Skip to main content
SpringerLink
Log in

The high-pressure phase of boron, γ-B28: Disputes and conclusions of 5 years after discovery

  • Boron and Boron-Rich Solids: To 5 Years of Discovery of Gamma-Boron
  • Production, Structure, Properties
  • Published:
Journal of Superhard Materials Aims and scope Submit manuscript

An Erratum to this article was published on 01 February 2012

Abstract

γ-B28 is a recently established high-pressure phase of boron. Its structure consists of icosa-hedral B12 clusters and B2 dumbbells in a NaCl-type arrangement (B2)δ+(B12)δ− and displays a significant charge transfer δ ∼ 0.5–0.6. The discovery of this phase proved to be essential for the understanding and construction of the phase diagram of boron. It was first experimentally obtained as a pure boron allotrope in early 2004 and its structure was discovered in 2006. This paper reviews recent results and contentious issues related to the equation of state, hardness, putative isostructural phase transformation at ∼40 GPa, and debates on the nature of chemical bonding in this phase. Our analysis confirms that (a) calculations based on density functional theory give an accurate description of its equation of state, (b) the reported isostructural phase transformation in γ-B28 is an artifact, (c) the best estimate of hardness of this phase is 50 GPa, (d) chemical bonding in this phase has a significant degree of ionicity. Apart from presenting an overview of the previous results within a consistent view grounded in experiment, thermodynamics and quantum mechanics, we present new results on Bader charges in γ-B28 using different levels of quantum-mechanical theory (GGA, exact exchange, and HSE06 hybrid functional), and show that the earlier conclusion about a significant degree of a partial ionicity in this phase is very robust. An additional insight into the nature of the partial ionicity is obtained from a number of boron structures theoretically constructed in this work.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Douglas, B.E. and Ho, S.-M., Structure and Chemistry of Crystalline Solids, New York: Springer, 2006.

    Google Scholar 

  2. Amberger, E. and Ploog, K., Bildung der Gitter des Reinen Bors, J. Less-Common Metals, 1971, vol. 23, pp. 21–31.

    Article  CAS  Google Scholar 

  3. Sanz, D.N., Loubeyre, P., and Mezouar, M., Equation of State and Pressure-Induced Amorphization of beta-Boron from X-ray Measurements up to 100 GPa, Phys. Rev. Lett., 2002, vol. 89, art. 245501 (4).

  4. Van Setten, M.J., Uijttewaal, M.A., de Wijs, G.A., and de Groot, R.A., Thermodynamic Stability of Boron: The Role of Defects and Zero Point Motion, J. Am. Chem. Soc., 2007, vol. 129, pp. 2458–2465.

    Article  Google Scholar 

  5. Widom, M. and Mikhalkovic, M., Symmetry-Broken Crystal Structure of Elemental Boron at Low Temperature, Phys. Rev. B, 2008, vol. 77, art. 064113.

  6. Ogitsu, T., Gygi, F., Reed, J., Motome, Y., Schwegler, E., and Galli, G., Imperfect Crystal and Unusual Semiconductor: Boron, a Frustrated Element, J. Am. Chem. Soc., 2009, vol. 131, pp. 1903–1909.

    Article  CAS  Google Scholar 

  7. Oganov, A.R., Chen, J., Gatti, C., Ma, Y.-M., Yu, T., Liu, Z., Glass, C.W., Ma, Y.-Z., Kurakevych, O.O., and Solo-zhenko, V.L., Ionic High-Pressure Form of Elemental Boron, Nature, 2009, vol. 457, pp. 863–867.

    Article  CAS  Google Scholar 

  8. Oganov, A.R. and Solozhenko, V.L., Boron: a Hunt for Superhard Polymorphs, J. Superhard Materials, 2009, vol. 31, no. 5, pp. 285–291.

    Article  Google Scholar 

  9. Wentorf, R.H., Jr., Boron: Another Form, Science, 1965, vol. 147, no. 3653, pp. 49–50.

    Article  CAS  Google Scholar 

  10. Oganov, A.R. and Glass, C.W., Crystal Structure Prediction Using ab initio Evolutionary Techniques: Principles and Applications, J. Chem. Phys., 2006, vol. 124, art. 244704.

  11. Oganov, A.R., Lyakhov, A.O., and Valle, M., How Evolutionary Crystal Structure Prediction Works and Why, Acc. Chem. Res., 2011, vol. 44, pp. 227–237.

