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Crystal Lab › Prototype structures › Trigonal

Rhombohedral LiZnPO₄ LiO₄PZn

Trigonal · space group R3 (No. 146) · Pearson hR42

Symmetry elements and Wyckoff positions (interactive)

Rhombohedral LiZnPO₄ in R3

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

Unit cell

Lattice constants
a = 13.628 Å, b = 13.628 Å, c = 9.096 Å; α = 90.00°, β = 90.00°, γ = 120.00°
Cell volume
1463.0 ų
Atoms in the conventional cell
126 (Li 18, O 72, P 18, Zn 18)
Formula units Z
18
Pearson symbol
hR42 — hexagonal / trigonal, rhombohedral lattice, 42 atoms per conventional cell
Symmetry operations
9 per cell

Crystallographic sites

SiteElementWyckoffMultiplicityxyz
Li1Li9b90.79400.98490.4143
Li2Li9b90.54650.68740.5763
O10O9b90.10740.21460.5831
O3O9b90.20810.07830.7195
O4O9b90.79710.92830.2241
O5O9b90.67340.01970.4177
O6O9b90.31770.00270.5849
O7O9b90.55310.77600.7492
O8O9b90.79620.53950.2795
O9O9b90.20550.07420.4432
P11P9b90.21030.01340.5822
P12P9b90.67960.13570.4177
Zn13Zn9b90.19360.21270.7501
Zn14Zn9b90.80620.79160.2478

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 126 atoms drawn above are these sites multiplied by all 9 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

AB4CD_hR42_146_2b_8b_2b_2b-001: the stoichiometry comes first (A, B, C… are the elements in alphabetical order of their site labels), then the Pearson symbol hR42, then the space-group number 146, then the Wyckoff letters occupied by each element in turn (Li: 9b; Li: 9b; O: 9b; O: 9b; O: 9b; O: 9b; O: 9b; O: 9b; O: 9b; O: 9b; P: 9b; P: 9b; Zn: 9b; Zn: 9b). Two structures with the same label are the same arrangement with different cell parameters or coordinates.

Other compounds with this structure

LiAlSiO₄ (α-eucryptite) <!--beginning with an

Note: Rhomb. LiZnPO₄.

Source

Coordinates and cell from the AFLOW Encyclopedia of Crystallographic Prototypes, entry AB4CD_hR42_146_2b_8b_2b_2b-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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