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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]).
[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).
