On the resolution function for powder diffraction with area detectors

In a powder diffraction experiment the resolution function defines the instrumental contribution to the peak widths as a function of the Bragg angle. The Caglioti formula is frequently applied to model the instrumental broadening and used in structural refinement. The parameters in the Caglioti formula are linked to physically meaningful parameters for most diffraction geometries. However, this link is lost for the now very popular powder diffraction geometry using large 2D area detectors. Here we suggest a new physical model for the instrumental broadening specifically developed for powder diffraction data measured with large 2D area detectors. The model is verified using data from two synchrotron diffraction beamlines with the Pilatus2M and MAR345 detectors. Finally, a functional form is proposed to replace the Caglioti formula for this geometry in the Rietveld method and profile refinements. The Caglioti function stemming from 1959 is not well suited to describing the resolution function of modern powder diffraction equipment with large 2D detectors. A new function is derived and verified, replacing the Caglioti function for this very popular geometry.