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Crystal Lab › Prototype structures › Trigonal

HP-Bi₂O₃

Trigonal · space group P31c (No. 159) · Pearson hP20

Symmetry elements and Wyckoff positions (interactive)

HP-Bi₂O₃ in P31c

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

Unit cell

Lattice constants
a = 7.749 Å, b = 7.749 Å, c = 6.302 Å; α = 90.00°, β = 90.00°, γ = 120.00°
Cell volume
327.7 ų
Atoms in the conventional cell
20 (Bi 8, O 12)
Formula units Z
4
Pearson symbol
hP20 — hexagonal / trigonal, primitive lattice, 20 atoms per conventional cell
Symmetry operations
6 per cell

Crystallographic sites

SiteElementWyckoffMultiplicityxyz
Bi1Bi2b20.33330.66670.0000
Bi2Bi6c60.33700.15400.0210
O3O6c60.45100.06100.2870
O4O6c60.14900.28200.0830

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 20 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

A2B3_hP20_159_bc_2c-001: the stoichiometry comes first (A, B, C… are the elements in alphabetical order of their site labels), then the Pearson symbol hP20, then the space-group number 159, then the Wyckoff letters occupied by each element in turn (Bi: 2b; Bi: 6c; O: 6c; O: 6c). Two structures with the same label are the same arrangement with different cell parameters or coordinates.

Note: HP.

Source

Coordinates and cell from the AFLOW Encyclopedia of Crystallographic Prototypes, entry A2B3_hP20_159_bc_2c-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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