Crystal Lab › Prototype structures › Hexagonal
Na₄Ge₁₃
Hexagonal · space group P6/m (No. 175) · Pearson hP58
Symmetry elements and Wyckoff positions (interactive)
Na₄Ge₁₃ in P6/m
SettingUnit cell
- Lattice constants
- a = 15.027 Å, b = 15.027 Å, c = 3.960 Å; α = 90.00°, β = 90.00°, γ = 120.00°
- Cell volume
- 774.5 ų
- Atoms in the conventional cell
- 58 (Na 20, Ge 38)
- Formula units Z
- 2
- Pearson symbol
- hP58 — hexagonal / trigonal, primitive lattice, 58 atoms per conventional cell
- Symmetry operations
- 12 per cell
Crystallographic sites
| Site | Element | Wyckoff | Multiplicity | x | y | z |
|---|---|---|---|---|---|---|
| Na7 | Na | 2d | 2 | 0.3333 | 0.6667 | 0.5000 |
| Ge1 | Ge | 2e | 2 | 0.0000 | 1.0000 | 0.0757 |
| Ge2 | Ge | 6j | 6 | 0.1524 | 0.5186 | 0.0000 |
| Ge3 | Ge | 6j | 6 | 0.4831 | 0.1841 | 0.0000 |
| Na8 | Na | 6j | 6 | 0.0696 | 0.2739 | 0.0000 |
| Ge4 | Ge | 6k | 6 | 0.0417 | 0.4473 | 0.5000 |
| Ge5 | Ge | 6k | 6 | 0.3695 | 0.1033 | 0.5000 |
| Ge6 | Ge | 12l | 12 | 0.0271 | 0.1088 | 0.4074 |
| Na9 | Na | 12l | 12 | 0.0636 | 0.2427 | 0.0626 |
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 58 atoms drawn above are these sites multiplied by all 12 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
A19B10_hP58_175_e2j2kl_djl-001: the stoichiometry comes first (A, B, C… are the elements in alphabetical order of their site labels), then the Pearson symbol hP58, then the space-group number 175, then the Wyckoff letters occupied by each element in turn (Na: 2d; Ge: 2e; Ge: 6j; Ge: 6j; Na: 6j; Ge: 6k; Ge: 6k; Ge: 12l; Na: 12l). 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 A19B10_hP58_175_e2j2kl_djl-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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