  Understanding the electronic charge distribution around oxygen vacancies in
transition metal and rare earth oxides is a scientific challenge of
considerable technological importance. We show how significant information
about the charge distribution around vacancies in cerium oxide can be gained
from a study of high resolution crystal structures of higher order oxides which
exhibit ordering of oxygen vacancies. Specifically, we consider the
implications of a bond valence sum analysis of Ce$_{7}$O$_{12}$ and
Ce$_{11}$O$_{20}$. To illuminate our analysis we show alternative
representations of the crystal structures in terms of orderly arrays of
co-ordination defects and in terms of flourite-type modules. We found that in
Ce$_{7}$O$_{12}$, the excess charge resulting from removal of an oxygen atom
delocalizes among all three triclinic Ce sites closest to the O vacancy. In
Ce$_{11}$O$_{20}$, the charge localizes on the next nearest neighbour Ce atoms.
Our main result is that the charge prefers to distribute itself so that it is
farthest away from the O vacancies. This contradicts \emph{the standard picture
of charge localisation} which assumes that each of the two excess electrons
localises on one of the cerium ions nearest to the vacancy. This standard
picture is assumed in most calculations based on density functional theory
(DFT). Based on the known crystal structure of Pr$_{6}$O$_{11}$, we also
predict that the charge in Ce$_{6}$O$_{11}$ will be found in the second
coordination shell of the O vacancy. Although this review focuses on bulk
cerium oxides our approach to characterising electronic properties of oxygen
vacancies and the physical insights gained should also be relevant to surface
defects and to other rare earth and transition metal oxides.
