Electron microscopy
Mirror Planes (m, σ) in Crystals
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The mirror planes of symmetry with Hermann-Mauguin symbol m denotes the direction normal to the mirror plane, i.e. the direction of the mirror plane is defined as the direction perpendicular to it. Note that a mirror is equivalent to roto-inversion -2.

Figure 1620a shows an example of mirror planes.

mirror plane

Figure 1620a. Example of mirror planes (from x, y, z to x, -y, z).

Mirror planes can be observed directly as mirror lines in the CBED pattern if the electron beam lies in the mirror plane of the symmetry. A vertical glide plane also results in a mirror line in the CBED pattern. At Bragg condition, a horizontal twofold axis or twofold screw axis in the ZOLZ along g presents a mirror line of symmetry onto disk g, and this line runs normal to g, and a horizontal mirror plane or glide plane leads to a centric distribution of intensity in every CBED disk.

As an example, the three space groups C2/m, C2 and Cm have the same systematic forbidden reflections which are caused by the C-centering (h+k = 2n+1). The other symmetry operations in the three space groups, e.g. 2-fold rotation axis (2) and mirror plane (m) in the C2/m space group, do not cause forbidden reflections. Other examples of mirror-plane applications are listed in Table 1620.

Table 1620. Examples of mirror-plane applications.

Applications Page on the EM book
Determination of space groups page1669

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. Figure 1620b 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.

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

Figure 1620b. CBED pattern taken from a KOs2O6 crystal along [001] zone axis. [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.