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.) |
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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.
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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 |
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[-1 1 1] tetragonal rutile TiO2 [1] |
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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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