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Crystal Lab › Prototype structures › Trigonal

Th₂Zn₁₇

Trigonal · space group R-3m (No. 166) · Pearson hR19

Symmetry elements and Wyckoff positions (interactive)

Th₂Zn₁₇ in R-3m

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

Unit cell

Lattice constants
a = 9.030 Å, b = 9.030 Å, c = 13.200 Å; α = 90.00°, β = 90.00°, γ = 120.00°
Cell volume
932.1 ų
Atoms in the conventional cell
57 (Th 6, Zn 51)
Formula units Z
3
Pearson symbol
hR19 — hexagonal / trigonal, rhombohedral lattice, 19 atoms per conventional cell
Symmetry operations
36 per cell

Crystallographic sites

SiteElementWyckoffMultiplicityxyz
Th1Th6c60.00000.00000.3333
Zn2Zn6c60.00000.00000.0970
Zn3Zn9d90.50000.00000.5000
Zn4Zn18f180.33330.00000.0000
Zn5Zn18h180.16670.83330.5000

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 57 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

A2B17_hR19_166_c_cdfh-001: the stoichiometry comes first (A, B, C… are the elements in alphabetical order of their site labels), then the Pearson symbol hR19, then the space-group number 166, then the Wyckoff letters occupied by each element in turn (Th: 6c; Zn: 6c; Zn: 9d; Zn: 18f; Zn: 18h). Two structures with the same label are the same arrangement with different cell parameters or coordinates.

Other compounds with this structure

Ba₂Mg₁₇, Ce₂Co₁₇, Ce₂Fe₁₇, Ce₂Zn₁₇, Dy₂Co₁₇, Dy₂Fe₁₇, Dy₂Zn₁₇, Er₂Zn₁₇, Gd₂Co₁₇, Gd₂Fe₁₇, Gd₂Zn₁₇, Hf₂Be₁₇, Ho₂Co₁₇, Ho₂Zn₁₇, La₂Zn₁₇, Lu₂Zn₁₇, Nb₂Be₁₇, Nd₂Co₁₇, Nd₂Fe₁₇, Nd₂Zn₁₇, Pr₂Co₁₇, Pr₂Fe₁₇, Pr₂Zn₁₇, Pu₂Zn₁₇, Sm₂Co₁₇, Sm₂Fe₁₇, Sm₂Zn₁₇, Ta₂Be₁₇, Tb₂Co₁₇, Tb₂Fe₁₇, Tb₂Zn₁₇, Th₂Co₁₇, Th₂Fe₁₇, Th₂Zn₁₇, Ti₂Be₁₇, Tm₂Zn₁₇, U₂Zn₁₇, Y₂Co₁₇, Y₂Fe₁₇, Y₂Zn₁₇, Yb₂Zn₁₇, Zr₂Be₁₇, Al₂Ce₂Co₁₅, Ce₂Mn₇Al₁₀ <!--beginning with an

Source

Coordinates and cell from the AFLOW Encyclopedia of Crystallographic Prototypes, entry A2B17_hR19_166_c_cdfh-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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