Generating the atomic pair distribution function without instrument or emission profile contributions

A method for generating the atomic pair distribution function (PDF) from powder diffraction data by the removal of instrument contributions, such as K α 2 from laboratory instruments or peak asymmetry from neutron time-of-flight data, has been implemented in the computer programs TOPAS and TOPAS-Academic . The resulting PDF is sharper, making it easier to identify structural parameters. The method fits peaks to the reciprocal-space diffraction pattern data whilst maximizing the intensity of a background function. The fit to the raw data is made `perfect' by including a peak at each data point of the diffraction pattern. Peak shapes are not changed during refinement and the process is a slight modification of the deconvolution procedure of Coelho [ J. Appl. Cryst. (2018), 51 , 112–123]. Fitting to the raw data and subsequently using the calculated pattern as an estimation of the underlying signal reduces the effects of division by small numbers during atomic scattering factor and polarization corrections. If the peak shape is sufficiently accurate then the fitting process should also be able to determine the background if the background intensity is maximized; the resulting calculated pattern minus background should then comprise coherent scattering from the sample. Importantly, the background is not allowed complete freedom; instead, it comprises a scan of an empty capillary sample holder with a maximum of two additional parameters to vary its shape. Since this coherent scattering is a calculated pattern, it can be easily recalculated without instrumental aberrations such as capillary sample aberration or K α 2 from laboratory emission profiles. Additionally, data reduction anomalies such as incorrect integration of data from two-dimensional detectors, resulting in peak position errors, can be easily corrected. Multiplicative corrections such as polarization and atomic scattering factors are also performed. Once corrected, the pattern can be scaled to produce the total scattering structure factor F ( Q ) and from there the sine transform is applied to obtain the pair distribution function G ( r ).