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Crystal Lab › Prototype structures › Trigonal

ε-Hf₃N₂

Trigonal · space group R-3m (No. 166) · Pearson hR6

Symmetry elements and Wyckoff positions (interactive)

ε-Hf₃N₂ in R-3m

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

Unit cell

Lattice constants
a = 3.206 Å, b = 3.206 Å, c = 23.262 Å; α = 90.00°, β = 90.00°, γ = 120.00°
Cell volume
207.1 ų
Atoms in the conventional cell
18 (Hf 9, N 9)
Formula units Z
9
Pearson symbol
hR6 — hexagonal / trigonal, rhombohedral lattice, 6 atoms per conventional cell
Symmetry operations
36 per cell

Crystallographic sites

SiteElementWyckoffMultiplicityxyz
Hf1Hf3a30.00000.00000.0000
N3N3b30.00000.00000.5000
Hf2Hf6c60.00000.00000.2222
N4N6c60.00000.00000.3889

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 18 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

AB_hR6_166_ac_bc-001: the stoichiometry comes first (A, B, C… are the elements in alphabetical order of their site labels), then the Pearson symbol hR6, then the space-group number 166, then the Wyckoff letters occupied by each element in turn (Hf: 3a; N: 3b; Hf: 6c; N: 6c). 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 AB_hR6_166_ac_bc-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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