Rietveld refinements performed on mesoporous ceria layers at grazing incidence

Seven diffraction patterns were collected on a 100 nm Gd-doped ceria layer deposited on a silicon wafer under asymmetric reflection conditions. As the grazing-incidence angle decreases, large shifts (a few tens of degrees) and broadenings (two degrees below the critical angle) of hkl reflections are apparent in the diffraction patterns. The impact of these aberrations on the positions and profiles of the Bragg peaks is studied in detail in this work. On the basis of this analysis, diffraction patterns collected at different angles of incidence could then be refined using a unique structural model. From these refinements, the evolution of the coherent diffracting domains, the strain and the microstrain can clearly be traced as a function of depth.