Allotropes of boron

Short description: Different forms of boron

Amorphous powder boron Boron (likely mixed allotropes)

Boron can be prepared in several crystalline and amorphous forms. Well known crystalline forms are α-rhombohedral (α-R), β-rhombohedral (β-R), and β-tetragonal (β-T). In special circumstances, boron can also be synthesized in the form of its α-tetragonal (α-T) and γ-orthorhombic (γ) allotropes. Two amorphous forms, one a finely divided powder and the other a glassy solid, are also known.[1][2] Although at least 14 more allotropes have been reported, these other forms are based on tenuous evidence or have not been experimentally confirmed, or are thought to represent mixed allotropes, or boron frameworks stabilized by impurities.[3][2][4][5] Whereas the β-rhombohedral phase is the most stable and the others are metastable, the transformation rate is negligible at room temperature, and thus all five phases can exist at ambient conditions. Amorphous powder boron and polycrystalline β-rhombohedral boron are the most common forms. The latter allotrope is a very hard[n 1] grey material, about ten percent lighter than aluminium and with a melting point (2080 °C) several hundred degrees higher than that of steel.[6]

Elemental boron has been found in star dust and meteorites, but does not exist in the high oxygen environment of Earth. It is difficult to extract from its compounds. The earliest methods involved reduction of boric oxide with metals such as magnesium or aluminium. 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.[7][8] Very pure boron, for use in the semiconductor industry, is produced by the decomposition of diborane at high temperatures, followed by purification via zone melting or the Czochralski process.[9] Even more difficult to prepare are single crystals of pure boron phases, due to polymorphism and the tendency of boron to react with impurities; typical crystal size is ~0.1 mm.[10]

## Contents

* 1 Summary of properties
* 2 α-rhombohedral boron
* 3 α-tetragonal boron
* 4 β-rhombohedral boron
* 5 β-tetragonal boron
* 6 γ-boron
* 7 Cubic boron
* 8 High-pressure superconducting phase
* 9 Borophene
* 10 Borospherene
* 11 Amorphous boron
* 12 Notes
* 13 References
* 14 Bibliography
* 15 External links

## Summary of properties

Boron phase  | α-R  | α-T  | β-R  | β-T  | γ  | amorphous

|
|
|
|
|
|

Powder

Glassy

Symmetry  | Rhombohedral  | Tetragonal | Rhombohedral  | Tetragonal  | Orthorhombic | Semi-
random  | Semi-
random
25px  | 25px  | 25px  | 25px  | 25px
Occurrence  | common  | special  | common  | common  | special  |  |
Atoms/unit cell[11] | 12  | 50  | 105‒108  | 192  | 28  |  |
Density (g/cm3)[1] | 2.46  | 2.29‒2.39[12] | 2.35  | 2.36  | 2.52  | 1.73  | 2.34–35
Vickers hardness[13][14] | 42 GPa  |  | 45 GPa  |  | 50–58 GPa  |  |
Bulk modulus[14][15] | 224 GPa  |  | 184 GPa  |  | 227 GPa  |  |
Band gap (eV)  | 2[16] | 1.55[17] | 1.6[18] | 1.16[19] | 2.1[14] | 0.56–0.71[20] |
Color  | Crystals are
clear red  | Black and
opaque, with
metallic lustre  | Dark to shiny
silver-grey  | Black/red  | Dark grey  | Black to
brown  | Opaque
black
Source  | [21] | [22] | [1][2] | [n 2][23] | [n 3] | [24] | [1]
Year first reported[25] | 1958  | 1943/1973[n 4] | 1957  | 1960  | 2009[26] | 1808  | 1911[27][28]

* An extract of a phase diagram for boron (α and β are the rhombohedral phases; T is β-tetragonal)[11][n 5]

* Structure of α-R boron

* Structure of β-R boron

* Structure of γ-boron

## 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 five electrons. However, boron has only three 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 three adjacent atoms.[15]

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

## α-tetragonal boron

Pure α-tetragonal can only be synthesized as thin layers deposited on an underlying substrate of isotropic boron carbide (B50C2) or nitride (B50N2).[1] Most examples of α-tetragonal boron[29] are in fact boron-rich carbide or nitrides.[30][31]

