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Crystal Lab › Prototype structures › Hexagonal

CsC₈

Hexagonal · space group P6222 (No. 180) · Pearson hP27

Symmetry elements and Wyckoff positions (interactive)

CsC₈ in P6222

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

Unit cell

Lattice constants
a = 4.960 Å, b = 4.960 Å, c = 17.847 Å; α = 90.00°, β = 90.00°, γ = 120.00°
Cell volume
380.3 ų
Atoms in the conventional cell
27 (Cs 3, C 24)
Formula units Z
3
Pearson symbol
hP27 — hexagonal / trigonal, primitive lattice, 27 atoms per conventional cell
Symmetry operations
12 per cell

Crystallographic sites

SiteElementWyckoffMultiplicityxyz
Cs4Cs3d30.50000.00000.5000
C1C6i60.66670.33330.0000
C2C6i60.83330.66670.0000
C3C12k120.16670.33330.3333

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 27 atoms drawn above are these sites multiplied by all 12 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

A8B_hP27_180_2ik_d-001: the stoichiometry comes first (A, B, C… are the elements in alphabetical order of their site labels), then the Pearson symbol hP27, then the space-group number 180, then the Wyckoff letters occupied by each element in turn (Cs: 3d; C: 6i; C: 6i; C: 12k). 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 A8B_hP27_180_2ik_d-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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