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Crystal Lab › Prototype structures › Trigonal

ThB₂C

Trigonal · space group R-3m (No. 166) · Pearson hR12

Symmetry elements and Wyckoff positions (interactive)

ThB₂C in R-3m

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

Unit cell

Lattice constants
a = 6.676 Å, b = 6.676 Å, c = 11.376 Å; α = 90.00°, β = 90.00°, γ = 120.00°
Cell volume
439.1 ų
Atoms in the conventional cell
36 (Th 9, C 9, B 18)
Formula units Z
9
Pearson symbol
hR12 — hexagonal / trigonal, rhombohedral lattice, 12 atoms per conventional cell
Symmetry operations
36 per cell

Crystallographic sites

SiteElementWyckoffMultiplicityxyz
Th3Th3a30.00000.00000.0000
Th4Th6c60.00000.00000.3142
C2C9d90.50000.00000.5000
B1B18g180.27670.00000.5000

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 36 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

A2BC_hR12_166_g_d_ac-001: the stoichiometry comes first (A, B, C… are the elements in alphabetical order of their site labels), then the Pearson symbol hR12, then the space-group number 166, then the Wyckoff letters occupied by each element in turn (Th: 3a; Th: 6c; C: 9d; B: 18g). Two structures with the same label are the same arrangement with different cell parameters or coordinates.

Other compounds with this structure

β-UB₂C (HT) <!--beginning with an

Source

Coordinates and cell from the AFLOW Encyclopedia of Crystallographic Prototypes, entry A2BC_hR12_166_g_d_ac-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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