Calculations were made of the energetics of reduced rutile crystals containing (a) an isolated {132} crystallographic shear plane, (b) an ordered array of {132} crystallographic shear planes corresponding to an oxide of composition Ti20O39, (c) a vacancy disc lying on {132} planes and (d) an ordered array of vacancy discs lying on {132} planes, which gave the crystal a composition of Ti20O39. The calculations were performed by using the polarizable point ion shell model, and by taking the electronic polarizabilities of the ions into account. The results showed that the crystallographic shear planes were preferred to vacancy discs, and that this was largely due to the electronic polarization energy terms. The enthalpy of formation of an isolated {132} crystallographic shear plane in rutile was calculated. A comparison with an estimate of the enthalpy of formation of the vacancy disc suggested that vacancy discs would be converted into crystallographic shear planes in real crystals and would not exist as discrete defects. The change in the energy terms as the polarizabilities of the ions varied was also calculated in order to quantify the relationship between preferred defect structure and dielectric constant. It was found that a change in dielectric constant did not have a significant effect upon the stability of vacancy discs, but did have a large effect upon the energetics of crystallographic shear planes, which suggests that crystallographic shear planes were only favoured in crystals of high dielectric constant. It was shown that electronic polarizability was of importance in stabilizing {132} crystallographic shear planes and that the polarizability of the O2- ions, in particular, was of great significance.

Energy Calculations for Planar Faults in Reduced Rutile (TiO2). Aizawa, K., Iguchi, E., Tilley, R.J.D.: Proceedings of the Royal Society A, 1984, 394[1807], 299-327