Crystal Lab › Prototype structures › Hexagonal
Tl₃Ga₉S₁₃O₂
Hexagonal · space group P-6 (No. 174) · Pearson hP27
Symmetry elements and Wyckoff positions (interactive)
Tl₃Ga₉S₁₃O₂ in P-6
SettingUnit cell
- Lattice constants
- a = 9.598 Å, b = 9.598 Å, c = 7.433 Å; α = 90.00°, β = 90.00°, γ = 120.00°
- Cell volume
- 593.0 ų
- Atoms in the conventional cell
- 27 (S 13, Tl 3, O 2, Ga 9)
- Formula units Z
- 1
- Pearson symbol
- hP27 — hexagonal / trigonal, primitive lattice, 27 atoms per conventional cell
- Symmetry operations
- 6 per cell
Crystallographic sites
| Site | Element | Wyckoff | Multiplicity | x | y | z |
|---|---|---|---|---|---|---|
| S4 | S | 1a | 1 | 1.0000 | 0.0000 | 0.0000 |
| Tl8 | Tl | 1b | 1 | 1.0000 | 0.0000 | 0.5000 |
| Tl9 | Tl | 1c | 1 | 0.3333 | 0.6667 | 0.0000 |
| Tl10 | Tl | 1d | 1 | 0.3333 | 0.6667 | 0.5000 |
| O3 | O | 2i | 2 | 0.6667 | 0.3333 | 0.2610 |
| Ga1 | Ga | 3j | 3 | 0.7902 | 0.7403 | 0.0000 |
| S5 | S | 3j | 3 | 0.3753 | 0.3257 | 0.0000 |
| S6 | S | 3k | 3 | 0.3583 | 0.3307 | 0.5000 |
| Ga2 | Ga | 6l | 6 | 0.5274 | 0.4200 | 0.2649 |
| S7 | S | 6l | 6 | 0.6498 | 0.6898 | 0.2554 |
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 27 atoms drawn above are these sites multiplied by all 6 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
A9B2C13D3_hP27_174_jl_i_ajkl_bcd-001: the stoichiometry comes first (A, B, C… are the elements in alphabetical order of their site labels), then the Pearson symbol hP27, then the space-group number 174, then the Wyckoff letters occupied by each element in turn (S: 1a; Tl: 1b; Tl: 1c; Tl: 1d; O: 2i; Ga: 3j; S: 3j; S: 3k; Ga: 6l; S: 6l). 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 A9B2C13D3_hP27_174_jl_i_ajkl_bcd-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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