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Crystal Lab › Prototype structures › Trigonal

Ce₅Co₁₉

Trigonal · space group R-3m (No. 166) · Pearson hR24

Symmetry elements and Wyckoff positions (interactive)

Ce₅Co₁₉ in R-3m

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

Unit cell

Lattice constants
a = 4.939 Å, b = 4.939 Å, c = 48.710 Å; α = 90.00°, β = 90.00°, γ = 120.00°
Cell volume
1029.0 ų
Atoms in the conventional cell
72 (Ce 15, Co 57)
Formula units Z
3
Pearson symbol
hR24 — hexagonal / trigonal, rhombohedral lattice, 24 atoms per conventional cell
Symmetry operations
36 per cell

Crystallographic sites

SiteElementWyckoffMultiplicityxyz
Ce1Ce3a30.00000.00000.0000
Co4Co3b30.00000.00000.5000
Ce2Ce6c60.00000.00000.0830
Ce3Ce6c60.00000.00000.1540
Co5Co6c60.00000.00000.2500
Co6Co6c60.00000.00000.3330
Co7Co6c60.00000.00000.4170
Co8Co18h180.50000.50000.1250
Co9Co18h180.50000.50000.0420

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 72 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

A5B19_hR24_166_a2c_b3c2h-001: the stoichiometry comes first (A, B, C… are the elements in alphabetical order of their site labels), then the Pearson symbol hR24, then the space-group number 166, then the Wyckoff letters occupied by each element in turn (Ce: 3a; Co: 3b; Ce: 6c; Ce: 6c; Co: 6c; Co: 6c; Co: 6c; Co: 18h; Co: 18h). Two structures with the same label are the same arrangement with different cell parameters or coordinates.

Other compounds with this structure

Ce₅Co₁₉, La₅Co₁₉, Nd₅Co₁₉, Nd₅Ni₁₉, Pr₅Co₁₉, Pr₅Ni₁₉, Sm₅Co₁₉, Y₅Co₁₉ <!--beginning with an

Source

Coordinates and cell from the AFLOW Encyclopedia of Crystallographic Prototypes, entry A5B19_hR24_166_a2c_b3c2h-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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