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Intrinsic hardness of crystalline solids

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

The current status of various theoretical approaches to the “prediction” of material hardness has been reviewed. It is shown that the simple empirical correlation with the shear moduli generally provide very good estimates of the Vickers hardness. Semi-empirical models based solely on the strength of the chemical bonds, although performed as well, are theoretically incomplete. First-principles calculations of the ideal stress and shear strength is perhaps the most reliable and theoretically sound approach available to compare theoretical predictions with experiment.

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References

  1. O’Neill, H., The Hardness of Metals and Its Measurement, London: Chapman and Hall, 1934.

    Google Scholar 

  2. Malzbender, J., Comment on Hardness Definitions, J. Euro. Ceramics Soc., 2003, vol. 23, pp. 1355.

    Article  CAS  Google Scholar 

  3. Brazhkin, V., Dubrovinskaia, N., Nicol, M., Novikov, N., Riedel, R., Solozhenko, V., and Zhao, Y., What Does “Harder than Diamond” Mean?, Nature Materials, 2004, vol. 3, no. 9, pp. 576–577.

    Article  CAS  Google Scholar 

  4. Fischer-Cripps, C., Introduction to Contact Mechanics, Heidelberg: Springer, 2000.

    Google Scholar 

  5. Beer, F.P., Johnston, J.E., Russell, D., and Dewolf, J.T., Mechanics of Materials, McGraw-Hill, 2001, 3rd edition.

  6. Cohen, M.L., Predicting New Solids and Their Properties, Philos. Trans. R. Soc., London, Ser. A, 1991, vol. 334, no. 1635, pp. 501–513.

    Article  CAS  Google Scholar 

  7. Nabarro, R.N., Theory of Crystal Dislocation, New York: Dover Publications, 1987, Dover Edition.

    Google Scholar 

  8. Teter, D.M., Computational Alchemy: the Search for New Superhard Materials, 1998, vol. 23, pp. 22–27.

    CAS  Google Scholar 

  9. Gilman, J.J., Physical Chemistry of Intrinsic Hardness, Mater. Sci Eng., A, 1996, vol. 209, pp. 74–81.

    Article  Google Scholar 

  10. Pauling, L., The Nature of Chemical Bond, Ithaca, New York: Cornell University Press, 1939.

    Google Scholar 

  11. Albright, T.A., Burdett, J.K., Whangbo, M.-Y., Orbital Interactions in Chemistry, New York: John Wiley & Sons, 1984.

    Google Scholar 

  12. Walsh, A.D.J., The Electronic Orbitals, Shapes, and Spectra of Polyatomic Molecules. Part III. HAB and HAAH molecules, J. Chem. Soc. (London), 1953, pp. 2288–2296.

  13. Jhi, S.-H., Ihm, J., Louie, S.G., and Cohen, M.L., Electronic Mechanism of Hardness Enhancement in Transition Metal Carbonitrides, Nature, 1999, vol. 399, pp. 132.

    Article  CAS  Google Scholar 

  14. Cohen, M.L., Calculation of Bulk Moduli of Diamond and Zinc-Blende Solids, Phys. Rev. B, 1986, vol. 32, no. 12, pp. 7988–7991.

    Article  Google Scholar 

  15. Phillips, J.C., Bonds and Bands in Semiconductors, New York: Academic Press, 1973.

    Google Scholar 

  16. Phillips, J.C., Ionicity of the Chemical Bond in Crystals, Rev. Mod. Phys., 1970, vol. 42, no. 3, pp. 317–356.

    Article  CAS  Google Scholar 

  17. Liu, A. and Cohen, M.L., Prediction of New Low Compressibility Solids, Science, 1989, vol. 245, pp. 841–842.

    Article  CAS  Google Scholar 

  18. Gao, F.M., He, J.L., Wu, E.D., Liu, S.M., Yu, D.L., Li, D.C., Zhang, S.Y., and Tian, Y.J., Hardness of Covalent Crystals, Phys. Rev. Lett., 2003, vol. 91, p. 015502.

    Article  Google Scholar 

  19. Grimvall, G., Thermophysical Properties of Materials, Amsterdam: Elsevier, 1999.

    Google Scholar 

  20. Martin, R.M., Electronic Structure: Basic Theory and Practical Methods, Cambridge: University Press, 2004.

    Google Scholar 

  21. Solozhenko, V.L., Dub, S.N., and Novikov, N.V., Mechanical Properties of Cubic BC2N, a New Superhard Phase, Diamond and Related Materials, 2001, vol. 10, no. 12, pp. 2228–2231.