## β-rhombohedral boron

β-rhombohedral boron has a unit cell containing 105–108 (ideally exactly 105) atoms. Most atoms form B12 discrete icosahedra; a few form partially interpenetrating icosahedra, and there are two deltahedral B10 units, and a single central B atom.[32] For a long time, it was unclear whether the α or β phase is most stable at ambient conditions; however, gradually a consensus was reached that the β phase is the most thermodynamically stable allotrope. It exhibits a Mohs hardness of 9.5, and is one of the hardest pure elements, only surpassed by carbon (as diamond).[11][33][34][35][36][37]

## β-tetragonal boron

The β phase 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).[38] Further studies have reproduced the synthesis and confirmed the absence of impurities in this phase.[39][40][41][42]

## γ-boron

γ-boron: Comparison of X-ray diffraction data of Wentorf[43] (bottom) with the modern data[11]

The γ-phase can be described as a NaCl-type arrangement of two types of clusters, B12 icosahedra and B2 pairs. It can be produced by compressing other boron phases to 12–20 GPa and heating to 1500–1800 °C, and remains stable at ambient conditions.[11][14] There is evidence of significant charge transfer from B2 pairs to the B12 icosahedra in this structure;[11] in particular, lattice dynamics suggests the presence of significant long-range electrostatic interactions.

This phase was reported by Wentorf in 1965;[43][44] however, neither structure nor chemical composition were established. The structure was solved using ab initio crystal structure prediction calculations[11] and confirmed using single crystal X-ray diffraction.[14]

## Cubic boron

Sullenger et al. (1969)[39] and McConville et al. (1976)[45] reported a cubic allotrope of boron, obtained in argon plasma experiments, with a unit cell of 1705±3 atoms and a density of 2.367 g/cm3. While this allotrope is occasionally mentioned in the literature,[46] no subsequent work appears to have been published either confirming or discrediting its existence. Donohue (1982) commented[47] that the number of atoms in the unit cell did not appear to be icosahedrally related (the icosahedron being a motif common to boron structures).

## 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 6 K at 160 GPa to 11 K at 250 GPa.[48] This structural transformation occurs at pressures at which theory predicts the icosahedra will dissociate.[49] Speculation as to the structure of this phase has included face-centred cubic (analogous to Al); α-Ga, and body-centred tetragonal (analogous to In).[50] It has also been suggested that the nonmetal-metal transition is simply the result of a band gap closure, as occurs with iodine, rather than a structural transition.[51]

## Borophene

Main article: Chemistry:Borophene

There exist several two-dimensional forms of boron (together called borophenes), and even more are predicted theoretically.[52]

## Borospherene

The discovery of the quasispherical allotropic molecule borospherene (B40) was announced in July 2014.[53]

## Amorphous boron

Amorphous boron contains B12 regular icosahedra that are randomly bonded to each other without long range order.[54] 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.[55] Amorphous boron nanowires (30–60 nm thick)[56] or fibers[57] 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.[56]

## Notes

1. ↑ Vickers hardness comparable to that of cubic boron nitride
2. ↑ Black when viewed by reflected light; red by transmitted light
3. ↑ High purity amorphous boron powder is black whereas impure samples have a brown appearance: Lidin R. A. (1996). Inorganic substances handbook. New York: Begell House. p. 22; Zenkov, V. S. (2006). "Adsorption-chemical activity of finely-dispersed amorphous powders of brown and black boron used in synthesizing metal borides". Powder Metallurgy and Metal Ceramics 45 (5–6): 279–282 (279). doi:10.1007/s11106-006-0076-z. ; Loryan, V. E.; Borovinskaya, I. P.; Merzhanov, A. G. (2011). "On combustion of boron in nitrogen gas". International Journal of Self-Propagating High-Temperature Synthesis 20 (3): 153–155. doi:10.3103/S106138621103006X. ; Kanel, G. I.; Utkin, A. V.; Razorenov, S. V. (2009). "Rate of the energy release in high explosives containing nano-size boron particles". Central European Journal of Energetic Materials 6 (1): 15–30 (18). http://www.wydawnictwa.ipo.waw.pl/cejem/vol-6-1-2009/Kanel.pdf.
4. ↑ 1943 was when the supposed structure was first reported; 1973 was when it was first reported that pure α-tetragonal boron can only be synthesized as thin layers deposited on an underlying substrate of isotropic boron carbide or nitride: Kunzmann, P. M. (1973). Structural studies on the crystal chemistry of icosahedral boron framework structure derivatives. PhD thesis. Cornell University; Amberger, E. (1981). "Elemental boron". In Buschbeck, K. C.. Gmelin handbook of inorganic and organometallic chemistry: B Boron, Supplement 2 (8th ed.). Berlin: Springer-Verlag. pp. 1–112 (60–61). ISBN 3-540-93448-0.
5. ↑ Other (different) phase diagrams have been reported:, Shirai, K. (2010). "Electronic structures and mechanical properties of boron and boron-rich crystals (part 2)". Journal of Superhard Materials 2 (5): 336–345 (337). doi:10.3103/S1063457610050059. http://dspace.nbuv.gov.ua/handle/123456789/63488. ; Parakhonskiy, G.; Dubrovinskaia, N.; Bykova, E.; Wirth, R.; Dubrovinsky, L. (2011). "Experimental pressure-temperature phase diagram of boron: resolving the long-standing enigma". Scientific Reports 1 (96): 1–7 (2). doi:10.1038/srep00096. PMID 22355614. Bibcode: 2011NatSR...1E..96P.

