CBED Pattern Symmetries for Crystal Determination
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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 β-pyrochlore oxide superconductor KOs2O6 was determined by CBED technique (see page1903 for details).

Table 2694 lists the CBED pattern symmetries, showing diffraction-group 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
1R
1n
2
1
2
none
1
none
2
2
2
1
none
2
none
21R
2R
1
1
1
none
2R
none
21R
2
2
2
none
21R
none
mR
m
1
1
m
1
mR
m1R
m
m
m
1
m
1
m
m1R
2mm
m
2
2mm
1
m1R
2mRmR
2mm
2
1
m
2
---
2mm1R
2mm
2mm
2mm
1
m
2
---
2RmmR
m
m
1
m
2R
---
2mm1R
2mm
2mm
2
2mm
21R
---
4
4
4
1
none
2
none
41R
4R
4
2
1
none
2
none
41R
4
4
2
none
21R
none
4mRmR
4mm
4
1
m
2
---
4mm1R
4mm
4mm
4mm
1
m
2
---
4RmmR
4mm
2mm
1
m
2
---
4mm1R
4mm
4mm
2
2mm
21R
---
3
3
3
1
none
1
none
31R
31R
6
3
2
none
1
none
3mR
3m
3
1
m
1
mR
3m1R
3m
3m
3m
1
m
1
m
3m1R
6mm
3m
2
2mm
1
m1R
6
6
6
1
none
2
none
61R
6R
3
3
1
none
2R
none
61R
6
6
2
none
21R
none
6mRmR
6mm
6
1
m
2
---
6mm1R
6mm
6mm
6mm
1
m
2
---
6RmmR
3m
3m
1
m
2R
---
6mm1R
6mm
6mm
2
2mm
21R
---
* 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] zone-axis Si crystal. The non-uniform 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 6-fold 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 two-dimensional projections. In Figure 2694 (a), a bright ring with dashed spots marked by the red arrow presents 3-fold rotational symmetry. However, this 3-fold 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.

CBED diffraction pattern from [111] Si obtained at low (main pattern) and high (inset) camera-lengths
Conventional single crystal diffraction pattern from [111] Si, showing 6-fold symmetry.
(a)
(b)
Figure 2694. (a) CBED diffraction pattern from a [111] Si crystal obtained at small (main pattern) and large (inset) camera-lengths, [3] and (b) Conventional single crystal diffraction pattern from [111] Si, showing 6-fold 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.

 

 

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