Electron microscopy
 
P42/mnm (D4h14, 136) Space Group
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Table 3018a. P42/mnm (D4h14, 136) space group.

Name in the International Tables for Crystallography
P42/mnm (simplified from P42/m2l/n2/m: the symbol 42 means that an axis of the fourth order is a screw axis, with translation on half a period along this axis on rotation by angle π/2 or 360/4 degrees, and the symbol n means that two of the four vertical planes are planes of sliding reflection.) P
123 4/mmm
Crystal system
Tetragonal 4/mmm
Asymm
0 ≤ x ≤ 1/2 and 0 ≤ y ≤ 1/2 and 0 ≤ z ≤ 1/2 and x ≤ y
16
Symmetry (atomic coordinates)
X, Y, Z; -X, -Y, Z; 1/2-Y, X+1/2, Z+1/2; Y+1/2, 1/2-X, Z+1/2; 1/2-X, Y+1/2, 1/2-Z; X+1/2, 1/2-Y, 1/2-Z; Y, X, -Z; -Y, -X, -Z; -X, -Y, -Z; X, Y, -Z; Y+1/2, 1/2-X, 1/2-Z; 1/2-Y, X+1/2, 1/2-Z; X+1/2, 1/2-Y, Z+1/2; 1/2-X, Y+1/2, Z+1/2; -Y, -X, Z; Y, X, Z
Wyckoff positions
Wyckoff positions Oriented site symmetry groups (Ej) Coordinates of the Wyckoff positions in the unit cell
2a m.mm (0, 0, 0), (1/2, 1/2, 1/2)
2b m.mm (0, 0, 1/2), (1/2, 1/2, 0)
4c 2/m.. (0, 1/2, 0), (0, 1/2, 1/2), (1/2, 0, 1/2), (1/2, 0, 0)
4d -4.. (0, 1/2, 1/4), (0, 1/2, 3/4), (1/2, 0, 1/4), (1/2, 0, 3/4)
4e 2.mm (0, 0, z), (1/2, 1/2, z+1/2), (1/2, 1/2, 1/2-z), (0, 0, -z)
4f m.2m (x, x, 0), (-x, -x, 0), (1/2-x, 1/2+x, 1/2), (1/2+x, 1/2-x, 1/2)
4g m.2m (x, -x, 0), (-x, x, 0), (1/2+x, 1/2+x, 1/2), (1/2-x, 1/2-x, 1/2)
8h 2.. (0, 1/2, z), (0, 1/2, z + 1/2), (1/2, 0,−z + 1/2), (1/2, 0,−z),
    (0, 1/2,−z), (0, 1/2,−z + 1/2), (1/2, 0, z + 1/2), (1/2, 0, z).
8i m.. (x, y, 0), (−x,−y, 0), (−y + 1/2, x + 1/2, 1/2), (y + 1/2,−x + 1/2, 1/2),
    (−x + 1/2, y + 1/2, 1/2), (x + 1/2,−y + 1/2, 1/2), (y, x, 0), (−y,−x, 0).
8j ..m (x, x, z), (−x,−x, z), (−x + 1/2, x + 1/2, z + 1/2), (x + 1/2,−x + 1/2, z + 1/2),
    (−x + 1/2, x + 1/2,−z + 1/2), (x + 1/2,−x + 1/2,−z + 1/2), (x, x,−z), (−x,−x,−z)
16k 1 (x, y, z), (-x, -y, z), (1/2-y, 1/2+x, 1/2+z), (1/2+y, 1/2-x, 1/2+z),
    (1/2-x, 1/2+y, 1/2-z), (1/2+x, 1/2-y, 1/2-z), (y, x, -z), (-y, -x, -z),
    (-x, -y, -z), (x, y, -z), (1/2+y, 1/2-x, 1/2-z), (1/2-y, 1/2+x, 1/2-z),
    (1/2+x, 1/2-y, 1/2+z), (1/2-x, 1/2+y, 1/2+z), (-y, -x, z), (y, x, z).
Material examples
MnF2: a = 0.4874 nm and c = 0.3310 nm.
NiF2: a = 0.4650 nm and c = 0.3084 nm.
SnO2: a = 0.4738 nm and c = 0.3187 nm.
TiO2: a = 0.4593 nm and c = 0.2959 nm: Ti at 0, 0, 0 and O at 0.3053, 0.3053, 0.
CoF2: a = 0.4695 nm and c = 0.3182 nm.

MgF2
α-MgH2

Table 3018b. Example of compounds with similar structures to BCC.

 
TiO2 (Rutile)
Cu2O (Cuprite)
Space group Im-3m P42/mnm Pm-3m Pn-3m
Compounds α-Fe, W, Nb, Ta, Na, K, Mo, V GeO2, SnO2, PbO2 CsI, CsBr, CsCl Pb2O, Ag2O

 

[-1 1 1] tetragonal rutile TiO2
[-1 1 1] tetragonal rutile TiO2 [1]
 

Figure 3018. Examples of indexed electron diffraction (or FFT) patterns of P42/mnm (136) crystals.

 

 

 

[1] Chaolun Liang, Wenxia Zhao, Xianfeng Yang, Mingmei Wu and Yexiang Tong, Applications of High Resolution Electron Microscopy in Structural Analysis of Nanoarrays, Current Microscopy Contributions to Advances in Science and Technology, 1271, 2012.

 

 

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