## References

1. ↑ 1.0 1.1 1.2 1.3 1.4 Wiberg 2001, p. 930.
2. ↑ 2.0 2.1 2.2 Housecroft & Sharpe 2008, p. 331.
3. ↑ Donohue 1982, p. 48.
4. ↑ Lundström, T. (2009). "The solubility in the various modifications of boron". in Zuckerman, J. J.; Hagen, A. P.. Inorganic reactions and methods. Vol. 13: The formation of bonds to group-I, -II, and -IIIB elements. New York: John Wiley & Sons. pp. 196–97. ISBN 978-0-470-14549-4.
5. ↑ Oganov et al. 2009, p. 863.
6. ↑ Lide, D. R., ed (2003). "Section 4, Properties of the Elements and Inorganic Compounds; Melting, boiling, and critical temperatures of the elements". CRC Handbook of Chemistry and Physics, 84th Edition. Boca Raton, Florida: CRC Press.
7. ↑ Stern, D. R.; Lynds, Lahmer (1958). "High-Purity Crystalline Boron". Journal of the Electrochemical Society 105 (11): 676. doi:10.1149/1.2428689.
8. ↑ Laubengayer, A. W.; Hurd, D. T.; Newkirk, A. E.; Hoard, J. L. (1943). "Boron. I. Preparation and properties of pure crystalline boron". Journal of the American Chemical Society 65 (10): 1924. doi:10.1021/ja01250a036.
9. ↑ Berger, L. I. (1996). Semiconductor materials. CRC Press. pp. 37–43. ISBN 0-8493-8912-7. https://archive.org/details/semiconductormat0000berg.
10. ↑ Will & Kiefer 2001.
11. ↑ 11.0 11.1 11.2 11.3 11.4 11.5 11.6 Oganov et al. 2009.
12. ↑ Amberger 1981, p. 60.
13. ↑ Solozhenko, V. L.; Kurakevych, O. O.; Oganov, A. R. (2008). "On the hardness of a new boron phase, orthorhombic γ-B28". Journal of Superhard Materials 30 (6): 428–429. doi:10.3103/S1063457608060117.
14. ↑ 14.0 14.1 14.2 14.3 14.4 Zarechnaya et al. 2009.
15. ↑ 15.0 15.1 Nelmes et al. 1993.
16. ↑ Madelung 1983, p. 10.
17. ↑ Uemura, Naoki; Shirai, Koun; Eckert, Hagen; Kunstmann, Jens (2016). "Structure, nonstoichiometry, and geometrical frustration of α-tetragonal boron". Physical Review B 93. doi:10.1103/PhysRevB.93.104101.
18. ↑ Madelung 1983, p. 11.
19. ↑ Hayami, Wataru (2015). "Structural stability and electronic properties of β-tetragonal boron: A first-principles study". Journal of Solid State Chemistry 221: 378–383. doi:10.1016/j.jssc.2014.10.012.
20. ↑ Madelung 1983, p. 12.
21. ↑ Donohue 1982, p. 57.
22. ↑ Hoard, J. L.; Hughes, R. E. (1967). "Chapter 2: Elementary boron and compounds of high boron content: Structure, properties and polymorphism". in Muetterties, E. L.. The chemistry of boron and its compounds. New York: John Wiley & Sons. pp. 25–154 (29, 82).
23. ↑ Donohue 1982, p. 78.
24. ↑ Oganov et al. 2009, pp. 863–64.
25. ↑ Donohue 1982, pp. 48, 57, 61.
26. ↑ γ-Boron was previously obtained in 1965, but its structure was not determined (see below).
27. ↑ Weintraub, E. (1911). "On the properties and preparation of the element boron". The Journal of Industrial and Engineering Chemistry 3 (5): 299–301 (299). doi:10.1021/ie50029a007. https://zenodo.org/record/1428712. "Both in appearance and in its curved conchoidal fracture the lump and the broken-up pieces most nearly resemble black diamond ... with an amorphous structure.".