    Article  CAS  Google Scholar 

  22. Simunek, A. and Vackar, J., Hardness of Covalent and Ionic Crystals: First-Principle Calculations, Phys. Rev. Lett., 2006, vol. 96, pp. 085501.

    Article  Google Scholar 

  23. Rafaja, D., Klemm, V., Motylenko, M., Schwarz, M.R., Barsukova, T., Kroke, E., Frost, D., Dubrovinsky, L., and Dubrovinskaia, N., Synthesis, Microstructure, and Hardness of Bulk Ultrahard BN Nanocomposites, J. Mat. Res., 2008, vol. 23, pp. 981–993.

    Article  CAS  Google Scholar 

  24. Irifune, T., Kurio, A., Sakamoto, S., Inoue, T., and Sumiya, H., Ultrahard Polycrystalline Diamond from Graphite, Nature, 2003, vol. 421, pp. 599–600.

    Article  CAS  Google Scholar 

  25. Schiotz, J., Di Tolla, F.D., and Jacobsen, K., Nature, 1998, vol. 391, pp. 561–563.

    Article  Google Scholar 

  26. Tse, J.S., Klug, D.D., and Gao, F.M., Hardness of Nanocrystalline Diamonds, Phys. Rev. B, 2006, vol. 73, pp. 140102.

    Article  Google Scholar 

  27. Halperin, W. P., Quantum Size Effects in Metal Particles, Rev. Mod. Phys., 1986, vol. 58, pp. 533–606.

    Article  CAS  Google Scholar 

  28. Wang, Y. and Herron, N., Quantum Size Effects on the Exciton Energy of CdS Clusters, Phys. Rev. B, 1990, vol. 42, p. 7253.

  29. Dubrovinskaia, N., Solozhenko, V.L., Miyajima, N., Dmitriev, V., Kurakevych, O.O., and Dubrovinsky, L., Superhard Nanocomposite of Dense Polymorphs of Boron Nitride: Noncarbon Material Has Reached Diamond Hardness, Appl. Phys. Lett., 2007, vol. 99, p. 101921.

    Google Scholar 

  30. Hall, E.O., Proc. Phys. Soc. London, Sect B, 1951, vol. 64, p. 747.

    Article  Google Scholar 

  31. Allen, L.C. and Capitani, J.F., What Is the Metallic Bond? J. Amer. Chem. Soc., 1994, vol. 116, p. 8810.

    Article  CAS  Google Scholar 

  32. Burdett, J.K. and Czech, P.T., What Is the Metallic Bond? J. Amer. Chem. Soc., 1994, vol. 116, pp. 8808–8809.

    Article  Google Scholar 

  33. Rousseau, R. and Tse, J.S., Rationalization of Structures of Binary Alloys in a Real Space Atomic Level Perspective, Prog. Theoret. Phys., 2000, Supplement no. 138, p. 47.

  34. Guo, X., Li, L., Liu, Z., Yu, D., He, J., Liu, R., Xu, B., Tian, Y., and Wang, H.-T., Hardness of Covalent Compounds: Roles of Metallic Component and d Valence Electrons, J. Appl. Phys., 2008, vol. 104, p. 023503.

    Article  Google Scholar 

  35. Cumberland, R.W., Weinberger, M.B., Gilman, J.J., Clark, S.M., Tolbert, S.H., and Kaner, R.B., Osmium Diboride, an Ultra-Incompressible, Hard Material, J. Amer. Chem. Soc., 2005, vol. 127, pp. 7264–7265.

    Article  CAS  Google Scholar 

  36. Hao, X., Xu, Y., Wu, Z., Zhou, D., Liu, X., and Meng, J., Elastic Anisotropy of OsB2 and RuB2 from First-Principles Study, J. Alloys Compounds, 2008, vol. 453, nos. 1–2, pp. 413–417.

    Article  CAS  Google Scholar 

  37. Chen, X-Q., Fu, C.L., Kremar, M., and Painter, G.S., Electronic and Structural Origin of Ultraincompressibility of 5d Transition Metal Diborides MB2 (M=W, Re, Os), Phys. Rev. Lett., 2008, vol. 100, pp. 196403 (4 p).

    Google Scholar 

  38. Chung, H.-Y., Yang, J.M., Tolbert, S.H., and Kaner, R.B., Anisotropic Mechanical Properties of Ultraincompressible, Hard Osmium Diboride, J. Mater. Res., 2008, vol. 23, no. 6, pp. 1797–1801.

