Using ab initio density functional theory calculations, the electron localization function (ELF) of typical transition metal carbide TiC and nitride TiN were computed and analyzed to reveal their nature of the chemical bonds. The ELF approach was initially validated through typical examples of covalent-bonding Diamond (C) and ionic-bonding sodium chloride NaCl. Our results clearly demonstrate the dominantly ionic bonding characteristics of TiC and TiN. It is also suggested that the high mechanical hardness of TiC and TiN can be explained without evoking strong covalence.
 A. Dunand, H. D. Flack and K. Yon, “Bonding Study of TiC and TiN. I. High-Precision X-Ray Diffraction Determination of the Valence-Electron Density Distribution, Debye-Waller Temperature Factors, and Atomic Static Displacements in TiC0.94 and TiN0.99,” Physical Review B, Vol. 31, No. 4, 1985, pp. 2299-2315.
K. Schwarz, “Band Structures and Chemical Bonding in Transition Metal Carbides and Nitrides,” Critical Reviews in Solid State and Materials Sciences, Vol. 13, No. 3, 1987, pp. 211-257. doi:10.1080/10408438708242178
A. D. Becke, “Local Exchange-Correlation Approximations and First-Row Molecular Dissociation Energies,” International Journal of Quantum Chemistry, Vol. 27, No. 5, 1985, pp. 585-594. doi:10.1002/qua.560270507
S. Kamran, K. Chen, L. Chen and L. Zhao, “Electronic Origin of Anomalously High Shear Modulus and Intrinsic Brittleness of Fcc Ir,” Journal of Physics: Condensed Matter, Vol. 20, No. 8, 2008, Article ID: 085221.
G. Kresse and J. Furthm?ller, “Efficiency of Ab Initio Total Energy Calculations for Metals and Semiconductors Using A Plane-Wave Basis Set,” Computational Materials Science, Vol. 6, No. 1, 1996, pp. 15-50.
G. Kresse and J. Furthm?ller, “Efficient Iterative Schemes for Ab Initio Total-Energy Calculations Using a Plane-Wave Basis Set,” Physical Review B , Vol. 54, No. 16, 1996, Article ID: 11169.
J. P. Perdew, J. A. Chevary, S. H. Vosko, K. A. Jackson, M. R. Pederson, D. J. Singh and C. Fiolhais, “Atoms, Molecules, Solids and Surfaces: Applications of the Generalized Gradient Approximation for Exchange and Correlation,” Physical Review B, Vol. 46, No. 11, 1992, pp. 6671-6687. doi:10.1103/PhysRevB.46.6671
K. Chen, L Zhao, J. Rodgers and J. S. Tse, “Alloying Effects on Elastic Properties of TiN-Based Nitrides,” Journal of Physics D: Applied Physics, Vol. 36, No. 21, 2003, Article ID: 2725.
K. Chen and L. Zhao, “Elastic Properties, Thermal Expansion Coefficients and Electronic Structures of
Ti0.75X0.25C Carbides,” Journal of Physics and Chemistry of Solids, Vol. 68, No. 9, 2007, pp. 1805-1811.
S. Kamran, K. Chen and L. Chen, “Semiempirical Formulae for Elastic Moduli and Brittleness of Diamondlike and Zinc-Blende Covalent Crystals,” Physical Review B, Vol. 77, No. 9, 2008, Article ID: 094109.
D. G. Clerc and H. M. Ledbetter, “Mechanical Hardness: Atomic-Level Calculations for Diamond-Like Materials,” Journal of Physical Chemistry A Solids, Vol. 59, No. 6-7, 1998, pp. 1071-1095.