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Crystal Lab › Prototype structures › Hexagonal

Tl₃Ga₉S₁₃O₂

Hexagonal · space group P-6 (No. 174) · Pearson hP27

Symmetry elements and Wyckoff positions (interactive)

Tl₃Ga₉S₁₃O₂ in P-6

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

Unit cell

Lattice constants
a = 9.598 Å, b = 9.598 Å, c = 7.433 Å; α = 90.00°, β = 90.00°, γ = 120.00°
Cell volume
593.0 ų
Atoms in the conventional cell
27 (S 13, Tl 3, O 2, Ga 9)
Formula units Z
1
Pearson symbol
hP27 — hexagonal / trigonal, primitive lattice, 27 atoms per conventional cell
Symmetry operations
6 per cell

Crystallographic sites

SiteElementWyckoffMultiplicityxyz
S4S1a11.00000.00000.0000
Tl8Tl1b11.00000.00000.5000
Tl9Tl1c10.33330.66670.0000
Tl10Tl1d10.33330.66670.5000
O3O2i20.66670.33330.2610
Ga1Ga3j30.79020.74030.0000
S5S3j30.37530.32570.0000
S6S3k30.35830.33070.5000
Ga2Ga6l60.52740.42000.2649
S7S6l60.64980.68980.2554

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 27 atoms drawn above are these sites multiplied by all 6 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

A9B2C13D3_hP27_174_jl_i_ajkl_bcd-001: the stoichiometry comes first (A, B, C… are the elements in alphabetical order of their site labels), then the Pearson symbol hP27, then the space-group number 174, then the Wyckoff letters occupied by each element in turn (S: 1a; Tl: 1b; Tl: 1c; Tl: 1d; O: 2i; Ga: 3j; S: 3j; S: 3k; Ga: 6l; S: 6l). 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 A9B2C13D3_hP27_174_jl_i_ajkl_bcd-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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