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CBED can be used to determine the symmetry of crystals:
i) Rotational axes can be observed directly in CBED patterns when the electron beam is aligned with the ratational axis.
ii) 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.
iii) 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.
iv) At Bragg condition, a horizontal mirror plane or glide plane leads to a centric distribution of intensity in every CBED disk.
v) Horizontal three, four, and sixfold axes do not induce useful CBED symmetries.
For instance, the symmetry, including the space group, of βpyrochlore oxide superconductor KOs_{2}O_{6} was determined by CBED technique (see page1903 for details).
Table 2694 lists the CBED pattern symmetries, showing diffractiongroup identification from bright field pattern (BP), whole pattern (WP), dark field pattern (DP) and ±g experimental diffraction pattern symmetries.
Table 2694. CBED pattern symmetries.
Diffraction group 
Bright field 
Whole pattern 
Dark field 
±G 
Projection diffraction group 
General 
Special 
General 
Special* 
1 
1 
1 
1 
none 
1 
none 
1_{R} 
1_{n}

2 
1 
2 
none 
1 
none 
2

2 
2 
1 
none 
2 
none 
21_{R} 
2_{R} 
1

1 
1 
none 
2_{R} 
none 
21_{R}

2 
2 
2 
none 
21_{R} 
none 
m_{R}

m 
1 
1 
m 
1 
m_{R} 
m1_{R} 
m

m 
m 
1 
m 
1 
m 
m1_{R}

2mm 
m 
2 
2mm 
1 
m1_{R} 
2m_{R}m_{R} 
2mm 
2 
1 
m 
2 
 
2mm1_{R} 
2mm

2mm 
2mm 
1 
m 
2 
 
2_{R}mm_{R}

m 
m 
1 
m 
2_{R} 
 
2mm1_{R}

2mm 
2mm 
2 
2mm 
21_{R} 
 
4

4 
4 
1 
none 
2 
none 
41_{R} 
4_{R}

4 
2 
1 
none 
2 
none 
41_{R}

4 
4 
2 
none 
21_{R} 
none 
4m_{R}m_{R}

4mm 
4 
1 
m 
2 
 
4mm1_{R} 
4mm

4mm 
4mm 
1 
m 
2 
 
4_{R}mm_{R}

4mm 
2mm 
1 
m 
2 
 
4mm1_{R}

4mm 
4mm 
2 
2mm 
21_{R} 
 
3

3 
3 
1 
none 
1 
none 
31_{R} 
31_{R}

6 
3 
2 
none 
1 
none 
3m_{R}

3m 
3 
1 
m 
1 
m_{R} 
3m1_{R} 
3m

3m 
3m 
1 
m 
1 
m 
3m1_{R}

6mm 
3m 
2 
2mm 
1 
m1_{R} 
6

6 
6 
1 
none 
2 
none 
61_{R} 
6_{R}

3 
3 
1 
none 
2_{R} 
none 
61_{R}

6 
6 
2 
none 
21_{R} 
none 
6m_{R}m_{R}

6mm 
6 
1 
m 
2 
 
6mm1_{R} 
6mm

6mm 
6mm 
1 
m 
2 
 
6_{R}mm_{R}

3m 
3m 
1 
m 
2_{R} 
 
6mm1_{R}

6mm 
6mm 
2 
2mm 
21_{R} 
 
* where dashes appears in column 7, the special symmetries can be deduced from columns 5 and 6 of this table (or from Table 1 in [1, 2]). 
As an example of CBED applications, Figure 2694 (a) shows a CBED diffraction pattern from a [111] zoneaxis Si crystal. The nonuniform intensity within the CBED discs as well as the lines and features inside the discs can be extremely useful in analysis of crystal structure. The symmetry of the patterns within the discs can be used to determine the point group symmetry of the crystal structure. The 6fold rotational symmetry of the white discs in the CBED pattern matchs the conventional FCC diffraction pattern as shown in Figure 2694 (b). Furthermore, CBED patterns are capable of providing information about the third dimension of crystals, but not just the twodimensional projections. In Figure 2694 (a), a bright ring with dashed spots marked by the red arrow presents 3fold rotational symmetry. However, this 3fold symmetry cannot be shown in conventional diffraction pattern, indicated by Figure 2694 (b). On the other hand, the rings of intensity fringes shown in the inset are related to the specimen thickness.


(a) 
(b) 
Figure 2694. (a) CBED diffraction pattern from a [111] Si crystal obtained at small (main
pattern) and large (inset) cameralengths, [3] and (b) Conventional single crystal
diffraction pattern from [111] Si, showing 6fold symmetry. 
[1] B. F. Buxton et al., Proc. R. Soc. Lond. A281, 188 (1976).
[2] B. F. Buxton et al., Philos. Trans. R. Soc. Long. A281, 171 (1976).
[3] D. B. Williams: Practical Analytical Electron Microscopy in Materials
Science (Philips Electron Optics Publishing Group, Mahwah, NJ
1984). Figure reprinted with the courtesy of FEI Company.
