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Crystal Lab › Prototype structures › Trigonal

Li₇Pb₂

Trigonal · space group P-3m1 (No. 164) · Pearson hP9

Symmetry elements and Wyckoff positions (interactive)

Li₇Pb₂ in P-3m1

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

Unit cell

Lattice constants
a = 4.710 Å, b = 4.710 Å, c = 8.589 Å; α = 90.00°, β = 90.00°, γ = 120.00°
Cell volume
165.0 ų
Atoms in the conventional cell
9 (Li 7, Pb 2)
Formula units Z
1
Pearson symbol
hP9 — hexagonal / trigonal, primitive lattice, 9 atoms per conventional cell
Symmetry operations
12 per cell

Crystallographic sites

SiteElementWyckoffMultiplicityxyz
Li1Li1a10.00001.00000.0000
Li2Li2c20.00001.00000.3333
Li3Li2d20.33330.66670.9167
Li4Li2d20.33330.66670.5833
Pb5Pb2d20.33330.66670.2500

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 9 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

A7B2_hP9_164_ac2d_d-001: the stoichiometry comes first (A, B, C… are the elements in alphabetical order of their site labels), then the Pearson symbol hP9, then the space-group number 164, then the Wyckoff letters occupied by each element in turn (Li: 1a; Li: 2c; Li: 2d; Li: 2d; Pb: 2d). 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 A7B2_hP9_164_ac2d_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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