Electron microscopy
Space Group P105/mmc
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Table 1450. P105/mmc space group.

Name in the International Tables for Crystallography
Crystal system
  Absence of reflections

Cause of extinction rule
The existence of c-glide plane or a 105 screw axis along the c-axis. c is the periodic axis.
Symmetry (atomic coordinates)
A 5-D super-space group, centrosymmetric
Crystal examples
Decagonal quasicrystals: d-Al72Ni20Co8, d-Co15Cu20Al65 (c = 0.4148 nm), Rh15Ni15Al70, d-Co15Ni15Al70 (c = 0.4081 nm), d-Mn16.5Pd13Al70.5 (c = 1.24 nm)

Both HAADF (high-angle annular dark-field) and ABF (annular bright-field) in a spherical aberration (Cs)-corrected STEM had been used to study the structure of an Al64Cu22Co14 decagonal quasicrystal (DQC) as shown in Figure 1450a. The bright dots in the HAADF-STEM image correspond to heavy atoms (z-contrast), while the projective positions of Al atoms, those of transition-metal (TM) Cu/Co atoms, and mixed sites (MSs) of Al and TM atoms in the ABF-STEM image are indicated by the dark dots. This alloy was prepared by annealing at 1173 K for 24 h, subsequently cooling down to 1073 K at a cooling rate of 2 K/h, keeping at 1073 K for 72 h, and finally quenching in water.

Al64Cu22Co14 decagonal quasicrystal

Figure 1450a. (a) HAADF-STEM image and (b) ABF-STEM image of an Al64Cu22Co14 decagonal quasicrystal (DQC). Adapted from [1]

Figure 1450b shows electron diffraction patterns of the Al64Cu22Co14 DQC (in Figure 1450a) taken with the incident beam parallel to three primary axes. The diffraction patterns taken along directions q and p indicate that the structure includes two layers along the ten-fold axis and thus has centrosymmetry. The reflections marked by the arrows in Figure 1450b (c) disappear due to the existence of a 105 screw axis in the space group of P105/mmc.

Al64Cu22Co14 decagonal quasicrystal (DQC) diffraction

Figure 1450b. Electron diffraction patterns of the Al64Cu22Co14 DQC (space group: P105/mmc): (a) In ten-fold symmetry, (b) Along direction q and (b) Along direction p. [1]

Figure 1450c (a) shows the magnified image of the red-boxed part in Figure 1450b. Figures 1450c (b) and (c) presents that almost all the brightest dots in the same part as Figure 1450c (a) are arranged in two types of pentagonal tilings with an edge-length of 0.76 nm. In the two types of pentagonal tilings, there are ten dots without definite symmetry as marked by the white arrows in Figure 1450c (d).

pentagonal tilings
pentagonal tilings
pentagonal tilings
pentagonal tilings
Figure 1450c. (a) Magnified image of the red-boxed part in Figure 1450b, (b) Highlighted type I of pentagonal tilings in red, (c) Highlighted type II of pentagonal tilings in green, and (d) Both types of pentagonal tilings.






[1] Kunio Yubuta, Kazuki Yamamoto, Akira Yasuhara and Kenji Hiraga, Structure of an AlCuCo Decagonal Quasicrystal Studied by Cs-Corrected STEM, Materials Transactions, 55(6), 866 (2014).