Combining a multi-analyzer stage with a two-dimensional detector for high-resolution powder X-ray diffraction: correcting the angular scale

Abstract

In a test experiment, a two-dimensional pixel detector was mounted on the nine-channel multi-analyzer stage of the high-resolution powder diffraction beamline ID22 at the ESRF. This detector replaces a bank of scintillation counters that detect the diffracted intensity passing via the analyzer crystals as the diffractometer arm is scanned. At each diffractometer detector arm angle 2Θ, a 2D image is recorded that displays nine distinct regions of interest corresponding to the diffraction signals transmitted by each of the analyzer crystals. Summing pixels from within each region of interest allows the diffracted intensity to be extracted for each channel. X-rays are diffracted from the sample at various angles, 2θ, into Debye–Scherrer cones. Depending on the azimuthal angle around the cone, diffracted photons satisfy the analyzer-crystal Bragg condition at different diffractometer 2Θ values and arrive on the detector at different horizontal (axial) positions. The more the azimuthal angle deviates from diffraction in the vertical plane, the lower the 2Θ angle at which it is transmitted by an analyzer crystal, and the greater the distance of the detecting pixel from the centerline of the detector. This paper illustrates how the axial resolution afforded by the pixel detector can be used to correct the apparent diffraction angle, 2Θ, given by the diffractometer arm to its true diffraction angle, 2θ. This allows a reduction in peak asymmetry at low angle, and even with a relatively small axial acceptance, the correction leads to narrower peaks than if no correction is applied. By varying axial acceptance with diffraction angle, it is possible to optimize angular resolution at low diffraction angles and counting statistics at high angles. In addition, there is an intrinsic peak broadening with increasing azimuthal angle, dependent on the axial beam and detector pixel sizes. This effect reduces with 2θ, as the curvature of the Debye–Scherrer cones decreases. This broadening can be estimated and used to help choose the axial range to include as a function of diffraction angle.