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Crystal Lab › Prototype structures › Hexagonal

Na₄Ge₁₃

Hexagonal · space group P6/m (No. 175) · Pearson hP58

Symmetry elements and Wyckoff positions (interactive)

Na₄Ge₁₃ in P6/m

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

Unit cell

Lattice constants
a = 15.027 Å, b = 15.027 Å, c = 3.960 Å; α = 90.00°, β = 90.00°, γ = 120.00°
Cell volume
774.5 ų
Atoms in the conventional cell
58 (Na 20, Ge 38)
Formula units Z
2
Pearson symbol
hP58 — hexagonal / trigonal, primitive lattice, 58 atoms per conventional cell
Symmetry operations
12 per cell

Crystallographic sites

SiteElementWyckoffMultiplicityxyz
Na7Na2d20.33330.66670.5000
Ge1Ge2e20.00001.00000.0757
Ge2Ge6j60.15240.51860.0000
Ge3Ge6j60.48310.18410.0000
Na8Na6j60.06960.27390.0000
Ge4Ge6k60.04170.44730.5000
Ge5Ge6k60.36950.10330.5000
Ge6Ge12l120.02710.10880.4074
Na9Na12l120.06360.24270.0626

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 58 atoms drawn above are these sites multiplied by all 12 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

A19B10_hP58_175_e2j2kl_djl-001: the stoichiometry comes first (A, B, C… are the elements in alphabetical order of their site labels), then the Pearson symbol hP58, then the space-group number 175, then the Wyckoff letters occupied by each element in turn (Na: 2d; Ge: 2e; Ge: 6j; Ge: 6j; Na: 6j; Ge: 6k; Ge: 6k; Ge: 12l; Na: 12l). 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 A19B10_hP58_175_e2j2kl_djl-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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