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Crystal Lab › Prototype structures › Trigonal

BaPb₃

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

Symmetry elements and Wyckoff positions (interactive)

BaPb₃ in R-3m

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

Unit cell

Lattice constants
a = 7.287 Å, b = 7.287 Å, c = 25.770 Å; α = 90.00°, β = 90.00°, γ = 120.00°
Cell volume
1185.1 ų
Atoms in the conventional cell
36 (Ba 9, Pb 27)
Formula units Z
9
Pearson symbol
hR12 — hexagonal / trigonal, rhombohedral lattice, 12 atoms per conventional cell
Symmetry operations
36 per cell

Crystallographic sites

SiteElementWyckoffMultiplicityxyz
Ba1Ba3a30.00000.00000.0000
Ba2Ba6c60.00000.00000.2222
Pb3Pb9e90.50000.00000.0000
Pb4Pb18h180.16670.83330.1111

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

AB3_hR12_166_ac_eh-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 (Ba: 3a; Ba: 6c; Pb: 9e; Pb: 18h). Two structures with the same label are the same arrangement with different cell parameters or coordinates.

Other compounds with this structure

GdAl₃, PuAl₃, TbAl₃, YAl₃ <!--beginning with an

Source

Coordinates and cell from the AFLOW Encyclopedia of Crystallographic Prototypes, entry AB3_hR12_166_ac_eh-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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