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Crystal Lab › Prototype structures › Trigonal

AgRuO₃

Trigonal · space group R-3c (No. 167) · Pearson hR20

Symmetry elements and Wyckoff positions (interactive)

AgRuO₃ in R-3c

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

Unit cell

Lattice constants
a = 5.226 Å, b = 5.226 Å, c = 32.358 Å; α = 90.00°, β = 90.00°, γ = 120.00°
Cell volume
765.4 ų
Atoms in the conventional cell
60 (Ag 12, Ru 12, O 36)
Formula units Z
12
Pearson symbol
hR20 — hexagonal / trigonal, rhombohedral lattice, 20 atoms per conventional cell
Symmetry operations
36 per cell

Crystallographic sites

SiteElementWyckoffMultiplicityxyz
Ag1Ag12c120.00000.00000.9304
Ru3Ru12c120.00000.00000.6684
O2O36f360.05110.33820.3004

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 60 atoms drawn above are these sites multiplied by all 36 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

AB3C_hR20_167_c_f_c-001: the stoichiometry comes first (A, B, C… are the elements in alphabetical order of their site labels), then the Pearson symbol hR20, then the space-group number 167, then the Wyckoff letters occupied by each element in turn (Ag: 12c; Ru: 12c; O: 36f). 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 AB3C_hR20_167_c_f_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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