Crystal Lab › Prototype structures › Tetragonal
Na₄Ge₉O₂₀
Tetragonal · space group I41/a (No. 88) · Pearson tI132
Symmetry elements and Wyckoff positions (interactive)
Na₄Ge₉O₂₀ in I41/a
SettingUnit cell
- Lattice constants
- a = 14.980 Å, b = 14.980 Å, c = 7.384 Å; α = 90.00°, β = 90.00°, γ = 90.00°
- Cell volume
- 1657.0 ų
- Atoms in the conventional cell
- 132 (Ge 36, Na 16, O 80)
- Formula units Z
- 4
- Pearson symbol
- tI132 — tetragonal, body-centred lattice, 132 atoms per conventional cell
- Symmetry operations
- 16 per cell
Crystallographic sites
| Site | Element | Wyckoff | Multiplicity | x | y | z |
|---|---|---|---|---|---|---|
| Ge1 | Ge | 4a | 4 | 0.0000 | 0.2500 | 0.1250 |
| Ge2 | Ge | 16f | 16 | 0.6366 | 0.5460 | 0.2009 |
| Ge3 | Ge | 16f | 16 | 0.0956 | 0.2180 | 0.4912 |
| Na4 | Na | 16f | 16 | 0.5878 | 0.5544 | 0.6702 |
| O5 | O | 16f | 16 | 0.0928 | 0.2127 | 0.2448 |
| O6 | O | 16f | 16 | 0.0824 | 0.2227 | 0.7476 |
| O7 | O | 16f | 16 | 0.6889 | 0.5739 | 0.4074 |
| O8 | O | 16f | 16 | 0.0253 | 0.0446 | 0.7555 |
| O9 | O | 16f | 16 | 0.6554 | 0.6088 | 0.0070 |
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 132 atoms drawn above are these sites multiplied by all 16 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
A9B4C20_tI132_88_a2f_f_5f-001: the stoichiometry comes first (A, B, C… are the elements in alphabetical order of their site labels), then the Pearson symbol tI132, then the space-group number 88, then the Wyckoff letters occupied by each element in turn (Ge: 4a; Ge: 16f; Ge: 16f; Na: 16f; O: 16f; O: 16f; O: 16f; O: 16f; O: 16f). Two structures with the same label are the same arrangement with different cell parameters or coordinates.
Source
Coordinates and cell from the AFLOW Encyclopedia of Crystallographic Prototypes, entry A9B4C20_tI132_88_a2f_f_5f-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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