A fundamental parameters approach to X-ray line-profile fitting

A convolution approach to X-ray powder line-profile fitting is developed in which the line shape is synthesized from the Cu Kα emission profile, the dimensions of the diffractometer and the physical variables of the specimen. In addition to the integrated intensities and 2θ positions of the line profiles, the parameters that may be fitted include the receiving-slit width, the receiving-slit length, the X-ray-source size, the angle of divergence of the incident beam, the X-ray attenuation coefficient of the specimen and the crystallite size. This is a self-consistent approach to fitting as the instrumental parameters are usually known by direct measurement. To minimize correlation between refined instrumental parameters, profiles at high and low 2θ values should be fitted simultaneously. The Cu Kα emission profile used in this work is based on recent monolithic double-crystal spectrometer measurements that have identified a doublet structure in both the Kα₁ and Kα₂ components. Fast and accurate convolution procedures have been developed and a mixture of multilinear regression and Gauss–Newton non-linear least squares with numerical differentials is used for fitting the profiles. The method is evaluated by fitting powder diffraction data from well crystallized specimens of MgO and Y₃Al₅O₁₂ (YAG). Testing has also been carried out by examining the changes in the fitted values after altering various instrumental parameters (e.g. receiving-slit width, detector defocus, receiving-slit length and inclusion of a monochromator).