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Crystal Lab › Prototype structures › Triclinic

α-K₂Bi₈Se₁₃ Bi₈K₂Se₁₃

Triclinic · space group P-1 (No. 2) · Pearson aP23

Symmetry elements and Wyckoff positions (interactive)

α-K₂Bi₈Se₁₃ in P-1

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

Unit cell

Lattice constants
a = 13.788 Å, b = 12.096 Å, c = 4.166 Å; α = 89.98°, β = 98.64°, γ = 87.96°
Cell volume
686.4 ų
Atoms in the conventional cell
23 (Se 13, Bi 8, K 2)
Formula units Z
1
Pearson symbol
aP23 — triclinic, primitive lattice, 23 atoms per conventional cell
Symmetry operations
2 per cell

Crystallographic sites

SiteElementWyckoffMultiplicityxyz
Se1Se1a10.00000.00000.0000
Bi2Bi2i20.88090.88030.4408
Bi3Bi2i20.37870.04640.1887
Bi4Bi2i20.15100.79400.0758
Bi5Bi2i20.56280.36710.2822
K6K2i20.83100.55100.4150
Se7Se2i20.26250.92670.6320
Se8Se2i20.03700.69770.5160
Se9Se2i20.77880.77070.8870
Se10Se2i20.50940.85360.2540
Se11Se2i20.28110.61690.1400
Se12Se2i20.58370.58860.2930

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 23 atoms drawn above are these sites multiplied by all 2 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

A8B2C13_aP23_2_4i_i_a6i-001: the stoichiometry comes first (A, B, C… are the elements in alphabetical order of their site labels), then the Pearson symbol aP23, then the space-group number 2, then the Wyckoff letters occupied by each element in turn (Se: 1a; Bi: 2i; Bi: 2i; Bi: 2i; Bi: 2i; K: 2i; Se: 2i; Se: 2i; Se: 2i; Se: 2i; Se: 2i; Se: 2i). 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 A8B2C13_aP23_2_4i_i_a6i-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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