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Crystal Lab › Prototype structures › Trigonal

TaTi₇ (BCC SQS-16)

Trigonal · space group R-3m (No. 166) · Pearson hR16

Symmetry elements and Wyckoff positions (interactive)

TaTi₇ (BCC SQS-16) in R-3m

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

Unit cell

Lattice constants
a = 9.252 Å, b = 9.252 Å, c = 11.331 Å; α = 90.00°, β = 90.00°, γ = 120.00°
Cell volume
840.0 ų
Atoms in the conventional cell
48 (Ta 6, Ti 42)
Formula units Z
6
Pearson symbol
hR16 — hexagonal / trigonal, rhombohedral lattice, 16 atoms per conventional cell
Symmetry operations
36 per cell

Crystallographic sites

SiteElementWyckoffMultiplicityxyz
Ta1Ta6c60.00000.00000.8750
Ti2Ti6c60.00000.00000.6250
Ti3Ti18h180.83330.16670.7917
Ti4Ti18h180.16670.83330.9583

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 48 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

AB7_hR16_166_c_c2h-001: the stoichiometry comes first (A, B, C… are the elements in alphabetical order of their site labels), then the Pearson symbol hR16, then the space-group number 166, then the Wyckoff letters occupied by each element in turn (Ta: 6c; Ti: 6c; Ti: 18h; Ti: 18h). Two structures with the same label are the same arrangement with different cell parameters or coordinates.

Note: BCC SQS-16.

Source

Coordinates and cell from the AFLOW Encyclopedia of Crystallographic Prototypes, entry AB7_hR16_166_c_c2h-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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