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Crystal Lab › Prototype structures › Trigonal

Li₁₃Sn₅

Trigonal · space group P-3m1 (No. 164) · Pearson hP18

Symmetry elements and Wyckoff positions (interactive)

Li₁₃Sn₅ in P-3m1

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

Unit cell

Lattice constants
a = 4.700 Å, b = 4.700 Å, c = 17.120 Å; α = 90.00°, β = 90.00°, γ = 120.00°
Cell volume
327.5 ų
Atoms in the conventional cell
18 (Li 13, Sn 5)
Formula units Z
1
Pearson symbol
hP18 — hexagonal / trigonal, primitive lattice, 18 atoms per conventional cell
Symmetry operations
12 per cell

Crystallographic sites

SiteElementWyckoffMultiplicityxyz
Li1Li1a10.00000.00000.0000
Sn8Sn1b10.00000.00000.5000
Li2Li2c20.00000.00000.6640
Li3Li2c20.00000.00000.1680
Li4Li2d20.33330.66670.4430
Li5Li2d20.33330.66670.9450
Li6Li2d20.33330.66670.7840
Li7Li2d20.33330.66670.6170
Sn10Sn2d20.33330.66670.1091
Sn9Sn2d20.33330.66670.2764

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 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

A13B5_hP18_164_a2c4d_b2d-001: the stoichiometry comes first (A, B, C… are the elements in alphabetical order of their site labels), then the Pearson symbol hP18, then the space-group number 164, then the Wyckoff letters occupied by each element in turn (Li: 1a; Sn: 1b; Li: 2c; Li: 2c; Li: 2d; Li: 2d; Li: 2d; Li: 2d; Sn: 2d; Sn: 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 A13B5_hP18_164_a2c4d_b2d-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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