Convergent-beam X-ray crystallography

Li, C.; Zakharova, M.; Prasciolu, M.; Wong, J.C.; Fleckenstein, H.; Ivanov, N.; Zhang, W.; Butola, M.; Dresselhaus, J.L.; Aquino, I.D.G.; Egorov, D.; Middendorf, P.; Henkel, A.; Klopprogge, B.; Klemeyer, L.; Beck, T.; Yefanov, O.; Barthelmess, M.; Sprenger, J.; Oberthuer, D.; Bajt, S.; Chapman, H.N.

doi:10.1107/S1600576726005236

Figure 1
The geometry of CBXD. (a) A crystal is placed in the beam focused by an X-ray lens (here, a pair of MLLs) and the diffraction pattern is recorded on a plane pixel array detector. (b) Of all rays provided by the lens, only those that satisfy the diffracting condition for an RLP $[{\bf G}_{{hk\ell}}]$ will reflect. A ray originating from an angle $[\phi_{y}]$ to the optical axis maps to a position $[\Delta f\tan\phi_{y}]$ on a crystal defocused by $[\Delta f]$ . (c) A volume in reciprocal space (blue shading) is formed by Ewald spheres rotated over a range of $[{\bf k}_{{\rm in}}]$ wavevectors as supplied by the lens. Any $[{\bf G}_{{hk\ell}}]$ within this volume will produce a reflection, $[{\bf k}_{{\rm out}}]$ . (d) The diffraction condition for $[{\bf G}_{{hk\ell}}]$ is satisfied for all wavevectors that lie on a Kossel circle $[{\bf k}_{\rm K}(\chi)]$ (shown in orange) in a plane perpendicular to and bisecting $[{\bf G}_{{hk\ell}}]$ . A Bragg streak and a deficiency line are generated if $[{\bf k}_{\rm K}(\chi)]$ passes through the lens aperture. (e) The deficiency line (in the projected lens pupil) and Bragg streak are approximately parallel on the detector and separated by an angle $[2\theta_{\rm B}]$ . (f) Crystal diffraction for a given incident ray path is found by integrating over all paths $[L_{{\rm in}}+L_{{\rm out}}]$ for all possible scattering locations s₀ along the incident path, assuming single scattering.

JOURNAL OF
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ISSN: 1600-5767

Volume 59| Part 4| August 2026| Pages 1200-1218

https://doi.org/10.1107/S1600576726005236

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