    Article  CAS  Google Scholar 

  39. Krenn, C.R., Roundy, D., Cohen, M.L., Chrzan, D.C., and Morris, J.W., Jr., Connecting Atomistic and Experimental Estimates of Ideal Strength, Phys. Rev. B, 2002, vol. 65, pp. 134111 (4 p.).

    Article  Google Scholar 

  40. Roundy, D., Krenn, C.R., Cohen, M.L., and Morris, J.W., Jr., The Ideal Strength of Tungsten, Philos. Mag., A, 2001, vol. 81, pp. 1725–1747.

    Article  CAS  Google Scholar 

  41. Ogata, S., Umeno, Y., and Kohyama, M., First-Principles Approaches to Intrinsic Strength and Deformation of Materials: Perfect Crystals, Nanostructures, Surfaces and Interfaces, Modeling and Simulation, Mater. Sci. Eng., 2009, vol. 17, no. 1, p. 013001.

    Google Scholar 

  42. Zhang, Y., Sun, H., and Chen, C., Ideal Tensile and Shear Strength of β-C3N4 from First-Principles Calculations, Phys. Rev. B, 2007, vol. 76, no. 14, pp. 144101 (6 p.).

    Article  Google Scholar 

  43. Chung, H.Y., Weinberger, M.B., Levine, J.B., Kavner, A., Yang, J.M., Tolbert, S., and Kaner, R.B., Synthesis of Ultraincompressible Superhard Rhenium Diboride at Ambient Pressure, Science, 2007, vol. 316, no. 5823, pp. 436–439.

    Article  CAS  Google Scholar 

  44. Yang, J., Sun, H., and Chen, C., Is Osmium Diboride an Ultrahard Material? J. Amer. Chem. Soc., 2008, vol. 130, no. 23, pp. 7200–7201.

    Article  CAS  Google Scholar 

  45. Clatterbuck, D.M., Chrzan, D.C., and Morris, J.W., Jr., The Ideal Strength of Iron in Tension and Shear, Acta Mater., 2003, vol. 51, pp. 2271–2283.

    Article  CAS  Google Scholar 

  46. Solozhenko, V.L., Kurakevych, O.O., Andrault, D., Le Godec, Y., and Mezouar, M., Ultimate Metastable Solubility of Boron in Diamond: Synthesis of Superhard Diamond-Like BC5, Phys. Rev. Lett., 2009, vol. 102, no. 1, pp. 015506 (4 p.).

    Article  Google Scholar 

  47. Yao, Y., Tse, J.S., and Klug, D.D., Crystal and Electronic Structure of Superhard BC5: First-Principles Structural Optimizations, Phys. Rev. B, 2009, vol. 80, no. 9, pp. 094106 (6 p.).

    Article  Google Scholar 

  48. Calandra, M. and Mauri, F., High-T c Superconductivity in Superhard Diamond-Like BC5, Phys. Rev. Lett., 2008, vol. 101, no. 1, pp. 016401 (4 p.).

    Article  Google Scholar 

  49. Jiang, C., Lin, Z., and Zhao, Y., Superhard Diamond-Like BC5: A First-Principles Investigation, Phys. Rev. B, 2009, vol. 80, no. 18, pp. 184101 (6 p.).

    Google Scholar 

  50. Lazar, P. and Podloucky, R., Mechanical Properties of Superhard BC5, Appl. Phys. Lett., 2009, vol. 94, no. 25, pp. 251904 (3 p.).

    Article  Google Scholar 

  51. Zhang, R.F., Veprek, S., and Argon, A.S., Effect of Nanometer-Sized Grains on the Superhardness of cBC5: A First-Principles Study, Phys. Rev. B, 2009, vol. 80, no. 23, pp. 233401 (4 p.).

    Article  Google Scholar 

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  1. Department of Physics and Engineering Physics, University of Saskatchewan, 116 Science Place, Saskatoon, Saskatchewan, SK S7N 5E2, Canada

    J. S. Tse

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Original Russian Text © J.S. Tse, 2010, published in Sverkhtverdye Materialy, 2010, Vol. 32, No. 3, pp. 46–65.

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Tse, J.S. Intrinsic hardness of crystalline solids. J. Superhard Mater. 32, 177–191 (2010). https://doi.org/10.3103/S1063457610030044

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  • DOI: https://doi.org/10.3103/S1063457610030044

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