Crystal Lab › Prototype structures › Hexagonal
LuMnO₃
Hexagonal · space group P63cm (No. 185) · Pearson hP30
Symmetry elements and Wyckoff positions (interactive)
LuMnO₃ in P63cm
SettingUnit cell
- Lattice constants
- a = 6.038 Å, b = 6.038 Å, c = 11.361 Å; α = 90.00°, β = 90.00°, γ = 120.00°
- Cell volume
- 358.7 ų
- Atoms in the conventional cell
- 30 (Lu 6, O 18, Mn 6)
- Formula units Z
- 6
- Pearson symbol
- hP30 — hexagonal / trigonal, primitive lattice, 30 atoms per conventional cell
- Symmetry operations
- 12 per cell
Crystallographic sites
| Site | Element | Wyckoff | Multiplicity | x | y | z |
|---|---|---|---|---|---|---|
| Lu1 | Lu | 2a | 2 | 0.0000 | 0.0000 | 0.2739 |
| O4 | O | 2a | 2 | 0.0000 | 0.0000 | 0.9715 |
| Lu2 | Lu | 4b | 4 | 0.3333 | 0.6667 | 0.2304 |
| O5 | O | 4b | 4 | 0.3333 | 0.6667 | 0.0190 |
| Mn3 | Mn | 6c | 6 | 0.3355 | 0.0000 | 0.9992 |
| O6 | O | 6c | 6 | 0.3070 | 0.0000 | 0.1642 |
| O7 | O | 6c | 6 | 0.3614 | 0.0000 | 0.8362 |
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 30 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
ABC3_hP30_185_ab_c_ab2c-001: the stoichiometry comes first (A, B, C… are the elements in alphabetical order of their site labels), then the Pearson symbol hP30, then the space-group number 185, then the Wyckoff letters occupied by each element in turn (Lu: 2a; O: 2a; Lu: 4b; O: 4b; Mn: 6c; O: 6c; O: 6c). Two structures with the same label are the same arrangement with different cell parameters or coordinates.
Other compounds with this structure
DyMnO₃, EuMnO₃, LuFeO₃, GdMnO₃, HoMnO₃, InMnO₃, TmFeO₃, YMnO₃ <!--beginning with an
Source
Coordinates and cell from the AFLOW Encyclopedia of Crystallographic Prototypes, entry ABC3_hP30_185_ab_c_ab2c-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.