Skip to content

Crystal Lab › Prototype structures › Trigonal

Ba₄NbRu₃O₁₂

Trigonal · space group R-3m (No. 166) · Pearson hR20

Symmetry elements and Wyckoff positions (interactive)

Ba₄NbRu₃O₁₂ in R-3m

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

Unit cell

Lattice constants
a = 5.757 Å, b = 5.757 Å, c = 28.587 Å; α = 90.00°, β = 90.00°, γ = 120.00°
Cell volume
820.6 ų
Atoms in the conventional cell
60 (Nb 3, Ru 9, Ba 12, O 36)
Formula units Z
3
Pearson symbol
hR20 — hexagonal / trigonal, rhombohedral lattice, 20 atoms per conventional cell
Symmetry operations
36 per cell

Crystallographic sites

SiteElementWyckoffMultiplicityxyz
Nb3Nb3a30.00000.00000.0000
Ru6Ru3b30.00000.00000.5000
Ba1Ba6c60.00000.00000.1293
Ba2Ba6c60.00000.00000.2868
Ru7Ru6c60.00000.00000.4122
O4O18h180.49230.50770.1224
O5O18h180.50550.49450.2933

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

A4BC12D3_hR20_166_2c_a_2h_bc-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 166, then the Wyckoff letters occupied by each element in turn (Nb: 3a; Ru: 3b; Ba: 6c; Ba: 6c; Ru: 6c; O: 18h; O: 18h). Two structures with the same label are the same arrangement with different cell parameters or coordinates.

Other compounds with this structure

Ir₄NbRu₃O₁₂, Mn₄NbRu₃O₁₂, Rh₄NbRu₃O₁₂ <!--beginning with an

Source

Coordinates and cell from the AFLOW Encyclopedia of Crystallographic Prototypes, entry A4BC12D3_hR20_166_2c_a_2h_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.

← Ce₄Ga₅Rh₉  ·  Space group R-3m (75 prototypes)  ·  All prototypes  ·  CeAuAl₄Ge₂ →