron atoms was discovered and named B36 "borophene".[1]

Figure 9. 2D (boron) crystal structure of β12 borophene prepared experimentally. (Figure from Wikimedia under the Creative Common License)

References

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