Alternative Diffusion Models

Studies on the effect of p(O2) on the chemical diffusion coefficient (1173 K-1373 K) for undoped TiO2 single crystal were also reported by Lee and Yoo [37]. The

interpretation of their diffusion data is based on their electrical conductivity versus рСОг) dependencies, which revealed three slopes of log о versus log pfO^, includ­ing -1/6, -1/5, and -1/4 at high, medium, and low p/O^ ranges, respectively. Their equilibration time is limited to 1500 s.

In reduced conditions, the data of Lee and Yoo [37] exhibits a linear dependence of log Dchem versus log p(O2), which is similar to that in Figure 6.9. Lee and Yoo reported that their equilibration kinetics data in oxidizing conditions [p(O2) > 10 Pa] involves double-fold kinetics, including the faster kinetics within 0-200 s and the slower kinetics in the range 200-1000 s. The time range related to the experiment of Lee and Yoo [37], including the faster and slower kinetics, corresponds to the case of Kinetics Regime I observed by Nowotny et al. [29, 31]. According to Lee and Yoo [37], the related double-fold kinetic data is determined by the transport of oxygen vacancies (slower defects) and titanium interstitials (faster defects). The chemical diffusion data of Lee and Yoo [37] at 1273 K are shown in Figure 6.19 along with the data of Nowotny et al. [28] determined in the Kinetics Regime I at the same tempera­ture (1273 K). As seen, the data of Lee and Yoo is scattered around certain areas, which are shaded in Figure 6.19. The difference between the upper and the lower areas, which according to Lee and Yoo [37] is related to the diffusion of tetravalent titanium interstitials and oxygen vacancies, respectively, is by the factor of about 2. At the same time, the scatter is close to one order of magnitude. It is interesting to note, that despite different models applied in the interpretation of the equilibration kinetics, the diffusion data obtained by Lee and Yoo [37] and Nowotny et al. [28] are similar in their absolute values.

6.2 CONCLUDING REMARKS

Knowledge of the mass transport kinetics, described by the diffusion data, is essential in the processing of oxide semiconductors using gas/solid and solid/solid reactions. Knowledge of this data is essential in the selection of optimal processing conditions in order to form the systems that are well defined in terms of either uniform distri­bution of specific lattice species (extrinsic and intrinsic) or controlled concentration gradients.

The self diffusion data, describing the transport kinetics of ions and atoms (both intrinsic and extrinsic) are essential in the assessment of the transport kinetics in the absence of chemical potential gradient. On the other hand, the chemical diffusion
data are needed for the selection of temperature and time required for the removal of chemical concentration gradients imposed during equilibration.

Lack of knowledge of diffusion data may lead to the formation of specimens that exhibit undesired concentration gradients or, in certain cases, intergranular precipi­tates. The schematic representation of the effect of doping on possible distribution of dopants is shown in Figure 6.20 [38]. The first doping represents the deposition of small islets on the surface at the absence of surface and bulk diffusion (Figure 6.20a). The effect of this kind of doping on properties depends on the surface coverage, the size of the islets and the nature of the interface formed between the islets and the TiO2 grain. This form of doping was reported in the studies of the effect of WO3 on the properties of the WO3/TiO2 system [39]. Figure 6.20b represents the dopant forming a thin surface layer and a grain boundary layer while the bulk remains undoped. The third doping process (Figure 6.20c), which involves limited lattice penetration, results in the formation of strong concentration gradients in the vicinity of grain boundaries. Figure 6.20d represents limited lattice penetration leading to the formation of compo­sitional gradients within the grains. Figure 6.20e represents the system in equilibrium. Such system is well defined in terms of uniform distribution of the dopant.

Diffusion data in oxides, such as rutile, depend on nonstoichiometry and the related oxygen-to-titanium ratio. Therefore, the diffusion data are well defined when the specimen is equilibrated with the gas phase of controlled oxygen activity. Most of the diffusion data available so far concern TiO2 that is equilibrated with respect to fast defects; oxygen vacancies and titanium interstitials. It is important to note, however, that the properties of TiO2 are strongly influenced by the concentration of titanium vacancies as well. So far, little is known on the effect of these defects on self diffusion data. Therefore, the available diffusion data for TiO2 require verification on the effect of titanium vacancies.