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Crystal Lab › Prototype structures › Trigonal

Ni₁₃Ga₃Ge₆

Trigonal · space group P3121 (No. 152) · Pearson hP66

Symmetry elements and Wyckoff positions (interactive)

Ni₁₃Ga₃Ge₆ in P3121

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

Unit cell

Lattice constants
a = 7.849 Å, b = 7.849 Å, c = 15.036 Å; α = 90.00°, β = 90.00°, γ = 120.00°
Cell volume
802.2 ų
Atoms in the conventional cell
66 (Ga 9, Ni 39, Ge 18)
Formula units Z
3
Pearson symbol
hP66 — hexagonal / trigonal, primitive lattice, 66 atoms per conventional cell
Symmetry operations
6 per cell

Crystallographic sites

SiteElementWyckoffMultiplicityxyz
Ga1Ga3a30.49610.00000.3333
Ni6Ni3a30.99900.00000.3333
Ni7Ni3b30.00430.00000.8333
Ni8Ni3b30.49410.00000.8333
Ga2Ga6c60.30930.19260.4206
Ge3Ge6c60.61620.30690.5782
Ge4Ge6c60.33900.17030.7514
Ge5Ge6c60.31110.11780.0894
Ni10Ni6c60.50100.00110.6659
Ni11Ni6c60.67830.33900.7456
Ni12Ni6c60.33820.17750.9259
Ni13Ni6c60.33810.16150.2526
Ni9Ni6c60.50340.99770.4970

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 66 atoms drawn above are these sites multiplied by all 6 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

A3B6C13_hP66_152_ac_3c_a2b5c-001: the stoichiometry comes first (A, B, C… are the elements in alphabetical order of their site labels), then the Pearson symbol hP66, then the space-group number 152, then the Wyckoff letters occupied by each element in turn (Ga: 3a; Ni: 3a; Ni: 3b; Ni: 3b; Ga: 6c; Ge: 6c; Ge: 6c; Ge: 6c; Ni: 6c; Ni: 6c; Ni: 6c; Ni: 6c; Ni: 6c). 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 A3B6C13_hP66_152_ac_3c_a2b5c-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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