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Crystal Lab › Prototype structures › Trigonal

P3 La₃BWO₉ BLi₃O₉W

Trigonal · space group P3 (No. 143) · Pearson hP28

Symmetry elements and Wyckoff positions (interactive)

P3 La₃BWO₉ in P3

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

Unit cell

Lattice constants
a = 8.843 Å, b = 8.843 Å, c = 5.575 Å; α = 90.00°, β = 90.00°, γ = 120.00°
Cell volume
377.6 ų
Atoms in the conventional cell
28 (B 2, W 2, La 6, O 18)
Formula units Z
2
Pearson symbol
hP28 — hexagonal / trigonal, primitive lattice, 28 atoms per conventional cell
Symmetry operations
3 per cell

Crystallographic sites

SiteElementWyckoffMultiplicityxyz
B1B1a10.00000.00000.3600
B2B1a10.00000.00000.8400
W11W1b10.33330.66670.2500
W12W1c10.66670.33330.7700
La3La3d30.36300.08400.2290
La4La3d30.27800.36500.7370
O10O3d30.61700.14300.9960
O5O3d30.17200.05600.8390
O6O3d30.13800.16900.4180
O7O3d30.18100.49800.9830
O8O3d30.72800.19800.5940
O9O3d30.13400.50200.4270

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 28 atoms drawn above are these sites multiplied by all 3 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

AB3C9D_hP28_143_2a_2d_6d_bc-001: the stoichiometry comes first (A, B, C… are the elements in alphabetical order of their site labels), then the Pearson symbol hP28, then the space-group number 143, then the Wyckoff letters occupied by each element in turn (B: 1a; B: 1a; W: 1b; W: 1c; La: 3d; La: 3d; O: 3d; O: 3d; O: 3d; O: 3d; O: 3d; O: 3d). Two structures with the same label are the same arrangement with different cell parameters or coordinates.

Note: Trigonal.

Source

Coordinates and cell from the AFLOW Encyclopedia of Crystallographic Prototypes, entry AB3C9D_hP28_143_2a_2d_6d_bc-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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