Electrical conductivity below 3 K of slightly reduced oxygen-deficient rutileTiO2−x

From electrical resistivity and Hall coefficient measurements below 3 K on slightly reduced, semiconductive rutile single crystals with oxygen deficiencies ${\mathit{O}}_{\mathit{d}}$ between 3.7×${10}^{18}$/${\mathrm{cm}}^3$ and 5.5×${10}^{19}$/${\mathrm{cm}}^3$, it is concluded that the electrical conduction takes place by means of a defect-level permutation conduction mechanism involving Ti interstitial donors. In the range of 3.7×${10}^{18}$/${\mathrm{cm}}^3$≤${\mathit{O}}_{\mathit{d}}$≤2×${10}^{19}$/${\mathrm{cm}}^3$ the electrical resistivity decreases with increasing ${\mathit{O}}_{\mathit{d}}$, while in the range of 2×${10}^{19}$/${\mathrm{cm}}^3$≤${\mathit{O}}_{\mathit{d}}$≤5.5×${10}^{19}$/${\mathrm{cm}}^3$ it increases with increasing ${\mathit{O}}_{\mathit{d}}$. Values of ${\mathit{O}}_{\mathit{d}}$ between 8×${10}^{18}$/${\mathrm{cm}}^3$ and 2×${10}^{19}$/${\mathrm{cm}}^3$ correspond to the so-called intermediate concentration range of the impurity (defect) conduction, but the transition to metallic-type conduction does not occur because of a change in the defect structures, i.e., the formation of planar defects and the clustering of Ti interstitial donors at higher oxygen deficiencies.