Thermal conductivity and thermoelectric power of titanium carbide single crystals

We have studied the thermal conductivity and thermoelectric power of single crystals of titanium carbide (${\mathrm{TiC}}_{\mathit{x}}$). This material crystallizes in the sodium chloride structure for a range of stoichiometries. We have investigated samples with x=0.88, 0.93, and 0.95. The thermal conductivity contains both a lattice (phonon) and an electronic component. Near room temperature the electronic component, as estimated from the Wiedemann-Franz law, comprises up to 25% of the total heat conduction in this system, but this value decreases as the temperature is lowered, and below 100 K nearly all of the heat is carried by lattice vibrations. Though not playing a direct role in the heat conduction at low temperatures, the carriers are nevertheless effective scatterers of lattice vibrations in this regime and are primarily responsible for limiting the phonon thermal conductivity below 100 K. At higher temperatures, the lattice conductivity is limited mainly by carbon-vacancy scattering and phonon-phonon umklapp processes. The thermopower of these crystals deviates significantly from that expected for a simple electron-diffusion process. This behavior is shown to be quantitatively consistent with scattering of the s-band transport electrons into d states as described by Mott’s model of transport in transition metals.