Geometrical equatorial aberrations in a Bragg-Brentano powder diffractometer with a linear position-sensitive detector

The use of a position-sensitive detector with a Bragg-Brentano diffractometer implies the registration of the diffracted beam at a finite distance from the true focusing point. This gives rise to an aberration which is characterized by the peak intensity profile I(y) and its parameters, the shift of the centre of gravity <y> and the profile variation W. These are calculated in terms of exact expressions and approximate results. The obtained closed formulae for <y> and W augment analogous calculations for other aberrations, tabulated by Parrish and Wilson in the International Tables for X-ray Crystallography (Vol. III, 1995). Calculation of the peak profiles is verified by experiment.