On the resolution function for powder diffraction with area detectors

Abstract

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.

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

“…Correspondingly, the final correction is applied according to the simplified eqn (2).For all silicon data, we observed a slight mismatch between the modelled curve and the experimental data at higher angular values. This misinterpretation of the angular position, due to the parallax effect observed with the large flat area detector, 40,51 is particularly evident for patterns acquired with a high sample displacement, namely when the jar is aligned significantly far from the ideal tangential position to the beam path. To overcome this problem, an empirical correction has been added to the sample displacement function as follows:The corrected peak split function models this further aberration in excellent detail (Fig.…”

“…Following from our recent advances on data collection and analysis for TRIS-XRPD, we questioned the limits of the functions that we used for data analysis and, in particular, how the output values extracted by the Rietveld refinements are affected by the jar alignment. We here report a detailed study on the instrumental resolution function for TRIS milling experiments (IRF, the function that defines the instrumental contribution to the peak widths as a function of the Bragg angle) 40 using data collected from a standard material under the same experimental conditions. We describe how our IRF leads to robust data analysis strategies for the evaluation of the microstructural parameters of milling reactions and transformations.…”

A multipurpose laboratory diffractometer for operando powder X-ray diffraction investigations of energy materials

“…Apart from the detector distance, the instrumental line broadening Á2 (FWHM) is also determined by other geometrical parameters, including the X-ray beam size or the sample dimensions, the pixel size with the point-spread function of the detector, and the absorption thickness of the sensitive detection layer (Chernyshov et al, 2021). In addition, the beam divergence and the wavelength dispersion of the Mo K emission line influence the peak widths of the reflections and therefore limit the angular resolution (Mendenhall et al, 2019).…”

How nanoporous silicon-polypyrrole hybrids flex their muscles in aqueous electrolytes: In operando high-resolution x-ray diffraction and electron tomography-based micromechanical computer simulations

“…The angular uncertainty δ θ of the X-ray diffraction measured at the detector can be estimated by [52] (δ θ…”