Energy Calculations for Planar Faults in Reduced Rutile (TiOFormula)

K. Aizawa, E. Iguchi, R. J. D. Tilley
1984 Proceedings of the Royal Society A  
Calculations have been made of the energetics of reduced rutile (Ti0 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 Ti20O39, (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 Ti20O39. The calculations were made by using the polarizable point ion shell model, and by taking the electronic polarizabilities of
more » ... larizabilities of the ions in volved into account. The results show th a t the c.s. planes are preferred to vacancy discs, and th a t 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 th a t vacancy discs will be con verted 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. I t was found th a t 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 th a t c.s. planes are only favoured in crystals of high dielectric constant. I t is shown th a t electronic polarizability is of im portance in stabilizing {132} c.s. planes and th a t the polarizability of the O2-ions, in particular, is of great significance. I n t r o d u c t io n The nature of slightly sub-stoichiometric rutile (Ti0 2) has been the subject of a number of studies, which have established th a t a t greater degrees of reduction th an about Ti0 1>998 the change in anion to cation stoichiometry is accounted for by the formation of crystallographic shear (c.s.) planes. Much of the experimental evidence for this and the earlier studies have been reviewed by Anderson & Tilley (1974) and Bursill & Hyde (1972) . The previous results can be summarized by stating th a t in slightly reduced rutile the c.s. planes lie upon {132} planes. They are fairly randomly distributed a t first, bu t as reduction increases there is an increasing tendency for clusters of c.s. planes [ 299 ]
doi:10.1098/rspa.1984.0081 fatcat:amga2o47gjfpjl5ctey7tvlafe