  Three dimensional difference pair distribution functions from X-ray and
neutron diffraction experiments are reported for yttria stabilized zirconia
(Zr$_{0.82}$Y$_{0.18}$O$_{1.91}$). We use a quantitative analysis of the
signatures in the 3D-$\Delta$PDFs to establish that oxygen ions neighbouring a
vacancy shift by 0.515(5)~\AA\ along $\langle 1,0,0 \rangle$ towards the
vacancy while metal ions neighbouring a vacancy shift by 0.269(2)~\AA\ along
$\langle 1,1,1 \rangle$ away from the vacancy. The neutron 3D-$\Delta$PDF shows
a tendency for vacancies to cluster along $\langle
\frac{1}{2},\frac{1}{2},\frac{1}{2}\rangle$, which results in 6-fold
coordinated metal ions.
