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Towards the theory of hardness of materials

  • Theory of Hardness and Superhard Materials
  • Production, Structure, Properties
  • Published:
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Abstract

Recent studies have shown that hardness, a complex property, can be calculated using very simple approaches or even analytical formulae. These form the basis for evaluating controversial experimental results (as we illustrate for TiO2-cotunnite) and enable a systematic search for novel hard materials, for instance, using global optimization algorithms (as we show on the example of SiO2 polymorphs).

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References

  1. Brookes, C.A. and Brookes, E.J., Diamond in Perspective-a Review of Mechanical Properties of Natural Diamond, Diamond Relat. Mater., 1991, vol. 1, pp. 13–17.

    Article  CAS  Google Scholar 

  2. Irifune, T., Kurio, A., Sakamoto, S., et al., Ultrahard Polycrystalline Diamond from Graphite, Nature, 2003, vol. 421, pp. 599–600.

    Article  CAS  Google Scholar 

  3. Solozhenko, V.L., High-Pressure Synthesis of Novel Superhard Phases in the B-C-N System: Recent Achievements, High Pressure Res., 2009, vol. 29, pp. 612–617.

    Article  CAS  Google Scholar 

  4. Tse, J.S., Intrinsic Hardness of Crystalline Solids, J. Superhard Mater., 2010, vol. 32, no. 3, pp. 177–191.

    Article  Google Scholar 

  5. Gao, F.M. and Gao, L.H., Microscopic Models of Hardness, ibid., 2010, vol. 32, no. 3, pp. 148–166.

    Article  Google Scholar 

  6. Gao, F.M., He, J.L., Wu, E.D., et al., Hardness of Covalent Crystals, Phys. Rev. Lett. 2003, vol. 91, art. 0155021.

  7. Simunek, A. and Vackar, J., Hardness of Covalent and Ionic Crystals: First-Principle Calculations, ibid., 2006, vol. 96, art. 0855011.

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

  9. Mukhanov, V. A., Kurakevych, O. O., and Solozhenko, V. L., The Interrelation between Hardness and Compressibility of Substances and their Structure and Thermodynamic Properties, J. Superhard Mater., 2008, vol. 30, pp. 368–378.

    Article  Google Scholar 

  10. Simunek, A., Anisotropy of Hardness from First Principles: The Cases of ReB2 and OsB2, Phys. Rev. B, 2009, vol. 80, art. 060103.

  11. Mao, W.L., Mao, H.K., Eng, P.J., et al., Bonding Changes in Compressed Superhard Graphite, Science, 2003, vol. 302, pp. 425–427.

    Article  CAS  Google Scholar 

  12. Li, Q., Ma, Y., Oganov, A.R., et al., Superhard Monoclinic Polymorph of Carbon, Phys. Rev. Lett., 2009, vol. 102, pp. 175506.

    Article  Google Scholar 

  13. Bundy, F.P., Hall, H.T., Strong, H.M., and Wentorf, R.H., Man-Made Diamonds, Nature, 1955, vol. 176, pp. 51–55.

    Article  CAS  Google Scholar 

  14. Bovenkerk, H.P., Bundy, F.P., Hall, H.T., et al., Preparation of Diamond, ibid., 1959, vol. 184, pp. 1094–1098.

    Article  CAS  Google Scholar 

  15. Wentorf, R.H., Cubic Form of Boron Nitride, J. Chem. Phys., 1957, vol. 26, p. 956.

    Article  CAS  Google Scholar 

  16. Solozhenko, V.L., Andrault, D., Fiquet, G., et al., Synthesis of Superhard Cubic BC2N, Appl. Phys. Lett., 2001, vol. 78, pp. 1385–1387.

    Article  CAS  Google Scholar 

  17. Solozhenko, V.L., Synthesis of Novel Superhard Phases in the B-C-N System, High Press. Res., 2002, vol. 22, pp. 519–524.

    Article  Google Scholar 

  18. Solozhenko, V.L., Kurakevych, O.O., Andrault, D., et al., Ultimate Metastable Solubility of Boron in Diamond: Synthesis of Superhard Diamond-Like BC5, Phys. Rev. Lett., 2009, vol. 102, art. 015506.

  19. Oganov, A.R., Chen, J., Gatti, C. et al., Ionic High-Pressure Form of Elemental Boron, Nature, 2009, vol. 457, pp. 863–867.

    Article  CAS  Google Scholar 

  20. 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 

  21. Dubrovinsky, L.S., Dubrovinskaia, N.A., Swamy, V., et al., Materials Science-the Hardest Known Oxide, Nature, 2001, vol. 410, pp. 653–654.

