Analysis of Diffuse Scattering from Single Crystals via the Reverse Monte Carlo Technique. II. The Defect Structure of Calcium-Stabilized Zirconia

The results of an attempt to use reverse Monte Carlo (RMC) refinement to fit a model structure to the diffuse X-ray and neutron scattering of the complex defect structure of calcium-stabilized cubic zirconia (Ca-CSZ), composition Zr_0.85Ca_0.15O_1.85, are reported. This is the first attempt to use the RMC method to analyse single-crystal diffuse scattering of a disordered system containing both chemical disorder and associated displacement disorder. The possibilities and problems of the RMC method for this kind of disordered system are discussed and the method is compared with techniques used in previous studies of the diffuse scattering of CSZs. The study has revealed that the application of RMC to single-crystal data needs to take into account two seemingly incompatible requirements. When the model crystal is large, relatively low-noise calculated diffraction patterns can be obtained but the model contains so many degrees of freedom that the fit obtained does not properly reflect the short-range properties inherent in the data. On the other hand, when the model crystal is small the calculated patterns are very noisy and the efficacy of the fit is again compromised. Despite these limitations the results obtained in the present study do appear to present a qualitative picture of the local ordering consistent with previous studies. The present RMC refinements of Ca-CSZ support the previously postulated oxygen-vacancy ordering scheme, i.e. vacancy pairs separated by 1/2〈111〉 along the body diagonal of oxygen cubes which contain a cation. The cations are disturbed from their average positions in such a way that if either of the two bridging oxygen sites between a pair of cations separated by 1/2〈110〉 is vacant, then the cations are found to have moved further apart than the average distance, whereas when both bridging oxygen sites are occupied a closer than average distance is observed. A new result from this RMC study is that a negative occupancy correlation exists between Ca neighbours separated by 1/2〈110〉 and 〈100〉, i.e. there is a tendency to avoid Ca-Ca nearest or next-nearest neighbours.