We present a simple tight-binding parametrization for TiC that is capa
ble of giving qualitatively accurate results for a range of properties
. The systematic procedure used to develop these parameters is describ
ed, and the transferability of the model is tested. We use the model t
o account for the existence of substoichiometric titanium carbide, and
the variation of its lattice constant with vacancy concentration. We
show that the unusual lattice constant trend arises from the fact that
the lattice relaxation around a vacancy is highly localized. The phys
ical origin of this localization is the strongly anisotropic strengthe
ning of bonds around a vacancy, which follows from the quantum mechani
cal nature of the bonding.