    CAS  Google Scholar 

  12. Li, Q., Ma, Y., Oganov, A.R., Wang, H.B., Wang, H., Xu, Y., Cui, T., Mao, H.-K., and Zou, G., Superhard Monoclinic Polymorph of Carbon, Phys. Rev. Lett., 2009, vol. 102, art. 175506 (4).

  13. Weintraub, E., On the Properties and Preparation of the Element Boron, J. Ind. Eng. Chem., 1911, vol. 3, no. 5, pp. 299–301.

    Article  CAS  Google Scholar 

  14. Brazhkin, V.V., Interparticle Interaction in Condensed Media: Some Elements Are “More Equal than Others”, Physics Uspekhi, 2009, vol. 52, no. 4, pp. 369–376.

    Article  CAS  Google Scholar 

  15. Zhu, Q., Oganov, A.R., Salvado, M., Pertierra, P., and Lyakhov, A.O., Denser than Diamond: ab initio Search for Superdense Carbon Allotropes, Phys. Rev. B, 2011, vol. 83, art. 193410.

  16. Gabunia, D., Tsagareishvili, O., Darsavelidze, G., Lezhava, G., Antadze, M., and Gabunia, L., Preparation, Structure and Some Properties of Boron Crystals with Different Content of 10B and 11B Isotopes, J. Solid State Chem., 2004, vol. 177, pp. 600–604.

    Article  CAS  Google Scholar 

  17. Amberger, E. and Stumpf, W., Boron, Gmelin Handbook of Inorganic Chemistry, Berlin: Springer-Verlag, 1960, pp. 112–238.

    Google Scholar 

  18. Solozhenko, V.L., Kurakevych, O.O., and Oganov, A.R., On the Hardness of a New Boron Phase, Orthorhombic γ-B28, J. Superhard Mater., 2008, vol. 30, no. 6, pp. 428–429.

    Article  Google Scholar 

  19. Will, G. and Kiefer, B., Electron Deformation Density in Alpha-Boron, Z. Anorg. Allg. Chem., 2001, vol. 627, pp. 2100–2104.

    Article  CAS  Google Scholar 

  20. Zarechnaya, E.Y., Dubrovinsky, L., Dubrovinskaia, N., Miyajima, N., Filinchuk Y., Chernyshov, D., and Dmitriev, V., Synthesis of an Orthorhombic High-Pressure Boron Phase, Sci. Tech. Adv. Mat., 2008, vol. 9, art. 044209.

  21. Zarechnaya, E.Y., Dubrovinsky, L., Dubrovinskaia, N., Filinchuk, Y., Chernyshov, D., Dmitriev, V., Miyajima, N., El Goresy, A., Braun, H.F., Van Smaalen, S., Kantor, I., Kantor, A., Prakapenka, V., Hanfland, M., Mikhailushkin, A.S., Abrikosov, I.A., and Simak, S.I., Superhard Semiconducting Optically Transparent High-Pressure Phase of Boron, Phys. Rev. Lett., 2009, vol. 102, art. 185501.

  22. Oganov, A.R., Solozhenko, V.L., Kurakevych, O.O., Gatti, C., Ma, Y.M., Chen, J., Liu, Z., and Hemley, R.J., Comment on ’superhard Semiconducting Optically Transparent High-Pressure Phase of Boron’, 2009, http://arxiv.org/abs/0908.2126.

  23. Slack, G.A., Hejna, C.I., Garbauskas, M.F., and Kasper, J.S., The Crystal Structure and Density of β-Rhombohedral Boron, J. Sol. State Chem., 1988, vol. 76, pp. 52–63.

    Article  CAS  Google Scholar 

  24. Vlasse, M., Naslain, R., Kasper, J.S., and Ploog, K., Crystal Structure of Tetragonal Boron Related to α-AlB12, J. Sol. State Chem., 1979, vol. 28, pp. 289–301.

    Article  CAS  Google Scholar 

  25. Le Godec, Y., Kurakevych, O.O., Munsch, P., Garbarino, G., and Solozhenko, V.L., Equation of State of Ortho-rhombic Boron, γ-B28, Solid State Comm., 2009, vol. 149, pp. 1356–1358.

    Article  Google Scholar 

  26. Jiang, C., Lin, Z., Zhang, J., and Zhao, Y., First-Principles Prediction of Mechanical Properties of gamma-Boron, Appl. Phys. Lett., 2009, vol. 94, art. 191906.

  27. Rulis, P., Wang, L., and Ching, W.Y., Prediction of γ-B28 ELNES with Comparison to α-B12, Phys. Stat. Sol. (RRL), 2009, vol. 3, 133–135.

