Crystal Lab › Prototype structures › Trigonal
Trigonal Li₄P₂O₇ Li₄O₇P₂
Trigonal · space group P3212 (No. 153) · Pearson hP39
Symmetry elements and Wyckoff positions (interactive)
Trigonal Li₄P₂O₇ in P3212
SettingUnit cell
- Lattice constants
- a = 5.170 Å, b = 5.170 Å, c = 18.972 Å; α = 90.00°, β = 90.00°, γ = 120.00°
- Cell volume
- 439.1 ų
- Atoms in the conventional cell
- 39 (O 21, Li 12, P 6)
- Formula units Z
- 3
- Pearson symbol
- hP39 — hexagonal / trigonal, primitive lattice, 39 atoms per conventional cell
- Symmetry operations
- 6 per cell
Crystallographic sites
| Site | Element | Wyckoff | Multiplicity | x | y | z |
|---|---|---|---|---|---|---|
| O1 | O | 3a | 3 | 0.5294 | 0.4706 | 0.6667 |
| Li2 | Li | 6c | 6 | 0.0878 | 0.8125 | 0.7797 |
| Li3 | Li | 6c | 6 | 0.7692 | 0.1777 | 0.7786 |
| O4 | O | 6c | 6 | 0.1396 | 0.4951 | 0.7437 |
| O5 | O | 6c | 6 | 0.4052 | 0.2150 | 0.7805 |
| O6 | O | 6c | 6 | 0.6886 | 0.7738 | 0.7767 |
| P7 | P | 6c | 6 | 0.4300 | 0.4920 | 0.7451 |
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 39 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
A4B7C2_hP39_153_2c_a3c_c-001: the stoichiometry comes first (A, B, C… are the elements in alphabetical order of their site labels), then the Pearson symbol hP39, then the space-group number 153, then the Wyckoff letters occupied by each element in turn (O: 3a; Li: 6c; Li: 6c; O: 6c; O: 6c; O: 6c; P: 6c). Two structures with the same label are the same arrangement with different cell parameters or coordinates.
Note: Trigonal.
Source
Coordinates and cell from the AFLOW Encyclopedia of Crystallographic Prototypes, entry A4B7C2_hP39_153_2c_a3c_c-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.