Distinguishing space groups by electron channelling: centrosymmetric full-Heusler or non-centrosymmetric half-Heusler?

Hansen, V.; Kosinskiy, A.; Taftø, J.

doi:10.1107/S2053273319016942

Acta Crystallographica Section A
Acta Crystallographica
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Figure 2
(a), (b) Two-beam calculations of the wavefield modulation for the centrosymmetric model, space group $[Fm{\overline 3}m]$ (No. 225), with the Bragg condition fulfilled for (a) the $[{\overline 1}{\overline 1}{\overline 1}]$ reflection and (b) the 111 reflection. (c), (d) Similarly for the non-centrosymmetric model, space group $[F{\overline 4}3m]$ (No. 216). In the analytical calculations for both the centrosymmetric and non-centrosymmetric models, the origin is chosen at the same position within the figure (vertical dotted line). The origin for both models is at the position resulting in a real and positive structure factor for the 111 reflection (and thus also for the $[{\overline 1}{\overline 1}{\overline 1}]$ reflection). This origin is in the Sn plane in the centrosymmetric model and the crystal had to be shifted by 25°/360° parts on the repetition unit for the non-centrosymmetric model.

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ISSN: 2053-2733

Volume 76| Part 2| March 2020| Pages 211-213

https://doi.org/10.1107/S2053273319016942

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