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Crystal Lab › Prototype structures › Trigonal

Ce₇Ga₁₁Rh₁₈

Trigonal · space group R-3m (No. 166) · Pearson hR36

Symmetry elements and Wyckoff positions (interactive)

Ce₇Ga₁₁Rh₁₈ in R-3m

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

Unit cell

Lattice constants
a = 5.592 Å, b = 5.592 Å, c = 67.955 Å; α = 90.00°, β = 90.00°, γ = 120.00°
Cell volume
1840.3 ų
Atoms in the conventional cell
108 (Ce 21, Ga 33, Rh 54)
Formula units Z
3
Pearson symbol
hR36 — hexagonal / trigonal, rhombohedral lattice, 36 atoms per conventional cell
Symmetry operations
36 per cell

Crystallographic sites

SiteElementWyckoffMultiplicityxyz
Ce1Ce3a30.00000.00000.0000
Ga5Ga3b30.00000.00000.5000
Ce2Ce6c60.00000.00000.0524
Ce3Ce6c60.00000.00000.1553
Ce4Ce6c60.00000.00000.1046
Ga6Ga6c60.00000.00000.4447
Ga7Ga6c60.00000.00000.2778
Ga8Ga6c60.00000.00000.3334
Ga9Ga6c60.00000.00000.2223
Ga10Ga6c60.00000.00000.3887
Rh11Rh18h180.50280.49720.1391
Rh12Rh18h180.49970.50030.0831
Rh13Rh18h180.50020.49980.0276

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 108 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

A7B11C18_hR36_166_a3c_b5c_3h-001: the stoichiometry comes first (A, B, C… are the elements in alphabetical order of their site labels), then the Pearson symbol hR36, then the space-group number 166, then the Wyckoff letters occupied by each element in turn (Ce: 3a; Ga: 3b; Ce: 6c; Ce: 6c; Ce: 6c; Ga: 6c; Ga: 6c; Ga: 6c; Ga: 6c; Ga: 6c; Rh: 18h; Rh: 18h; Rh: 18h). 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 A7B11C18_hR36_166_a3c_b5c_3h-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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