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Crystal Lab › Prototype structures › Trigonal

Ta₂VC₂

Trigonal · space group R-3m (No. 166) · Pearson hR6

Symmetry elements and Wyckoff positions (interactive)

Ta₂VC₂ in R-3m

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

Unit cell

Lattice constants
a = 3.041 Å, b = 3.041 Å, c = 21.816 Å; α = 90.00°, β = 90.00°, γ = 120.00°
Cell volume
174.7 ų
Atoms in the conventional cell
18 (V 3, C 9, Ta 6)
Formula units Z
3
Pearson symbol
hR6 — hexagonal / trigonal, rhombohedral lattice, 6 atoms per conventional cell
Symmetry operations
36 per cell

Crystallographic sites

SiteElementWyckoffMultiplicityxyz
V4V3a30.00000.00000.0000
C1C3b30.00000.00000.5000
C2C6c60.00000.00000.3889
Ta3Ta6c60.00000.00000.2222

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 18 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

A3B2C_hR6_166_ac_c_b-001: the stoichiometry comes first (A, B, C… are the elements in alphabetical order of their site labels), then the Pearson symbol hR6, then the space-group number 166, then the Wyckoff letters occupied by each element in turn (V: 3a; C: 3b; C: 6c; Ta: 6c). 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 A3B2C_hR6_166_ac_c_b-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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