![]() ![]() The same kind of crude information can be extracted from charge density plots, where bond paths, nuclear sites, and cage structures as in benzene molecules are associated with the critical points of the dynamical system defined by the charge density gradient, i.e., saddle points, maxima and minima, respecttively. Thus ELF provides a faithful and direct space depiction of electron distribution with no restrictions on the size or the type of the system to be probed. As discussed by Becke and Edgecombe, the local value of ELF at position indicates the probability of finding an electron at that locality given the existence of neighbouring electrons. The denominator of Equation (1), which depends on the kinetic energy, is related to the leading term in the Taylor expansion of conditional pair probability. In the absence of significant electronic populations, ELF dwindles to nullity. The electron localization function (ELF), which is inversely proportional to the square of the ratio of the kinetic energy of the system under study D and the kinetic energy characteristic of a homogeneous electron gas D h to within an additive constant of unitary magnitude, gauges electron dispersiveness at position :Īs can be seen from Equation (1), ELF equals 0.5 in the case of a metallic or jellium-like electron distribution and it approaches unity for highly localized electronic clouds. In the present article, we shall expostulate that in both cases, the bonds are essentially ionic dominated and that this ionic character is capable of explaining the mechanical properties of TiC and TiN. Despite the fact that most researchers acknowledge some ionic features in the Ti-X bonds, the generally accepted viewpoint categorizes TiC and TiN as either covalent materials or substances with mixed bonding characteristics. Their results, although not indicative of notable overall covalence, are suggestive of “dominant covalency” in TiX bonds with the exception of Ti-O bonds. In a more recent investigative endeavour, Mizuno and co-workers computed bond overlap population densities and densities of states for a host of TiX compounds (where X could be B, C, N, O, Si, P or S) using firstprinciple calculations with numerical atomic orbitals. The latter proposition is adopted in the subsequent pieces of research, since it provides an explanation for the unusual mechanical and thermal properties of TiX compounds. In an early complementary density functional theory (DFT) base study of TiC and TiN bonding, however, Blaha and co-authors suggested the possibility of a charge transfer due to orbital overlaps as an alternative mechanism pointing to covalent bonding. In their exhaustive experimental studies of TiC and TiN bonds, Dunand and collaborators reported high resolution diffraction results exploited to generate charge density plots hinting at electron transfer from metallic s and d orbitals to nonmetallic p and s orbitals, and devoid of any trace of shared electronic clouds in the interstitial regions segregating the nuclei, as is the case with ionic bonds. In contrast, the electric transport properties of TiX compounds evince sharp resemblance to metallic resistivity. ![]() Mechanical features such as high hardness and brittleness, and thermodynamic characteristics like high melting points are commonly believed to result from covalent bonding or some residual covalence in bonds of mixed nature. The mechanical, thermo-physical and dielectric properties exhibited by titanium carbide (TiC), titanium nitride (TiN) and similar titanium-metalloid (TiX) compounds, on the one hand, render the aforesaid substances appealing candidates for myriads of technological applications, and on the other hand, serve as motivation to a considerable number of investigations aiming at elucidating the nature of chemical bonds involved therein. It is also suggested that the high mechanical hardness of TiC and TiN can be explained without evoking strong covalence. ![]() Our results clearly demonstrate the dominantly ionic bonding characteristics of TiC and TiN. ![]() The ELF approach was initially validated through typical examples of covalent-bonding Diamond (C) and ionic-bonding sodium chloride NaCl. 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. Keywords: Ab Initio Calculation Chemical Bond Electron Localized Function TiC TiN 1National Research Council Canada, Aerospace Portfolio, Ottawa, CanadaĢAstronomy and Physics Department, Saint Mary’s University, Halifax, CanadaĮmail: Jrevised Septemaccepted September 15, 2012 ![]()
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