Crystal Lab › Prototype structures › Trigonal
β-Potassium Nitrate (KNO₃)
Trigonal · space group R-3m (No. 166) · Pearson hR8
Symmetry elements and Wyckoff positions (interactive)
β-Potassium Nitrate (KNO₃) in R-3m
SettingUnit cell
- Lattice constants
- a = 5.425 Å, b = 5.425 Å, c = 9.836 Å; α = 90.00°, β = 90.00°, γ = 120.00°
- Cell volume
- 250.7 ų
- Atoms in the conventional cell
- 24 (K 3, N 3, O 18)
- Formula units Z
- 3
- Pearson symbol
- hR8 — hexagonal / trigonal, rhombohedral lattice, 8 atoms per conventional cell
- Symmetry operations
- 36 per cell
Crystallographic sites
| Site | Element | Wyckoff | Multiplicity | x | y | z |
|---|---|---|---|---|---|---|
| K1 | K | 3a | 3 | 0.0000 | 0.0000 | 0.0000 |
| N2 | N | 3b | 3 | 0.0000 | 0.0000 | 0.5000 |
| O3 | O | 18h | 18 | 0.1300 | 0.8700 | 0.4750 |
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 24 atoms drawn above are these sites multiplied by all 36 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
ABC6_hR8_166_a_b_h-001: the stoichiometry comes first (A, B, C… are the elements in alphabetical order of their site labels), then the Pearson symbol hR8, then the space-group number 166, then the Wyckoff letters occupied by each element in turn (K: 3a; N: 3b; O: 18h). Two structures with the same label are the same arrangement with different cell parameters or coordinates.
Other compounds with this structure
NaNO₃ <!--beginning with an
Note: \beta-KNO₃ Structure.
Source
Coordinates and cell from the AFLOW Encyclopedia of Crystallographic Prototypes, entry ABC6_hR8_166_a_b_h-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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