Notes on the handling of position and broadening errors in deconvoluted X-ray diffraction line profiles

In deconvolution procedures of X-ray diffraction line profiles, a non-ideal standard specimen often has to be used to measure the broadening due to the instrumental aberrations and the X-ray spectrum used. This leads to a non-ideal standard line profile at an incorrect sin 0 range with an incorrect broadening. Large errors in the structural parameters to be determined may result. These errors can be minimized by choosing a proper origin for the evaluation of the Fourier series of the line profiles measured. Rules are presented for the necessary shifts of the origin of a non-ideal standard line profile compared to the origin of the line profile to be analyzed. If these shifts of origin are carried out, errors are still present from the difference in broadening between ideal and non-ideal standard specimens. Simple correction factors are presented to eliminate also these errors. The treatment is given for non-ideal standard specimens with (i) an incorrect spacing, (ii) an incorrect specimen transparency and (iii) remaining structural defects.