Deconvolution of instrumental aberrations for synchrotron powder X-ray diffractometry

A method to remove the effects of instrumental aberrations from the whole powder diffraction pattern measured with a high-resolution synchrotron powder diffractometer is presented. Two types of asymmetry in the peak profiles caused by (i) the axial-divergence aberration of the diffractometer (diffractometer aberration) and (ii) the aberration of the monochromator and focusing optics on the beamline (beamline aberration) are both taken into account. The method is based on the whole-pattern deconvolution by Fourier technique combined with the abscissa-scale transformation appropriate for each instrumental aberration. The experimental powder diffraction data of LaB₆ (NIST SRM660) measured on beamline BL-4B₂ at the Photon Factory in Tsukuba have been analysed by the method. The formula of the scale transformation for the diffractometer aberration has a priori been derived from the instrumental function with geometric parameters of the optics. The strongly deformed experimental peak profiles at low diffraction angles have been transformed to sharp peak profiles with less asymmetry by the deconvolution of the diffractometer aberration. The peak profiles obtained by the deconvolution of the diffractometer aberration were modelled by an asymmetric model profile function synthesized by the convolution of the extended pseudo-Voigt function and an asymmetric component function with an empirical asymmetry parameter, which were linearly dependent on the diffraction angle. Fairly symmetric peak profiles have been obtained by further deconvolution of the empirically determined asymmetric component of the beamline aberration.