    Article  CAS  Google Scholar 

  28. Zarechnaya, E., Dubrovinskaia, N., Caracas, R., Merlini, M., Hanfland, M., Filinchuk, Y., Chernyshov, D., Dmitriev, V., and Dubrovinsky, L., Pressure-Induced Isostructural Phase Transformation in γ-B28, Phys. Rev. B, 2010, vol. 82, art. 184111.

  29. Haussermann, U. and Milhaylushkin, A.S., Structure and Bonding of γ-B28: Is the High Pressure Form of Elemental Boron Ionic? Inorg. Chem., 2010, vol. 49, pp. 11270–11275.

    Article  CAS  Google Scholar 

  30. Isaev, E.I., Simak, S.I., Mikhaylushkin, A.S., Vekilov, Yu.Kh., Zarechnaya, E.Yu., Dubrovinsky, L., Dubrovinskaia, N., Merlini, M., Hanfland, M., and Abrikosov, I.A., Impact of Lattice Vibrations on Equation of State of the Hardest Boron Phase, Phys. Rev. B, 2011, vol. 83, art. 132106.

  31. Mondal, S., van Smaalen, S., Schonleber, A., Filinchuk, Y., Chernyshov, D., Simak, S.I., Mikhaylushkin, A.S., Abrikosov, I.A., Zarechnaya, E., Dubrovinsky, L., and Dubrovinskaia, N., Electron-Deficient and Polycenter Bonds in the High-Pressure γ-B28 Phase of Boron, Phys. Rev. Lett., 2011, vol. 106, art. 215502.

  32. Christy, A.G., Isosymmetric Structural Phase Transitions: Phenomenology and Examples, Acta Cryst. B, 1995, vol. 51, pp. 753–757.

    Article  Google Scholar 

  33. Oganov, A.R. and Lyakhov, A.O., Towards the Theory of Hardness of Materials, J. Superhard Mater., 2010, vol. 32, no. 3, pp. 143–147.

    Article  Google Scholar 

  34. Zhou, W., Sun, H., and Chen, C., Soft Bond-Deformation Paths in Superhard γ-Boron, Phys. Rev. Lett., 2010, vol. 105, art. 215503.

  35. Zhou, X.-F., Tian, Y., and Wang, H.-T., Large Shear Strength Enhancement of Gamma-Boron by Normal Compression, J. Superhard Mater., 2011, vol. 33, no. 6, pp. 401–408.

    Article  Google Scholar 

  36. Mukhanov, V.A., Kurakevych, O.O., and Solozhenko, V.L., The Interrelation between Hardness and Compressibility of Substances and Their Structure and Thermodynamic Properties, ibid., 2008, vol. 30, no. 6, pp. 368–378.

    Article  Google Scholar 

  37. Chen, X.-Q., Niu, H., Li, D., and Li, Y., Modeling Hardness of Polycrystalline Materials and Bulk Metallic Glasses, Intermetallics, 2011, vol. 19, pp. 1275–1281.

    Article  CAS  Google Scholar 

  38. Oganov, A.R., Theory of Superhard Materials, In: Comprehensive Hard Materials Review, Elsevier, 2013, Submitted.

  39. Li, K.Y., Wang, X.T., Zhang, F.F., and Xue, D.F., Electronegativity Identification of Novel Superhard Materials, Phys. Rev. Lett., 2008, vol. 100, art. 235504.

  40. Lyakhov, A.O. and Oganov, A.R., Evolutionary Search for Superhard Materials: Methodology and Applications to Forms of Carbon and TiO2, Phys. Rev. B, 2011, vol. 84, art. 092103.

  41. Zhu, Q., Jung, D.Y., Oganov, A.R., Gatti, C., Glass, C.W., and Lyakhov, A.O., Xenon Oxides and Silicates at High Pressures, 2011, Submitted.

  42. Batsanov, S.S., Strukturnaya Khimiya. Fakty i Zavisimosti (Structural Chemistry. Book of Facts), Moscow: Dialogue-MGU, 2000.

    Google Scholar 

  43. Bader, R.F.W., Atoms in Molecules. A Quantum Theory, Oxford: Oxford University Press, 1990.

    Google Scholar 

  44. Heyd, J., Scuseria, G.E., and Ernzerhof, M., Hybrid Functionals Based on a Screened Coulomb Potential, J. Chem. Phys., 2006, vol. 124, art. 219906.

  45. Perdew, J.P., Burke, K. and Ernzerhof, M., Generalized Gradient Approximation Made Simple, Phys. Rev. Lett., 1996, vol. 78, pp. 3865–3868.

