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Crystal Lab › Prototype structures › Triclinic

Na₂Cu₃Ge₄O₁₂

Triclinic · space group P-1 (No. 2) · Pearson aP21

Symmetry elements and Wyckoff positions (interactive)

Na₂Cu₃Ge₄O₁₂ in P-1

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

Unit cell

Lattice constants
a = 6.182 Å, b = 7.691 Å, c = 5.472 Å; α = 102.39°, β = 93.07°, γ = 87.58°
Cell volume
253.6 ų
Atoms in the conventional cell
21 (Cu 3, Ge 4, Na 2, O 12)
Formula units Z
1
Pearson symbol
aP21 — triclinic, primitive lattice, 21 atoms per conventional cell
Symmetry operations
2 per cell

Crystallographic sites

SiteElementWyckoffMultiplicityxyz
Cu1Cu1a10.00000.00000.0000
Cu2Cu2i20.16320.82310.4873
Ge3Ge2i20.22090.36760.3067
Ge4Ge2i20.39880.18280.7615
Na5Na2i20.24940.59550.9174
O6O2i20.00530.22460.2331
O7O2i20.40210.31840.0644
O8O2i20.36460.34930.5772
O9O2i20.17490.05500.7197
O10O2i20.65800.09650.7305
O11O2i20.12730.58430.2996

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 21 atoms drawn above are these sites multiplied by all 2 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

A3B4C2D12_aP21_2_ai_2i_i_6i-001: the stoichiometry comes first (A, B, C… are the elements in alphabetical order of their site labels), then the Pearson symbol aP21, then the space-group number 2, then the Wyckoff letters occupied by each element in turn (Cu: 1a; Cu: 2i; Ge: 2i; Ge: 2i; Na: 2i; O: 2i; O: 2i; O: 2i; O: 2i; O: 2i; O: 2i). 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 A3B4C2D12_aP21_2_ai_2i_i_6i-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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