Scattering of Electrons by Vacancies in Nonstoichiometric Crystals of Titanium Carbide

A study has been made of the influence of carbon vacancies on the resistivity of titanium carbide, a refractory hard metal. Crystals were obtained with vacancies in concentrations of from 3 to 20%. The vacancies were introduced into the fcc carbon sublattice of the rock salt structure of TiC by controlling the C/Ti ratio during crystal growth. The vacancy concentration in some crystals was further reduced by preferential vaporization of Ti at high temperatures and in others by addition of {~}1% boron to release carbon to the lattice through the formation of TiB₂ precipitates. Measurements were then made of resistivity as a function of vacancy concentration at 77 and 298^∘{}K. On some samples, the Hall coefficient was also measured. The resistivity shows a monotonic increase with increasing vacancy concentration and has a large residual value, whereas the Hall coefficient is relatively independent of vacancy concentration but increases at low temperatures. The data are analyzed using Matthiessen's rule and the Bloch-Gr\"uneisen formula and interpreted using Mott's band model for transition metals. A value for the added resistivity per atomic percent carbon vacancies in TiC was obtained: 16{μ}{Ω} cm. This value is an order of magnitude larger than that for the noble metals. A four part explanation is offered: TiC has a smaller number of conduction electrons per atom, the scattering probability is higher in TiC because of the high density of states in a d-like band overlapping the s-like conduction band, the screening of a vacancy is less effective because of the smaller number of conduction electrons, and the effective charge of a vacancy is probably greater than $1e$. The room-temperature resistivity of stoichiometric TiC, as inferred in the analysis, is 70±{}10{μ}{Ω}cm.