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Crystal Lab › Prototype structures › Trigonal

CsV₆Sb₆

Trigonal · space group R-3m (No. 166) · Pearson hR13

Symmetry elements and Wyckoff positions (interactive)

CsV₆Sb₆ in R-3m

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

Unit cell

Lattice constants
a = 5.558 Å, b = 5.558 Å, c = 35.165 Å; α = 90.00°, β = 90.00°, γ = 120.00°
Cell volume
940.6 ų
Atoms in the conventional cell
39 (Cs 3, Sb 18, V 18)
Formula units Z
3
Pearson symbol
hR13 — hexagonal / trigonal, rhombohedral lattice, 13 atoms per conventional cell
Symmetry operations
36 per cell

Crystallographic sites

SiteElementWyckoffMultiplicityxyz
Cs1Cs3a30.00000.00000.0000
Sb2Sb6c60.00000.00000.8659
Sb3Sb6c60.00000.00000.5984
Sb4Sb6c60.00000.00000.2651
V5V18h180.16670.83330.2009

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 39 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

AB6C6_hR13_166_a_3c_h-001: the stoichiometry comes first (A, B, C… are the elements in alphabetical order of their site labels), then the Pearson symbol hR13, then the space-group number 166, then the Wyckoff letters occupied by each element in turn (Cs: 3a; Sb: 6c; Sb: 6c; Sb: 6c; V: 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 AB6C6_hR13_166_a_3c_h-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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