4mm Symmetry in Electron Diffraction Patterns  Practical Electron Microscopy and Database   An Online Book  

Microanalysis  EM Book http://www.globalsino.com/EM/  


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Figure 3001a shows 4mm net symmetry in ZOLZ [001] zoneaxis of cubic Zr_{41}Ti_{14}Cu_{12.5}Ni_{10}Be_{22.5} with space group Fm3m. Figure 3001a. 4mm net symmetry in ZOLZ [001] zoneaxis of cubic Zr_{41}Ti_{14}Cu_{12.5}Ni_{10}Be_{22.5} ( a = 1.185 nm) [1].
Figure 3001b shows the CBED pattern of βpyrochlore oxide superconductor KOs_{2}O_{6} along the [001] zone axis. [2] The square array with small dark disks near the center is zeroorder Laue zone (ZOLZ) and the surrounding circle formed by the highly contrasted disks is firstorder Laue zone (FOLZ). The magnified image of the inset presents a fourfold rotational symmetry along the c* axis and two mirror symmetries m_{a} and m_{b}, indicating that the whole pattern (WP) has 4mm symmetry. Figure 3001b. CBED pattern taken from a KOs_{2}O_{6} crystal along [001] zone axis. [2] 4mm1_{R} 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 4mm1_{R} diffraction group symmetry is m3m. Note that the projectiondiffraction symmetry can never be lower than the wholepattern symmetry since the wholepattern symmetry reflects the symmetry of the full threedimensional (3D) crystal.
[1] Q. Wei, N. Wanderka, P. SchubertBischoff, and MP. Macht, S. Friedrich, Crystallization phases of the Zr41Ti14Cu12.5Ni10Be22.5 alloy after slow solidification, J. Mater. Res., 15 (8) 1729, (2000).


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