FourFold Rotational Symmetry & its Axis in Crystals  Practical Electron Microscopy and Database   An Online Book  

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


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Figure 1617a (a) shows a fourfold rotation axis in crystallography, and Figure 1617a (b) shows the twofold, threefold and fourfold axes in a cubic structure. Figure 1617a. (a) A fourfold axis, and (b) The twofold, threefold and fourfold axes in a cubic structure. Figure 1617b shows that two parallel 4fold axes of rotation generate translational symmetry at the same distance of separation as in the original pair. Figure 1617b. Two parallel 4fold axes of rotation generating translational symmetry. Figure 1617c shows the CBED pattern of βpyrochlore oxide superconductor KOs_{2}O_{6} along the [001] zone axis. [1] 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 1617c. CBED pattern taken from a KOs_{2}O_{6} crystal along [001] zone axis. [1]
[1] JunIchi Yamaura, Zenji Hiroi, Kenji Tsuda, Koichi Izawa, Yasuo Ohishi, Satoshi Tsutsui, Reexamination of the crystal structure of the βpyrochlore oxide superconductor KOs2O6 by Xray and convergentbeam electron
diffraction analyses, Solid State Communications 149 (2009) 3134.


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