Rietveld refinement of powder X-ray diffraction data on nanocrystalline anatase samples prepared using various sol–gel methods showed that the samples contained high concentrations (up to 20%) of Ti vacancies, and that these levels decreased with increasing crystallite size. Debye-function modelling of anatase clusters having various well-defined sizes, shapes and stoichiometries confirmed that the Ti vacancy concentrations obtained by Rietveld refinement were correct. However, the Debye modelling showed that, for nanocrystals smaller than about 4nm, Rietveld modelling gave artificially high cell parameters. Density function theory calculations showed that the Ti vacancies were stable defects when the vacancy sites were charge-balanced by the incorporation of protons.

Titanium Vacancy Defects in Sol–Gel Prepared Anatase. I.E.Grey, N.C.Wilson: Journal of Solid State Chemistry, 2007, 180[2], 670-8