Abstract
Based on the electron-holding energy per unit volume, we extend the concept of hardness to atomic stiffness, ionic stiffness and bond hardness, investigating the nature of material hardness at these three levels. We find that the stiffness of isolated atoms or ions has no direct connection with the hardness of materials, whereas material hardness is directly related to bond hardness, which is essentially determined by the electron-holding energy of its constituent chemical bonds per unit volume. We establish a model for identifying the hardness of materials on the basis of bond hardness. This work offers a deeper understanding of the nature of material hardness at the atomic level, and provides a practical guide in the search for new superhard materials.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Liu A Y, Cohen M L. Prediction of new low compressibility solids. Science, 1989, 245(4920): 841–842
Gao F M, He J L, Wu E D, et al. Hardness of covalent crystals. Phys Rev Lett, 2003, 91(1): 015502
Simunek A, Vackar J. Hardness of covalent and ionic crystals: First-principle calculations. Phys Rev Lett, 2006, 96(8): 085501
Gilman J J. Physical chemistry of intrinsic hardness. Mater Sci Eng A, 1996, 209(1–2): 74–81
Pearson R G. Hard and soft acids and bases. J Am Chem Soc, 1963, 85(22): 3533–3539
Politzer P. A relationship between the charge capacity and the hardness of neutral atoms and groups. J Chem Phys, 1987, 86(2): 1072–1073
Parr R G, Pearson R G. Absolute hardness: Companion parameter to absolute electronegativity. J Am Chem Soc, 1983, 105(26): 7512–7516
Nagle J K. Atomic polarizability and electronegativity. J Am Chem Soc, 1990, 112(2): 4741–4747
Pauling L. Atomic radii and interatomic distances in metals. J Am Chem Soc, 1947, 69(3): 542–553
Li K, Xue D. Estimation of electronegativity values of elements in different valence states. J Phys Chem A, 2006, 110(39): 11332–11337
Lide D R. CRC Handbook of Chemistry and Physics. 84th ed. Boca Raton: CRC Press, 2003
Emsley J. The Elements. 2nd ed. New York: Oxford University Press, 1991
Shannon R D. Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides. Acta Crystallogr A, 1976, 32(5): 751–767
Gilman J J, Cumberland R W, Kaner R B. Design of hard crystals. Int J Metals Hard Mater, 2006, 24(1–2): 1–5
Li K, Wang X, Zhang F, et al. Electronegativity identification of novel superhard materials. Phys Rev Lett, 2008, 100(23): 235504
Inorganic Crystal Structure Database (Fachinformationszentrum Karlsruhe, Germany, release 2005)
Li K, Wang X, Xue D. Electronegativities of elements in covalent crystals. J Phys Chem A, 2008, 112(34): 7894–7897
Dubrovinsky L S, Dubrovinskaia N A, Swamy V, et al. The hardest known oxide. Nature, 2001, 410(6829): 653–654
Author information
Authors and Affiliations
Corresponding author
Additional information
Supported by National Natural Science Foundation of China (Grant No. 20471012), Program for New Century Excellent Talents in University (Grant No. NCET-05-0278) and Foundation for the Author of National Excellent Doctoral Dissertation of China (Grant No. 200322)
About this article
Cite this article
Li, K., Xue, D. Hardness of materials: studies at levels from atoms to crystals. Chin. Sci. Bull. 54, 131–136 (2009). https://doi.org/10.1007/s11434-008-0550-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11434-008-0550-8