Investigation of the Charge Distribution in Titanium Carbide Using Electromigration

The diffusion of carbon in single crystals of the compound $\mathrm{Ti}{\mathrm{C}}_x$ ($x\sim 0.9$) near 2000°C is shown to be influenced by the application of an electric field. This effect, electromigration, was studied using the electron probe microanalyzer to determine the carbon concentration profile. The effective charge $Z^{*}$ of the diffusing carbon particle was found to be positive. However, $Z^{*}$ includes both an electrostatic charge $Z$ and a term resulting from momentum exchange with the current carriers. It is argued that the momentum exchange term is small because the carrier concentration is low compared to most metals, and negative because the carriers are predominantly electrons rather than holes. Hence, the observation that $Z^{*}$ is positive indicates that $Z$ is also positive. C thus diffuses as a positive ion in TiC, though at a lattice site it may appear negative, as has been suggested by recent energy-band calculations and by electron spectroscopy and x-ray experiments, because of the overlap of Ti wave functions. An average value for the energy of motion of C (vacancies) in $\mathrm{Ti}{\mathrm{C}}_x$ of 4.8 ± 0.5 eV/atom was also obtained. This value is consistent with the results of Sarian on tracer diffusion of ${\mathrm{C}}^{14}$ in $\mathrm{Ti}{\mathrm{C}}_x$ crystals.