Type of Allotropes 

α-Boron (Rhombohedral)

It is a surprising fact that scientists found α-rhombohedral phase after they discovered the β-rhombohedral phase.

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citeID FrustBoron

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.

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citeID Strucboron
He, C., Zhong, J.X., Structures, stability, mechanical and electronic properties of α-boron and α*-boron. AIP Advances 2013,3, 042138. (https://doi.org/10.1063/1.4804138)

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.

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citeID 2DBoron

α-boron has band gap of 2.0eV and it is semi-conductor.

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citeID PreseBoron
Werheit, H., Present knowledge of electronic properties and charge transport of icosahedral boron-rich solids. Journal of Physics: Conference Series. 2009, 176(1). (https://doi.org/10.1088/1742-6596/176/1/012019)

Figure 3. a) & b) Rhombohedral crystal structure of α-boron. Figure created with VESTA

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citeID 2DBoron

. Structural information from ICSD

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citeID Revisit-alpha
Nishibori, E., et al., Revisit: High resolution charge density study of α-rhombohedral boron using third-generation SR data at SPring-8. Solid State Sciences, 2015, 47: p. 27-31 (https://doi-org.libproxy.aalto.fi/10.1016/j.solidstatesciences.2015.02.007)

.(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

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citeID CrysBoron
An, Q., Reddy, K.M., Xie, K.Y., Hemker, K.J., Goddard, W.A., New Ground-State Crystal Structure of Elemental Boron. Physical Review Letters 2016, 117, 1-16. (https://doi.org/10.1103/physrevlett.117.085501)

.The original β-B structure (called β-B105) was proposed in 1970 by Hoard.

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pages 268-277 citeID StrucBor
Hoard, J.L., et al., The structure analysis of β-rhombohedral boron. Journal of Solid State Chemistry, New York 14850 USA, 1970, 1(2). (https://doi.org/10.1016/0022-4596(70)90022-8)

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°

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citeID CrysBoron

. 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.

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citeID PreseBoron

Figure 4. Crystal structure of β-rhombohedral boron. Figure created with VESTA

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citeID FrustBor
Ogitsu, T et al., β-Rhombohedral Boron: At the Crossroads of the Chemistry of Boron and the Physics of Frustration. Chemical Reviews 2013,113, 3425–3449. (https://doi.org/10.1021/cr300356t)

using data from ICSD

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citeID StrucBor

. (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

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citeID HighPress
Oganov, A.R., Chen, J., Gatti, C., Ma, Y., Ma, Y., Glass, C.W., Liu, Z., Yu, T., Kurakevych, O.O., Solozhenko, V.L., Ionic high-pressure form of elemental boron. Nature 2009, 457, 863–867.. (https://doi.org/10.1038/nature07736)

. 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

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citeID 2DBoron

. 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.

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citeID HighPress

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.

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citeID BandgapBor
Chen, J., Liang, X.-., Yang, B., Girard, J., Drozd, V., & Liu, Z. Band Gap of Semiconducting High Pressure Phase of Boron, DEStech Transactions on Materials Science and Engineering, 2017,  176-177  (https://doi.org/10.12783/DTMSE%2FMSCE2016%2F10465)

Figure 5. Crystal structure of γ-Boron (Orthorhombic). Figure created with VESTA

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citeID JapPhaseBor
Shirai, K., Phase diagram of boron crystals. Japanese Journal of Applied Physics, 2017, 56, 01-04 05FA06. (https://doi.org/10.7567/jjap.56.05fa06)

using data from ICSD.

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citeID HighPhase
Yu Zarechnaya, E., Dubrovinsky, L., Dubrovinskaia, N., Miyajima, N., Filinchuk, Y., Chernyshov, D., Dmitriev, V., Synthesis of an orthorhombic high pressure boron phase. Science and Technology of Advanced Materials, 2008, 9, 1-3,044209. (https://doi.org/10.1088/1468-6996/9/4/044209)

(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.

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citeID FrustBor

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.

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citeID 2DBoron

 

Figure 6. Crystal structure of α-boron (tetragonal). Figure created with VESTA

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citeID 2DBoron

using data from ICSD.

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citeID StrucTetra
Hoard, J.L., Hughes, R.E., Sands, D.E., The Structure of Tetragonal Boron1. Journal of the American Chemical Society, 1958, 80, 4507–4515. (https://doi.org/10.1021/ja01550a019)

(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.

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citeID 2DBoron

Figure 7: β-Boron (tetragonal) crystal structure. Figure created with VESTA

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citeID 2DBoron

using data from ICSD.

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citeID CrysStruTeta
Vlasse, M., et al., Crystal structure of tetragonal boron related to α-AlB12. Journal of Solid State Chemistry, 1979. 28(3): p. 289-301. (https://doi-org.libproxy.aalto.fi/10.1016/0022-4596(79)90080-X)

 (Figure: Shadab Ishtiaq)

Figure 8.  β-Boron (tetragonal) crystal structure in (001) plane. Figure created with VESTA

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citeID 2DBoron

using data from ICSD.

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citeID CrysStruTeta

(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.

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citeID 2DBoron

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".

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citeID 2DBoron

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

References

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