Exploiting Friedel pairs to interpret scanning 3DXRD data from complex geological materials

Jacob, J.-B.; Wright, J.; Cordonnier, B.; Renard, F.

doi:10.1107/S1600576724009634

Figure 2
Friedel pair geometry for a s3DXRD acquisition in a reference frame fixed relative to the sample. (a) Sketch of the setup, with two detector positions at angles ω and ω + 180°, and an arbitrary translation t_y of the sample relative to the rotation center. A single hkl reflection arising from the green spot in the sample at rotation angle ω is shown, together with its paired reflection hkl occurring at ω + 180°. The two incident beams $[{\bf i}_{1}]$ and $[{\bf i}_{2}]$ are thin pencil beams of negligible dimension in y and z, and are coincident. The two diffracted beams $[{\bf u}_{1}]$ and $[{\bf u}_{2}]$ are also coincident and intersect the detector at $[{\bf P}_{1}]$ and $[{\bf P}_{2}]$ , respectively. (b) View of the plane containing $[{\bf i}_{1}]$ , $[{\bf i}_{2}]$ , $[{\bf u}_{1}]$ and $[{\bf u}_{2}]$ . $[2\theta]$ is the real scattering angle between $[{\bf i}_{1}]$ and $[{\bf u}_{1}]$ (or $[{\bf i}_{2}]$ and $[{\bf u}_{2}]$ ), and η is the azimuth angle on the detector. $[2\theta_{1}]$ and $[2\theta_{2}]$ are apparent scattering angles, computed assuming that the diffracting point in the sample has no offset along the x axis, i.e. it is at distance L from the detector. h₀ is the radial distance from the detector center to the spot, which would be observed both for $[{\bf P}_{1}]$ and $[{\bf P}_{2}]$ if there was no offset along the x axis. $[\delta_{h}]$ is the offset from this position resulting from the offset $[x_{\rm l}]$ of the diffracting source along the x axis.

JOURNAL OF
APPLIED
CRYSTALLOGRAPHY

ISSN: 1600-5767

Volume 57| Part 6| December 2024|

https://doi.org/10.1107/S1600576724009634

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