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Crystal Lab › Prototype structures › Hexagonal

K₂Ta₄O₉F₄

Hexagonal · space group P6 (No. 168) · Pearson hP57

Symmetry elements and Wyckoff positions (interactive)

K₂Ta₄O₉F₄ in P6

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

Unit cell

Lattice constants
a = 15.936 Å, b = 15.936 Å, c = 3.892 Å; α = 90.00°, β = 90.00°, γ = 120.00°
Cell volume
856.0 ų
Atoms in the conventional cell
57 (O 39, K 6, Ta 12)
Formula units Z
3
Pearson symbol
hP57 — hexagonal / trigonal, primitive lattice, 57 atoms per conventional cell
Symmetry operations
6 per cell

Crystallographic sites

SiteElementWyckoffMultiplicityxyz
O2O3c30.50000.00000.0000
K1K6d60.49650.17900.5550
O3O6d60.03500.18700.0070
O4O6d60.34900.03400.0180
O5O6d60.16800.38800.0100
O6O6d60.19500.56900.0200
O7O6d60.09300.45400.5390
O8O6d60.27300.09500.5550
Ta10Ta6d60.07890.43680.0710
Ta9Ta6d60.26340.09000.0860

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 57 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

A2B13C4_hP57_168_d_c6d_2d-001: the stoichiometry comes first (A, B, C… are the elements in alphabetical order of their site labels), then the Pearson symbol hP57, then the space-group number 168, then the Wyckoff letters occupied by each element in turn (O: 3c; K: 6d; O: 6d; O: 6d; O: 6d; O: 6d; O: 6d; O: 6d; Ta: 6d; Ta: 6d). 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 A2B13C4_hP57_168_d_c6d_2d-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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