Energy-band structure and binding mechanism of TiC

Energy bands have been calculated for TiC using crystal potentials based on the superposition of neutral atomic charge densities, on the superposition of charge densities from doubly ionized Ti(4s0)2+ and C(2p4)2-, and on an approximately self-consistent TiC charge distribution; decomposition of the wave functions into spherical harmonics within (touching) spheres about the Ti and C nuclei indicates in all three cases that the major contribution to the highest occupied bands is from the C-2p states, with the Ti-3d contributing a smaller amount, and the Ti-4s states contributing negligibly to the occupied states in the solid. Thus the binding is a mixture of covalent binding from bonding combinations of the C-2p and Ti-3d wave functions, and ionic binding due to the electron transfer from Ti to C. Because of the diffuse nature of the Ti-4s and C-2p wave functions involved, the spatial charge transfer is found to be much less than the number of electrons transferred from Ti to C states, however, and the simple ideas of ionicity are not appropriate to describing the characteristics of this material; the value of its “ionicity” depends strongly on the physical property being discussed.