Instrumental broadening and the radial pair distribution function with 2D detectors

The atomic pair distribution function (PDF) is a real-space representation of the structure of a material. Experimental PDFs are obtained using a Fourier transform from total scattering data which may or may not have Bragg diffraction peaks. The determination of Bragg peak resolution in scattering data from the fundamental physical parameters of the diffractometer used is well established, but after the Fourier transform from reciprocal to direct space, these contributions are harder to identify. Starting from an existing definition of the resolution function of large-area detectors for X-ray diffraction, this approach is expanded into direct space. The effect of instrumental parameters on PDF peak resolution is developed mathematically, then studied with modelling and comparison with experimental PDFs of LaB 6 from measurements made in different-sized capillaries.