    Article  CAS  Google Scholar 

  22. Leger, J.M., Haines, J., Schmidt, M., et al., Discovery of Hardest Known Oxide, ibid., 1996, vol. 383, p. 401.

    Article  CAS  Google Scholar 

  23. He, D.W., Zhao, Y.S., Daemen, L., et al., Boron Suboxide: As hard as Cubic Boron Nitride, Appl. Phys. Lett., 2002, vol. 81, pp. 643–645.

    Article  CAS  Google Scholar 

  24. Glass, C.W., Oganov, A.R., and Hansen, N., USPEX-Evolutionary Crystal Structure Prediction, Comp. Phys. Comm., 2006, vol. 175, pp. 713–720.

    Article  CAS  Google Scholar 

  25. Oganov, A.R., Glass, C.W., and Ono, S. High-Pressure Phases of CaCO3: Crystal Structure Prediction and Experiment, Earth Planet. Sci. Lett., 2006, vol. 241, pp. 95–103.

    Article  CAS  Google Scholar 

  26. 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.

  27. Lyakhov, A.O., Oganov, A.R., Glass, C.W., et al., USPEX, a Code for Evolutionary Optimization of Crystal Structures. Version 7.4.3. 20 January 2010. http://mysbfiles.stonybrook.edu/~aoganov/USPEX.html

  28. Sanders, M.J., Leslie, M., and Catlow, C.R.A., Interatomic Potentials for SiO2, J. Chem. Soc. Chem. Commun., 1984, vol. 19, pp. 1271–1273.

    Article  Google Scholar 

  29. Gale, J.D., GULP: Capabilities and Prospects, Z. Krist., 2005, vol. 220, pp. 552–554.

    Article  CAS  Google Scholar 

  30. Teter, D.M., Hemley, R.J., Kresse, G., and Hafner, J., High Pressure Polymorphism in Silica, Phys. Rev. Lett., 1998, vol. 80, pp. 2145–2148.

    Article  CAS  Google Scholar 

  31. Proserpio, D.M., Hoffmann, R., and Preuss, P., Possible Hard Materials Based on Interpenetrating Diamond-like Networks, J. Am. Chem. Soc., 1994, vol. 115, pp. 9634–9637.

    Article  Google Scholar 

  32. Hemley, R.J., Jephcoat, A.P., Mao, H.K., et al., Static Compression of H2O-Ice to 128 GPa (1.28 Mbar), Nature, 1987, vol. 330, pp. 737–740.

    Article  CAS  Google Scholar 

  33. Perdew, J.P., Burke, K., and Ernzerhof, M., Generalized Gradient Approximation Made Simple, Phys. Rev. Lett., 1996, vol. 77, pp. 3865–3868.

    Article  CAS  Google Scholar 

  34. Kresse, G. and Furthmüller, J., Efficient Iterative Schemes for ab initio Total-Energy Calculations Using a Plane Wave Basis Set, Phys. Rev. B, 1996, vol. 54, pp. 11169–11186.

    Article  CAS  Google Scholar 

  35. Oganov, A.R., Gillan, M.J., and Price, G.D., Structural Stability of Silica at High Pressures and Temperatures, ibid., 2005, vol. 71, art. 064104.

  36. Mukhanov, V.A., Kurakevych, O.O., and Solozhenko, V.L., Thermodynamic Model of Hardness: Particular Case of Boron-Rich Solids, J. Superhard Mater., 2010, vol. 32, no. 3, pp. 167–176.

    Article  Google Scholar 

  37. Li, Q., Wang, H., and Ma, Y.M., Predicting New Superhard Phases, ibid., 2010, vol. 32, no. 3, pp. 192–204.

    Article  Google Scholar 

  38. Shirai, K., Electronic Structure and Mechanical Properties of Boron and Boron-Rich Crystals, ibid., 2010, vol. 32, no. 3, pp. 205–225.

    Article  Google Scholar 

  39. Gao, F.M., Hou, L., and He, Y.H., Origin of Superhardness of Icosahedral B12 Materials, J. Phys. Chem. B, 2004, vol. 108, pp. 13069–13073.

    Article  CAS  Google Scholar 

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Authors and Affiliations

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

    A. R. Oganov & A. O. Lyakhov

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

    A. R. Oganov

Authors
  1. A. R. Oganov
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  2. A. O. Lyakhov
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Additional information

Original Russian Text © A.R. Oganov, A.O. Lyakhov, 2010, published in Sverkhtverdye Materialy, 2010, Vol. 32, No. 3, pp. 3–8.

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Oganov, A.R., Lyakhov, A.O. Towards the theory of hardness of materials. J. Superhard Mater. 32, 143–147 (2010). https://doi.org/10.3103/S1063457610030019

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  • DOI: https://doi.org/10.3103/S1063457610030019

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