Electron microscopy
Dynamical Extinction Lines in CBED Patterns
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Figure 1586 (a) shows the CBED pattern of β-pyrochlore oxide superconductor KOs2O6 along the [001] zone axis. [1] The square array with small dark disks near the center is zero-order Laue zone (ZOLZ) and the surrounding circle formed by the highly contrasted disks is first-order Laue zone (FOLZ). The magnified image of the inset presents a four-fold rotational symmetry along the c* axis and two mirror symmetries ma and mb, indicating that the whole pattern (WP) has 4mm symmetry. According to the general relationship among WPs, diffraction groups (DGs) and point groups (PGs) shown in a table in page2693, the diffraction groups for WP of 4mm symmetry is either 4mm or 4mm1R. The former is consistent with a non-centrosymmetric PG of 4mm (tetragonal structure), and the latter with a centrosymmetric PG of m-3m (cubic structure) or 4/mmm (tetragonal structure). Assuming the crystal system of KOs2O6 is cubic (confirmed by XRD), the PG can only m-3m.

Given the KOs2O6 crystal is in Fd-3m space group, in the magnified, indexed ZOLZ pattern in Figure 1586, the bright broad lines (indicated by the white arrows) are suggested at the position of 200-type reflections that are forbidden in Fd-3m. Such lines are called dynamical extinction lines in CBED patterns, which appear at the kinematically forbidden reflections caused by glide planes or screw axes due to dynamical diffraction at certain incident directions. For the KOs2O6 Fd-3m crystal, the presence of the dynamical extinction lines provides direct evidence of the existence of a d-glide symmetry. [2]

CBED pattern taken from a KOs2O6 crystal along [001] zone axis

Figure 1586. (a) CBED pattern taken from a KOs2O6 crystal along [001] zone axis. (b) Magnified pattern of the ZOLZ from (a). [1]






[1] Jun-Ichi Yamaura, Zenji Hiroi, Kenji Tsuda, Koichi Izawa, Yasuo Ohishi, Satoshi Tsutsui, Re-examination of the crystal structure of the β-pyrochlore oxide superconductor KOs2O6 by X-ray and convergent-beam electron diffraction analyses, Solid State Communications 149 (2009) 31-34.
[2] M. Tanaka, M. Terauchi, Convergent-Beam Electron Diffraction, JEOL-Maruzen, Tokyo, 1985.