Energy calculations for planar faults in reduced rutile (TiO ₂ )

Abstract

Calculations have been made of the energetics of reduced rutile (TiO 2 ) crystals containing ( a ) an isolated {132} c. s. plane, ( b ) an ordered array of {132} c. s. planes corresponding to an oxide of composition Ti 20 O 39 , ( c ) a vacancy disc lying on {132} planes and ( d ) an ordered array of vacancy discs lying on {132} planes, which gives the crystal a composition of Ti 20 O 39 . The calculations were made by using the polarizable point ion shell model, and by taking the electronic polarizabilities of the ions involved into account. The results show that the c. s. planes are preferred to vacancy discs, and that this is largely due to the electronic polarization energy terms. The enthalpy of formation of an isolated {132} c. s. plane in rutile was calculated. A comparison with an estimate of the enthalpy of formation of the vacancy disc suggests that vacancy discs will be converted into c. s. planes in real crystals and will not exist as discrete defects. The change of the energy terms as the polarizabilities of the ions varied was also calculated to quantify the relation 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 on the energetics of c. s. planes, which suggests that c. s. planes are only favoured in crystals of high dielectric constant. It is shown that electronic polarizability is of importance in stabilizing {132} c. s. planes and that the polarizability of the O 2 ─ ions, in particular, is of great significance.

Correlation between high ionic conductivity and twin structure of La0.95Sr0.05Ga0.9Mg0.1O3−δ

“…[54][55][56] the ionic arrangements at the walls between the adjacent twin domains must be incoherent in comparison with ionic arrangements within the domains. In order to relax the lattice distortion due to the incoherence, segregation of the oxygen vacancies near the walls may be required: this will be proved later.…”