Crystal Lab › Prototype structures › Tetragonal
β-Gd₂(MoO₄)₃
Tetragonal · space group P-421m (No. 113) · Pearson tP34
Symmetry elements and Wyckoff positions (interactive)
β-Gd₂(MoO₄)₃ in P-421m
SettingUnit cell
- Lattice constants
- a = 7.393 Å, b = 7.393 Å, c = 10.670 Å; α = 90.00°, β = 90.00°, γ = 90.00°
- Cell volume
- 583.2 ų
- Atoms in the conventional cell
- 34 (Mo 6, Gd 4, O 24)
- Formula units Z
- 2
- Pearson symbol
- tP34 — tetragonal, primitive lattice, 34 atoms per conventional cell
- Symmetry operations
- 8 per cell
Crystallographic sites
| Site | Element | Wyckoff | Multiplicity | x | y | z |
|---|---|---|---|---|---|---|
| Mo1 | Mo | 2a | 2 | 0.0000 | 0.0000 | 0.0000 |
| Gd2 | Gd | 4e | 4 | 0.6874 | 0.1874 | 0.7376 |
| Mo3 | Mo | 4e | 4 | 0.7066 | 0.2066 | 0.3569 |
| O4 | O | 4e | 4 | 0.6952 | 0.1952 | 0.5195 |
| O5 | O | 4e | 4 | 0.1289 | 0.6289 | 0.3109 |
| O6 | O | 8f | 8 | 0.0017 | 0.7761 | 0.7005 |
| O7 | O | 8f | 8 | 0.9607 | 0.8147 | 0.0955 |
The multiplicity and the Wyckoff letter say how many copies of the site the group makes in one cell and on which kind of symmetry element the site sits; the 34 atoms drawn above are these sites multiplied by all 8 operations. Press Wyckoff under Colour to see the sites, and tick a symmetry element on the left to see which atoms lie on it.
How to read the label
A2B3C12_tP34_113_e_ae_2e2f-001: the stoichiometry comes first (A, B, C… are the elements in alphabetical order of their site labels), then the Pearson symbol tP34, then the space-group number 113, then the Wyckoff letters occupied by each element in turn (Mo: 2a; Gd: 4e; Mo: 4e; O: 4e; O: 4e; O: 8f; O: 8f). Two structures with the same label are the same arrangement with different cell parameters or coordinates.
Other compounds with this structure
Dy₂(MoO₄)₃, Eu₂(MoO₄)₃, Gd₂(MoO₄)₃, Nd₂(MoO₄)₃, Pr₂(MoO₄)₃, Sm₂(MoO₄)₃, Tb₂(MoO₄)₃ <!--beginning with an
Note: \beta-Gd₂(MoO₄)₃.
Source
Coordinates and cell from the AFLOW Encyclopedia of Crystallographic Prototypes, entry A2B3C12_tP34_113_e_ae_2e2f-001 (M. J. Mehl et al., Comput. Mater. Sci. 136, S1 (2017); D. Hicks et al., ibid. 161, S1 (2019) and 199, 110450 (2021); S. Eckert et al., ibid. 240, 112988 (2024)). Symmetry elements, Wyckoff assignment and the diagram are computed on this page from the group operations.
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