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Crystal Lab › Prototype structures › Tetragonal

Bi₄Fe₅O₁₃F

Tetragonal · space group P42/mbc (No. 135) · Pearson tP108

Symmetry elements and Wyckoff positions (interactive)

Bi₄Fe₅O₁₃F in P42/mbc

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

Unit cell

Lattice constants
a = 8.300 Å, b = 8.300 Å, c = 18.057 Å; α = 90.00°, β = 90.00°, γ = 90.00°
Cell volume
1243.8 ų
Atoms in the conventional cell
108 (Fe 20, O 56, Bi 16, F 16)
Formula units Z
4
Pearson symbol
tP108 — tetragonal, primitive lattice, 108 atoms per conventional cell
Symmetry operations
16 per cell

Crystallographic sites

SiteElementWyckoffMultiplicityxyz
Fe3Fe4d40.00000.50000.2500
O6O8e80.00000.00000.0072
Fe4Fe8f80.00000.50000.0800
O7O8g80.32680.82680.2500
Fe5Fe8h80.85150.83880.0000
O8O8h80.13620.59000.0000
Bi1Bi16i160.67060.65920.1570
F2F16i160.02400.00000.2597
O10O16i160.58230.86030.3331
O9O16i160.29140.87600.5858

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 108 atoms drawn above are these sites multiplied by all 16 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

A4B4C5D14_tP108_135_i_i_dfh_egh2i-001: the stoichiometry comes first (A, B, C… are the elements in alphabetical order of their site labels), then the Pearson symbol tP108, then the space-group number 135, then the Wyckoff letters occupied by each element in turn (Fe: 4d; O: 8e; Fe: 8f; O: 8g; Fe: 8h; O: 8h; Bi: 16i; F: 16i; O: 16i; O: 16i). 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 A4B4C5D14_tP108_135_i_i_dfh_egh2i-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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