Diffraction group 4mm1_{R}  Practical Electron Microscopy and Database   An Online Book  

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


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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. Figure 1591 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. According to the general relationship among WPs, diffraction groups (DGs) and point groups (PGs) shown in a table in page2693, the diffraction groups for WP of 4mm symmetry is either 4mm or 4mm1_{R}. The former is consistent with a noncentrosymmetric PG of 4mm (tetragonal structure), and the latter with a centrosymmetric PG of m3m (cubic structure) or 4/mmm (tetragonal structure). Assuming the crystal system of KOs_{2}O_{6} is cubic (confirmed by XRD), the PG can only m3m. Figure 1591. 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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