Electron microscopy
P63/m (176) Space Group
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Table 1878. P63/m (176) space group.

Name in the International Tables for Crystallography
P63/m P
175 6/m
Crystal system
Hexagonal 6/m
0 ≤ x ≤ 2/3 and 0 ≤ y ≤ 2/3 and 0 ≤ z ≤ 1/4 and x ≤ (1+y)/2 and y ≤ min(1-x,(1+x)/2)
Forbidden reflections
Only one condition 000l: l ≠ 2n, which indicates 63-screw axis along the c direction in hexagonal systems.
Symmetry (atomic coordinates)
X, Y, Z; -Y, X-Y, Z; Y-X, -X, Z; -X, -Y, 1/2+Z; Y, Y-X, 1/2+Z; X-Y, X, 1/2+Z; -X, -Y, -Z; Y, Y-X, -Z; X-Y, X, -Z; X, Y, 1/2-Z; -Y, X-Y, 1/2-Z; Y-X, -X,1/2-Z
Crystal examples

Figure 1878 shows diffraction patterns of hexagonal La3Cu2VO9 (a ≈ 14.4 Å and c ≈ 10.7 Å) crystals in space group P63/m. The SAED pattern in Figure 1878 (a) presents the only forbidden spots along c axis (000l spots with odd l) which were found by tilting the TEM specimen (the same forbidden spots were found in [1-100] zone axis as well). The WP (whole-pattern) taken along the [1-100] zone axis exhibits a mirror plane perpendicular to the c-axis.

[11-20] SAED pattern of La3Cu2VO9
[1-100] zone-axis whole pattern showing the mirror plane perpendicular to the c-axis for La3Cu2VO9

Figure 1878. Diffraction patterns of hexagonal La3Cu2VO9: (a) [11-20] SAED pattern. The small arrows denote the forbidden reflections visible due to double diffraction. (b) Whole pattern along [1-100] zone-axis showing the mirror plane perpendicular to the c-axis. Adapted from [1]





[1] Sylvie Malo, Douglas A. Vander Griend, Kenneth R. Poeppelmeier, Yanguo Wang, Vinayak P. Dravid, Crystal symmetry of La3Cu2VO9 and La4Cu3MoO12 derived from the YAlO3 hexagonal structure by transmission electron microscopy, Solid State Sciences 3 (2001) 17–23.



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