28. ↑ Laubengayer, A. W.; Brandaur, A. E.; Brandaur, R. L. (1942). "Progress in the preparation and determination of the properties of boron". Journal of Chemical Education 19 (8): 382–85. doi:10.1021/ed019p382. Bibcode: 1942JChEd..19..382L. "Boron ... shows a considerable tendency to assume the vitreous condition ... Volatile compounds of boron such as the halides and the hydrides have been decomposed by passing their vapors through an arc or by bringing them in contact with a hot surface or filament. Boron of high purity is reported procurable by this method, but it is either a very fine powder or of vitreous structure.".
29. ↑ Hoard, J. L.; Hughes, R. E.; Sands, D. E. (1958). "The Structure of Tetragonal Boron". Journal of the American Chemical Society 80 (17): 4507. doi:10.1021/ja01550a019.
30. ↑ Hoard et al. 1970.
31. ↑ Amberger 1981, p. 61.
32. ↑ Wiberg 2001, p. 931.
33. ↑ Jemmis, E.D.; Balakrishnarajan, M.M.; Pancharatna, P.D. (2001). "A Unifying Electron-Counting Rule for Macropolyhedral Boranes, Metallaboranes, and Metallocenes". J. Am. Chem. Soc. 123 (18): 4313–4323. doi:10.1021/ja003233z. PMID 11457198.
34. ↑ Prasad, D.L.V.K.; Balakrishnarajan, M.M.; Jemmis, E.D. (2005). "Electronic structure and bonding of β-rhombohedral boron using cluster fragment approach". Phys. Rev. B 72 (19). doi:10.1103/PhysRevB.72.195102. Bibcode: 2005PhRvB..72s5102P.
35. ↑ van Setten M.J.; Uijttewaal M.A.; de Wijs G.A.; de Groot R.A. (2007). "Thermodynamic stability of boron: The role of defects and zero point motion". J. Am. Chem. Soc. 129 (9): 2458–2465. doi:10.1021/ja0631246. PMID 17295480. https://pure.rug.nl/ws/files/2796591/2007JAmChemSocvSetten.pdf. Retrieved 2019-12-01.
36. ↑ Widom M.; Mihalkovic M. (2008). "Symmetry-broken crystal structure of elemental boron at low temperature". Phys. Rev. B 77 (6). doi:10.1103/PhysRevB.77.064113. Bibcode: 2008PhRvB..77f4113W.
37. ↑ Kirk-Othmer, ed (2001-01-26) (in en). Kirk-Othmer Encyclopedia of Chemical Technology (1 ed.). Wiley. doi:10.1002/0471238961.0215181510011419.a01.pub2. ISBN 978-0-471-48494-3. https://onlinelibrary.wiley.com/doi/book/10.1002/0471238961.
38. ↑ Talley, La Placa & Post 1960.
39. ↑ 39.0 39.1 Sullenger et al. 1969.
40. ↑ Amberger, E.; Ploog, K. (1971). "Bildung der gitter des reinen bors". J. Less-Common Met. 23: 21. doi:10.1016/0022-5088(71)90004-X.
41. ↑ Ploog, K.; Amberger, E. (1971). "Kohlenstoff-induzierte gitter beim bor: I-tetragonales (B12)4B2C und (B12)4B2C2". J. Less-Common Met. 23: 33. doi:10.1016/0022-5088(71)90005-1.
42. ↑ Vlasse, M.; Naslain, R.; Kasper, J. S.; Ploog, K. (1979). "Crystal structure of tetragonal boron related to α-AlB12". Journal of Solid State Chemistry 28 (3): 289. doi:10.1016/0022-4596(79)90080-X. Bibcode: 1979JSSCh..28..289V.
43. ↑ 43.0 43.1 Wentorf 1965.
44. ↑ Zarechnaya, E. Y.; Dubrovinsky, L.; Dubrovinskaia, N.; Miyajima, N.; Filinchuk, Y.; Chernyshov, D.; Dmitriev, V. (2008). "Synthesis of an orthorhombic high pressure boron phase". Science and Technology of Advanced Materials 9 (4): 044209‒12. doi:10.1088/1468-6996/9/4/044209. PMID 27878026. Bibcode: 2008STAdM...9d4209Z.
