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Crystal Lab › Prototype structures › Trigonal

PrNiO₃ Rhombohedral Perovskite NiO₃Pr

Trigonal · space group R-3c (No. 167) · Pearson hR10

Symmetry elements and Wyckoff positions (interactive)

PrNiO₃ Rhombohedral Perovskite in R-3c

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

Unit cell

Lattice constants
a = 5.458 Å, b = 5.458 Å, c = 13.106 Å; α = 90.00°, β = 90.00°, γ = 120.00°
Cell volume
338.1 ų
Atoms in the conventional cell
30 (Pr 6, Ni 6, O 18)
Formula units Z
6
Pearson symbol
hR10 — hexagonal / trigonal, rhombohedral lattice, 10 atoms per conventional cell
Symmetry operations
36 per cell

Crystallographic sites

SiteElementWyckoffMultiplicityxyz
Pr3Pr6a60.00000.00000.2500
Ni1Ni6b60.00000.00000.0000
O2O18e180.44460.00000.2500

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 30 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_hR10_167_b_e_a-001: the stoichiometry comes first (A, B, C… are the elements in alphabetical order of their site labels), then the Pearson symbol hR10, then the space-group number 167, then the Wyckoff letters occupied by each element in turn (Pr: 6a; Ni: 6b; O: 18e). Two structures with the same label are the same arrangement with different cell parameters or coordinates.

Other compounds with this structure

HgMnO₃, LaAlO₃, LaNiO₃ <!--beginning with an

Note: Rhombohedral Perovskite.

Source

Coordinates and cell from the AFLOW Encyclopedia of Crystallographic Prototypes, entry AB3C_hR10_167_b_e_a-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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