Cerium oxide, or ceria, is an important material for solid oxide fuel cells and water splitting devices. Although the ceria surface is active in catalytic and electrochemical reactions, how its catalytic properties are affected by the surface structure under operating conditions is far from understood. We investigate the structure of the coherently strained $\mathrm{Ce}{\mathrm{O}}_{2}$ ultrathin films on yttria-stabilized zirconia (001) single crystals by specular synchrotron x-ray diffraction (XRD) under oxidizing conditions as a first step to study the surface structure in situ. An excellent agreement between the experiment data and the model is achieved by using a ``stacks and islands'' model that has a two-component roughness. One component is due to the tiny clusters of nanometer scale in lateral dimensions on each terrace, while the other component is due to slightly different $\mathrm{Ce}{\mathrm{O}}_{2}$ thickness that span over hundreds of nanometers on neighboring terraces. We attribute the nonuniform thickness to step depairing during the thin film deposition that is supported by the surface morphology results on the microscopic level. Importantly, our model also shows that the polarity of the ceria surface is removed by a half monolayer surface coverage of oxygen. The successful resolution of the ceria surface structure using in situ specular synchrotron XRD paves the way to study the structural evolution of ceria as a fuel cell electrode under catalytically relevant temperatures and gas pressures.
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