Electron microscopy
Whole-pattern symmetry
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Screw-axes and mirror planes can be deduced from CBED investigation by observing Gjönnes-Moodie (G-M) lines (or called G-M extinctions) and by determining whole-pattern (WP) symmetries, respectively. Whole-pattern symmetry [1] of electron diffraction or CBED patterns corresponds to the symmetry of the higher-order Laue zone (HOLZ) reflections and HOLZ Kikuchi lines shown in small camera length patterns and with a small convergence of beam, and presents mirror planes.

Figure 1600a shows the whole-pattern symmetry of the [0001] CBED pattern of T1 (Al2CuLi) crystals. The pattern symmetry is 6mm.

[0001] CBED patterns of T1 (Al2CuLi) crystals: whole-pattern symmetry (HOLZ)
Figure 1600a. Whole-pattern symmetry (HOLZ) of the [0001] CBED pattern of T1 (Al2CuLi) crystals. Adapted from [2]

Figure 1600b shows the CBED pattern of β-pyrochlore oxide superconductor KOs2O6 along the [001] zone axis. [3] 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.

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

Figure 1600b. CBED pattern taken from a KOs2O6 crystal along [001] zone axis. [3]

Note that the projection-diffraction symmetry can never be lower than the whole-pattern symmetry since the whole-pattern symmetry reflects the symmetry of the full three-dimensional (3-D) crystal.

Table 1600. Examples of whole-pattern applications.

Applications Page on the EM book
Determination of space groups page1669







[1] B. E Buxton, J.A. Eades, J.W. Steeds, and G.M. Rackham: Phil. Trans. Roy. Soc., vol. 281, A1301, pp. 171-94.
[2] Kenneth S. Vecchio and David B. WILLIAMS, Convergent Beam Electron Diffraction Analysis of the T1 (Al2CuLi) Phase in Al-Li-Cu Alloys, Metallurgical Transactions A, 19A, 1988-2885, (1988).
[3] 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.