Electron microscopy
R-3c (167) Space Group
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Table 3006. R-3c (167) space group.

Name in the International Tables for Crystallography
R-3c R
166 -3m
Crystal system
Trigonal -3m
36 Example of forbidden reflections in electron diffraction patterns {1 -1 0 0} reflections
0 ≤ x ≤ 2/3 and 0 ≤ y ≤ 2/3 and 0 ≤ z ≤ 1/12 and x ≤ (1+y)/2 and y ≤ min(1-x, (1+x)/2)
Symmetry (atomic coordinates)
X, Y, Z; -Y, X-Y, Z; Y-X, -X, Z; Y, X, 1/2-Z; X-Y, -Y, 1/2-Z; -X, Y-X, 1/2-Z; -X, -Y, -Z; Y, Y-X, -Z; X-Y, X, -Z; -Y, -X, 1/2+Z; Y-X, Y, 1/2+Z; X, X-Y, 1/2+Z; 2/3+X, 1/3+Y, 1/3+Z; 2/3-Y, 1/3+X-Y, 1/3+Z; 2/3+Y-X, 1/3-X, 1/3+Z; 2/3+Y, 1/3+X, 5/6-Z; 2/3+X-Y, 1/3-Y, 5/6-Z; 2/3-X, 1/3+Y-X, 5/6-Z; 2/3-X, 1/3-Y, 1/3-Z; 2/3+Y, 1/3+Y-X, 1/3-Z; 2/3+X-Y, 1/3+X, 1/3-Z; 2/3-Y, 1/3-X, 5/6+Z; 2/3+Y-X, 1/3+Y, 5/6+Z; 2/3+X, 1/3+X-Y, 5/6+Z; 1/3+X, 2/3+Y, 2/3+Z; 1/3-Y, 2/3+X-Y, 2/3+Z; 1/3+Y-X, 2/3-X, 2/3+Z; 1/3+Y, 2/3+X, 1/6-Z; 1/3+X-Y, 2/3-Y, 1/6-Z; 1/3-X, 2/3+Y-X, 1/6-Z; 1/3-X, 2/3-Y, 2/3-Z; 1/3+Y, 2/3+Y-X, 2/3-Z; 1/3+X-Y, 2/3+X, 2/3-Z; 1/3-Y, 2/3-X, 1/6+Z; 1/3+Y-X, 2/3+Y, 1/6+Z; 1/3+X, 2/3+X-Y, 1/6+Z
Crystal examples

VF3 (vanadium fluoride): V at 0, 0, 0 and F at 2/5, 0, 1/4.
Al2O3: Al at 0, 0, 0.355 and O at 0.303, 0, 0.25.
Centrosymmetric materials: lithium niobate (LiNBO3) and lithium tantalate (LiTaO3).




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