Electron microscopy
 
4mm Symmetry in Electron Diffraction Patterns
- Practical Electron Microscopy and Database -
- An Online Book -
Microanalysis | EM Book                                                                                   http://www.globalsino.com/EM/        

=================================================================================

 

Figure 3001a shows 4mm net symmetry in ZOLZ [001] zone-axis of cubic Zr41Ti14Cu12.5Ni10Be22.5 with space group Fm-3m.

4mm net symmetry in ZOLZ in [001] zone-axis of Zr41Ti14Cu12.5Ni10Be22.5

Figure 3001a.  4mm net symmetry in ZOLZ [001] zone-axis of cubic Zr41Ti14Cu12.5Ni10Be22.5 ( a = 1.185 nm) [1].

Figure 3001b shows the CBED pattern of β-pyrochlore oxide superconductor KOs2O6 along the [001] zone axis. [2] 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 3001b. CBED pattern taken from a KOs2O6 crystal along [001] zone axis. [2]

4mm1R is the only possible diffraction group symmetry with a 4mm whole pattern symmetry for the cubic <100>, <010> and <001> zone axes. In this case, the only crystal point group which permits a 4mm1R diffraction group symmetry is m-3m.

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.

 

 

 

 

[1] Q. Wei, N. Wanderka, P. Schubert-Bischoff, and M-P. Macht, S. Friedrich, Crystallization phases of the Zr41Ti14Cu12.5Ni10Be22.5 alloy after slow solidification, J. Mater. Res., 15 (8) 1729, (2000).
[2] 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.

 


=================================================================================