Studies of the Defect Structure of Nonstoichiometric Rutile, TiO[sub 2−x]

The electrical conductivity of single crystals of rutile was measured in the "c" and "a" directions over the temperature range 1000°–1500°C and from 1 to 10 −15 atm of oxygen. Based on the excellent fit observed between the theoretically derived relation and the experimental conductivity data, the nonstoichiometric defect structure of rutile was rationalized in terms of quasi‐free electrons and both triply and quadruply ionized titanium interstitials. In addition, this equation satisfies a contribution due to impurity conduction where is proportional to a temperature dependent concentration of ionized impurities or a contribution due to intrinsic conduction where is proportional to a temperature dependent concentration of holes in the valance band. The standard enthalpy of formation for the following defect reactions in rutile were determined from the temperature dependence of , , and obtained from the above relation and from the experimental expression for the temperature dependence of electron mobility. The values of , , and are in agreement, within experimental error, with those obtained in an earlier investigation based on conductivity measurements in the c direction only. If impurity conduction is involved, is equal to the standard enthalpy of formation for the ionization of an impurity. If intrinsic conduction is involved, is equal to the band gap energy which is thought to be between 3 and 4 ev for rutile. The ratio of electrical conductivities for the c and a direction is essentially independent of oxygen pressure above 1100°C; but at the lower temperatures, 1000° and 1100°C, the ratio is dependent on pressure in contradiction to the initial assumption that mobility is a function of temperature only.