On single crystal total scattering data reduction and correction protocols for analysis in direct space

We explore data reduction and correction steps and processed data reproducibility in the emerging single crystal total scattering based technique of three-dimensional differential atomic pair distribution function (3D-$\Delta$PDF) analysis. All steps from sample measurement to data-processing are outlined in detail using a CuIr$_2$S$_4$ example crystal studied in a setup equipped with a high-energy x-ray beam and a flat panel area detector. Computational overhead as it pertains to data-sampling and the associated data processing steps is also discussed. Various aspects of the final 3D-$\Delta$PDF reproducibility are explicitly tested by varying data-processing order and included steps, and by carrying out a crystal-to-crystal data comparison. We identify situations in which the 3D-$\Delta$PDF is robust, and caution against a few particular cases which can lead to inconsistent 3D-$\Delta$PDFs. Although not all the approaches applied here-in will be valid across all systems, and a more in-depth analysis of some of the effects of the data processing steps may still needed, the methods collected here-in represent the start of a more systematic discussion about data processing and corrections in this field.