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Crystal Lab › Prototype structures › Trigonal

Zr₂₁Re₂₅

Trigonal · space group R-3c (No. 167) · Pearson hR92

Symmetry elements and Wyckoff positions (interactive)

Zr₂₁Re₂₅ in R-3c

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

Unit cell

Lattice constants
a = 25.847 Å, b = 25.847 Å, c = 8.771 Å; α = 90.00°, β = 90.00°, γ = 120.00°
Cell volume
5074.6 ų
Atoms in the conventional cell
276 (Re 150, Zr 126)
Formula units Z
6
Pearson symbol
hR92 — hexagonal / trigonal, rhombohedral lattice, 92 atoms per conventional cell
Symmetry operations
36 per cell

Crystallographic sites

SiteElementWyckoffMultiplicityxyz
Re1Re6b60.00000.00000.0000
Re2Re18e180.06100.00000.2500
Re3Re18e180.44460.00000.2500
Zr7Zr18e180.69430.00000.2500
Re4Re36f360.15550.60850.4147
Re5Re36f360.82460.76580.7477
Re6Re36f360.88370.76500.5000
Zr10Zr36f360.89160.68710.7481
Zr8Zr36f360.10270.66460.2091
Zr9Zr36f360.88360.88390.5659

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 276 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

A25B21_hR92_167_b2e3f_e3f-001: the stoichiometry comes first (A, B, C… are the elements in alphabetical order of their site labels), then the Pearson symbol hR92, then the space-group number 167, then the Wyckoff letters occupied by each element in turn (Re: 6b; Re: 18e; Re: 18e; Zr: 18e; Re: 36f; Re: 36f; Re: 36f; Zr: 36f; Zr: 36f; Zr: 36f). Two structures with the same label are the same arrangement with different cell parameters or coordinates.

Other compounds with this structure

Hf₂₁Re₂₅, Mg₂₁Zn₂₅, Ti₂₁Mn₂₅, Ti₂₁Re₂₅ <!--beginning with an

Source

Coordinates and cell from the AFLOW Encyclopedia of Crystallographic Prototypes, entry A25B21_hR92_167_b2e3f_e3f-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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