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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

Setting
Loading the group…
x = 0.10, y = 0.17, z = 0.08

Unit 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

SiteElementWyckoffMultiplicityxyz
K1K3a30.00000.00000.0000
N2N3b30.00000.00000.5000
O3O18h180.13000.87000.4750

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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