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

Direct interpretation of the X-ray and neutron 3D-$\Delta$PDFs of yittria stabilized zirconia