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Crystal Lab › Prototype structures › Tetragonal

Na₄Ge₉O₂₀

Tetragonal · space group I41/a (No. 88) · Pearson tI132

Symmetry elements and Wyckoff positions (interactive)

Na₄Ge₉O₂₀ in I41/a

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

Unit cell

Lattice constants
a = 14.980 Å, b = 14.980 Å, c = 7.384 Å; α = 90.00°, β = 90.00°, γ = 90.00°
Cell volume
1657.0 ų
Atoms in the conventional cell
132 (Ge 36, Na 16, O 80)
Formula units Z
4
Pearson symbol
tI132 — tetragonal, body-centred lattice, 132 atoms per conventional cell
Symmetry operations
16 per cell

Crystallographic sites

SiteElementWyckoffMultiplicityxyz
Ge1Ge4a40.00000.25000.1250
Ge2Ge16f160.63660.54600.2009
Ge3Ge16f160.09560.21800.4912
Na4Na16f160.58780.55440.6702
O5O16f160.09280.21270.2448
O6O16f160.08240.22270.7476
O7O16f160.68890.57390.4074
O8O16f160.02530.04460.7555
O9O16f160.65540.60880.0070

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 132 atoms drawn above are these sites multiplied by all 16 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

A9B4C20_tI132_88_a2f_f_5f-001: the stoichiometry comes first (A, B, C… are the elements in alphabetical order of their site labels), then the Pearson symbol tI132, then the space-group number 88, then the Wyckoff letters occupied by each element in turn (Ge: 4a; Ge: 16f; Ge: 16f; Na: 16f; O: 16f; O: 16f; O: 16f; O: 16f; O: 16f). 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 A9B4C20_tI132_88_a2f_f_5f-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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