45. ↑ McConville, G. T.; Sullenger, D. B.; Zielinski, R. E.; Gubser, D. U.; Sands, D. E.; Cantrell, J. S. (1976). "Some physical properties of cubic boron". Physics Letters A 58 (4): 257‒259. doi:10.1016/0375-9601(76)90091-8. Bibcode: 1976PhLA...58..257M.
46. ↑ Amberger 1981, pp. 21, 27, 74.
47. ↑ Donohue 1982, p. 80.
48. ↑ Eremets, M. I. (2001). "Superconductivity in Boron". Science 293 (5528): 272–4. doi:10.1126/science.1062286. PMID 11452118. Bibcode: 2001Sci...293..272E.
49. ↑ Mailhiot, C.; Grant, J. B.; McMahan, A. K. (1990). "High-pressure metallic phases of boron". Phys. Rev. B 42 (14): 9033–9039. doi:10.1103/PhysRevB.42.9033. PMID 9995117. Bibcode: 1990PhRvB..42.9033M. https://zenodo.org/record/1233721.
50. ↑ Polian, A.; Ovsyannikov, S. V.; Gauthier, M.; Munsch, M.; Chervin, J-C; Lemarchand, G. (2010). "Boron and boron-rich solids at high pressures". in Boldyreva, E; Dera, P.. High-pressure crystallography: From fundamental phenomena to technological applications: Proceedings of the NATO Advanced Study Institute on High-Pressure Crystallography: Advanced Armor Materials and Protection from Explosives, Erice, Italy, 4‒14 June 2009. Dordrecht: Springer Science+Business Media. pp. 241‒250 (242). ISBN 978-90-481-9257-1.
51. ↑ Zhao, J.; Lu, J. P. (2002). "Pressure-induced metallization in solid boron". Physical Review B 66 (9): 092101 to 092105. doi:10.1103/PhysRevB.66.092101. Bibcode: 2002PhRvB..66i2101Z.
52. ↑ Mannix, A. J.; Zhou, X.-F.; Kiraly, B.; Wood, J. D.; Alducin, D.; Myers, B. D.; Liu, X.; Fisher, B. L. et al. (2015). "Synthesis of borophenes: Anisotropic, two-dimensional boron polymorphs" (in en). Science 350 (6267): 1513–1516. doi:10.1126/science.aad1080. PMID 26680195. Bibcode: 2015Sci...350.1513M.
53. ↑ Zhai, Hua-Jin; Zhao, Ya-Fan; Li, Wei-Li; Chen, Qiang; Bai, Hui; Hu, Han-Shi; Piazza, Zachary A.; Tian, Wen-Juan et al. (2014-07-13). "Observation of an all-boron fullerene". Nature Chemistry advance online publication (8): 727–731. doi:10.1038/nchem.1999. ISSN 1755-4349. PMID 25054944. Bibcode: 2014NatCh...6..727Z.
54. ↑ Delaplane, R. G.; Dahlborg, U.; Howells, W. S.; Lundström, T. (1988). "A neutron diffraction study of amorphous boron using a pulsed source". Journal of Non-Crystalline Solids 106 (1–3): 66–69. doi:10.1016/0022-3093(88)90229-3. Bibcode: 1988JNCS..106...66D.
55. ↑ Gillespie, J. S. Jr. (1966). "Crystallization of Massive Amorphous Boron". J. Am. Chem. Soc. 88 (11): 2423. doi:10.1021/ja00963a011.
56. ↑ 56.0 56.1 Wang & Duan 2003.
57. ↑ Johansson, S. (1992). "Microfabrication of three-dimensional boron structures by laser chemical processing". J. Appl. Phys. 72 (12): 5956. doi:10.1063/1.351904. Bibcode: 1992JAP....72.5956J.

## Bibliography

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* Madelung, O. (1983). Landolt-Bornstein numerical data and functional relationships in science and technology. New series. Group III. Volume 17: Semiconductors. Subvolume e: Physics of non-tetrahedrally bonded elements and binary compounds I. Springer-Verlag: New York. ISBN 0-387-11780-6.
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