Accurate extrinsic and intrinsic peak broadening modelling for time-resolved in situ ball milling reactions via synchrotron powder X-ray diffraction

The debate on the mechanisms which underpin mechanochemical reactions via ball mill grinding is still open. Our ability to accurately measure the microstructural (crystal size and microstrain) evolution of materials under milling conditions as well as their phase composition as a function of time is key to the in-depth understanding of the kinetics and driving forces of mechanochemical transformations. Furthermore, all ball milling reactions end with a steady state or milling equilibrium - represented by a specific phase composition and relative microstructure - that does not change as long as the milling conditions are maintained. The use of a standard sample is essential to determine the instrumental contribution to the X-ray powder diffraction (XRPD) peak broadening for time-resolved in situ (TRIS) monitoring of mechanochemical reactions under in operando conditions. Using TRIS-XRPD on a ball milling setup, coupled with low-energy synchrotron radiation, we investigated different data acquisition and analysis strategies on a silicon standard powder. The diffraction geometry and the microstructural evolution of the standard itself have been studied to model the instrumental contribution to XRPD peak broadening throughout the grinding activity. Previously proposed functions are here challenged and further developed. Importantly, we show that minor drifts of the jar position do not affect the instrumental resolution function significantly. We here report and discuss the results of such investigations and their application to TRIS-XRPD datasets of inorganic and organic ball mill grinding reactions.