Local atomic ordering in nanocrystalline ZrO$_{2}$ and Zr$_{x}$Ce$_{1-x}$O$_{2}$ studied with the Atomic Pair Distribution Technique.

A number of ZrO$_{2}$ and Zr$_{x}$Ce$_{1-x}$O$_{2}$ nanocrystalline samples have been prepared using different techniques, such as ball-milling (ZrO$_{2})$ and soft chemistry (ZrO$_{2}$ and Zr$_{x}$Ce$_{1-x}$O$_{2})$. The atomic-scale structure of these samples has been studied using high-energy x-ray diffraction and the atomic pair distribution function technique. For the ball-milled materials, the studies show that the parent crystalline material, monoclinic ZrO$_{2}$, evolves into a nanocrystalline phase that is locally similar to monoclinic zirconia but shows a cubic-type ordering at nanometer-range distances. The atomic-scale structure of the ZrO$_{2}$ samples obtained by soft chemistry techniques varies depending on the preparation method and the degree of structural coherence. The studies reveal that all samples show Zr-O distances typical for monoclinic-like local atomic ordering, while the Zr-Zr distances depend on the morphology of the samples. For the Zr$_{x}$Ce$_{1-x}$O$_{2}$ samples, interatomic distances typical for both monoclinic ZrO$_{2}$ and cubic CeO$_{2}$ are observed up to 5{\AA}, while the longer interatomic distances are attributed solely to a cubic-type structure. The result underlines the importance of local structural disorder and the medium-range order in stabilizing the technologically important cubic zirconia at room temperature.