X-ray diffraction computed tomography

XRD-CT employs a monochromatic pencil beam scanning approach and captures the diffraction signal in transmission geometry, producing a diffraction projection dataset. In this setup, the sample moves along an axis perpendicular to the beam's direction. It is illuminated with a monochromatic finely collimated or focused "pencil" X-ray beam. A 2D area detector then records the scattered X-rays, optimizing for best counting statistics and speed. Typically, the translational scan's size surpasses the sample's diameter, ensuring its full coverage at all assessed angles. The size of the translation step is commonly aligned with the X-ray beam's horizontal size. In a perfect scenario for any pencil-beam scanning tomographic method, the measured angles should match the number of translation steps multiplied by π/2, adhering to the Nyquist sampling theorem. However, this number can often be reduced in practice be equal to the number of translation steps without substantially compromising the quality of reconstructed images. The usual angular range spans from 0 to π.

In most studies, the predominant data reconstruction approach is the 'reverse analysis' introduced by Bleuet et al.[9] where each sinogram is treated independently yielding a new CT image. Most oftern the filtered back projection reconstruction algorithm [10] is employed to reconstruct the XRD-CT images. The outcome is an image in which every pixel, or more accurately voxel, equates to a local diffraction pattern. The reconstructed data can also be seen as a stack of 2D square images, where each image corresponds to an X-ray scattering angle.

XRD-CT makes the following assumptions:

• The sample is small and there are no significant parallax artefacts in the acquired diffraction data; when this assumption is not valid the reconstructed patterns contain a wide range of artefacts, such as inaccurate peak positions, peak shapes and even arteficial peak splitting
• The acquired XRD data are powder diffraction-like and do not contain spotty data
• The sample is not strongly absorbing the X-rays and there are no significant self-absorption problems in the acquired data
• The chemistry of the sample is not changing significantly during the XRD-CT scan

In practise, one or more of these assumptions are not valid and the data suffer from artefacts. There are strategies to remove or significantly all of these artefacts:

• Rather than employing the filtered back projection reconstruction algorithm to reconstruct the XRD-CT images, it is possible to use another reconstruction approach, termed "Direct Least Squares Reconstruction" (DLSR) to perform simultaneously peak fitting and tomographic reconstruction which takes into account the geometry of the experimental setup and yields parallax artefact-free reconstructed images.[11] Performing a 0 to 2π XRD-CT scan instead of 0 to π can lead to reconstructed patterns with accurate peak position but not peak shape.
• Spotty 2D XRD data acquired during the XRD-CT scan lead to streak or line artefacts in the reconstructed XRD-CT data; it is possible to remove or suppress these artefacts by applying filters during the azimuthal integration of the raw 2D diffraction patterns[12]
• The data can be corrected for self-absorption artefacts using an X-ray absorption-contrast CT scan of the same sample.
• If the solid-state chemistry of the sample is changing during the XRD-CT scan, then other data acquisition approaches can be employed that can improve the temporal resolution of the method, such as the interlaced approach[13][14]

Analyzing the local diffraction patterns can range from basic single-peak sequential batch fitting to a comprehensive one-step full-profile analysis, known as 'Rietveld-CT' (Wragg et al., 2015 [15]). The latter method stands out for its efficiency over the typical sequential method since it shares global parameters across all local models. Examples of these parameters include zero error and instrumental broadening, which enhance the refinement process's stability. To elaborate, each voxel in the restructured images is made up of a local model (like multi-phase scale factors, lattice parameters, and crystallite sizes) tailored to match the corresponding local diffraction pattern. This implies that only the overarching parameters are consistent across local models. However, the application of Rietveld-CT has been limited to small images, specifically those of 60 × 60 voxels, with the feasibility for larger images hinging on the computer memory available. Most often though full profile analysis of the local diffraction patterns is performed on a pixel-by-pixel or line-by-line basis using conventional XRD data analysis methods, such LeBail, Pawley and Rietveld. All these methods employ fitting based on the restructured diffraction patterns. Another approach which is also computational expensive is the DLSR which performs the tomographic data reconstruction and peak fitting in a single step.[11] Regardless of the chosen analytical method, the final output comprises images filled with localized physico-chemical information. Each physico-chemical image corresponds to the refined parameters present in the local models, which might include maps that correspond to scale factors, lattice parameters, and crystallite sizes.

• X-ray diffraction
• computed tomography
• powder diffraction
• 3DXRD
• synchrotron