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

Abstract

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)~Å along $⟨1,0,0⟩$ towards the vacancy while metal ions neighbouring a vacancy shift by 0.269(2)~Å along $⟨1,1,1⟩$ away from the vacancy. The neutron 3D-$\Delta$PDF shows a tendency for vacancies to cluster along $⟨\frac{1}{2},\frac{1}{2},\frac{1}{2}⟩$, which results in 6-fold coordinated metal ions.