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Crystal Lab › Prototype structures › Trigonal

Trigonal Li₄P₂O₇ Li₄O₇P₂

Trigonal · space group P3212 (No. 153) · Pearson hP39

Symmetry elements and Wyckoff positions (interactive)

Trigonal Li₄P₂O₇ in P3212

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

Unit cell

Lattice constants
a = 5.170 Å, b = 5.170 Å, c = 18.972 Å; α = 90.00°, β = 90.00°, γ = 120.00°
Cell volume
439.1 ų
Atoms in the conventional cell
39 (O 21, Li 12, P 6)
Formula units Z
3
Pearson symbol
hP39 — hexagonal / trigonal, primitive lattice, 39 atoms per conventional cell
Symmetry operations
6 per cell

Crystallographic sites

SiteElementWyckoffMultiplicityxyz
O1O3a30.52940.47060.6667
Li2Li6c60.08780.81250.7797
Li3Li6c60.76920.17770.7786
O4O6c60.13960.49510.7437
O5O6c60.40520.21500.7805
O6O6c60.68860.77380.7767
P7P6c60.43000.49200.7451

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 39 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

A4B7C2_hP39_153_2c_a3c_c-001: the stoichiometry comes first (A, B, C… are the elements in alphabetical order of their site labels), then the Pearson symbol hP39, then the space-group number 153, then the Wyckoff letters occupied by each element in turn (O: 3a; Li: 6c; Li: 6c; O: 6c; O: 6c; O: 6c; P: 6c). 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 A4B7C2_hP39_153_2c_a3c_c-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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