    Article  Google Scholar 

  46. Wells, A.F., Structural Inorganic Chemistry, Oxford: Clarendon Press, 1986.

    Google Scholar 

  47. Hayami, W., Theoretical Study of the Stability of AB12 (A = H-Ne) Icosahedral Clusters, Phys. Rev. B, 1999, vol. 60, pp. 1523–1526.

    Article  CAS  Google Scholar 

  48. Werheit, H., Luax, M., and Kuhlmann, U., Interband and Gap State Related Transitions in β-Rhombohedral Boron, Phys. Status Solidi B, 1993, vol. 176, pp. 415–432.

    Article  CAS  Google Scholar 

  49. Elliott, S.R., The Physics and Chemistry of Solids, New York: John Wiley and Sons, 1998.

    Google Scholar 

  50. Tsirelson, V.G., Evdokimova, O.A., Belokoneva, E.L., and Urusov, V.S., Electron Density Distribution and Bonding in Silicates. A Review of Recent Data, Phys. Chem. Minerals, 1990, vol. 17, pp. 275–292.

    Article  CAS  Google Scholar 

  51. Brown, I.D., Chemical and Steric Constraints in Inorganic Solids, Acta Cryst. B, 1992, vol. 48, 553–572.

    Article  Google Scholar 

  52. Edwards, B. and Ashcroft, N.W., Spontaneous Polarization in Dense Hydrogen, Nature, 1997, vol. 388, pp. 652–655.

    Article  CAS  Google Scholar 

  53. Ma, Y., Wang, Y., and Oganov, A.R., Absence of Superconductivity in the Novel High-Pressure Polymorph of MgB2. Phys. Rev. B, 2009, vol. 79, art. 054101.

  54. Tsagareishvili, O.A., Chkhartishvili, L.S., and Gabunia, D.L., Apparent Low-Frequency Charge Capacitance of Semiconducting Boron, Semiconductors, 2009, vol. 43, pp. 14–20.

    Article  CAS  Google Scholar 

  55. Macchi, P., On the Nature of Chemical Bonding in γ-Boron, J. Superhard Mater., 2011, vol. 33, no. 6, pp. 380–387.

    Article  Google Scholar 

  56. Le Godec, Y., Comparative Review of Theoretical and Experimental Equations of State of Orthorhombic Boron γ-B28, ibid., 2011, vol. 33, no. 6, pp. 388–393.

    Article  Google Scholar 

  57. Rulis, P., Wang, L., Walker, B., and Ching, W.-Y., Spectral Analysis of the Electronic Structure of γ-B28, ibid., 2011, vol. 33, no. 6, pp. 394–400.

    Article  Google Scholar 

  58. Veprek, S., Zhang, R.F., and Argon, A.S., Mechanical Properties and Hardness of Boron and Boron-Rich Solids, ibid., 2011, vol. 33, no. 6, pp. 409–420.

    Article  Google Scholar 

  59. Kurakevych, O.O. and Solozhenko, V.L., Experimental Study and Critical Review of Structural, Thermodynamic and Mechanical Properties of Superhard Refractory Boron Suboxide B6O, ibid., 2011, vol. 33, no. 6, pp. 421–428.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Geosciences, Department of Physics and Astronomy, and New York Center for Computational Science, Stony Brook University, Stony Brook, NY, 11794-2100, USA

    A. R. Oganov

  2. Geology Department, Moscow State University, 119992, Moscow, Russia

    A. R. Oganov

  3. LSPM-CNRS, Université Paris Nord, 93430, Villetaneuse, France

    V. L. Solozhenko & O. O. Kurakevych

  4. CNR-ISTM Istituto di Scienze e Tecnologie Molecolari, 20133, Milano, Italy

    C. Gatti

  5. IMPMC, Université P&M Curie, 75005, Paris, France

    Y. Le Godec

Authors
  1. A. R. Oganov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. L. Solozhenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. C. Gatti
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. O. O. Kurakevych
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Y. Le Godec
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Original English Text © A.R. Oganov, V.L. Solozhenko, C. Gatti, O.O. Kurakevych, Y. Le Godec, 2011, published in Sverkhtverdye Materialy, 2011, Vol. 33, No. 6, pp. 3–22.

An erratum to this article can be found at http://dx.doi.org/10.3103/S1063457612010108.

About this article

Cite this article

Oganov, A.R., Solozhenko, V.L., Gatti, C. et al. The high-pressure phase of boron, γ-B28: Disputes and conclusions of 5 years after discovery. J. Superhard Mater. 33, 363–379 (2011). https://doi.org/10.3103/S1063457612060019

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1063457612060019

Keywords

Search

Navigation