Quantitative powder diffraction using a (2+3) surface diffractometer and an area detector

TL;DR

This paper presents methods for converting surface diffractometer data into meaningful powder diffraction intensities, enabling profile refinement and analysis with enhanced control over scattering vectors.

Contribution

It provides detailed angle calculations and correction factors for (2+3) surface diffractometers with area detectors, facilitating direct use of measured intensities in powder diffraction analysis.

Findings

Derived correction factors for meaningful intensity calculation

Discussed limitations related to texture, refraction, and resolution

Enabled direct profile/Rietveld refinement with surface diffractometer data

Abstract

X-ray diffractometers primarily designed for surface x-ray diffraction are often used to measure the diffraction from powders, textured materials, and fiber-texture samples in so-called $2\theta$ scans. Unlike high-energy powder diffraction only a fraction of the powder rings is typically measured and the data consists of many detector images across the $2\theta$ range. Such diffractometers typically scan in directions not possible on a conventional lab-diffractometer, which gives enhanced control of the scattering vector relative to the sample orientation. There are, however, very few examples where the measured intensity is directly used, such as for profile/Rietveld refinement, as is common with other powder diffraction data. Although the underlying physics is known, converting the data is time-consuming and the appropriate corrections are dispersed across several publications, often not with powder diffraction in mind. In this paper we present the angle calculations and correction factors required to calculate meaningful intensities for $2\theta$ scans with a (2+3)-type diffractometer and an area detector. We also discuss some of the limitations with respect to texture, refraction, and instrumental resolution, and what kind of information one can hope to obtain.