Whole-powder-pattern fitting without reference to a structural model: application to X-ray powder diffraction data

The procedure of whole-powder-pattern fitting without reference to a structural model, first proposed by Pawley for use with neutron powder data [J. Appl. Cryst. (1981). 14, 357–361], was extended as a tool for analyzing X-ray whole-powder data. X-ray data for α-SiO₂, α-Al₂O₃ and CaCO₃ used as test samples were first analyzed by individual profile-fitting techniques to establish the angle-dependent profile-shape model. Then the results were incorporated into the profile model of whole-powder-pattern fitting, where peak maximum positions of individual reflections are a function of unit-cell parameters while integrated intensities are independent variables. Whole-powder-pattern fits for the test samples showed that the correction for peak shift has a large influence on the overall fit of the pattern and the accuracy of refined parameters. It is also important to take into account the asymmetry and the angular dependence of the intensity decay rate in modelling the diffraction profile. The method developed was applied to an analysis of the powder pattern of a mixed monoclinic tetragonal ZrO₂.