Crystal Lab › Prototype structures › Hexagonal

Ta₂₁Te₁₃

Hexagonal · space group P6mm (No. 183) · Pearson hP136

Symmetry elements and Wyckoff positions (interactive)

Ta₂₁Te₁₃ in P6mm

Setting

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Model atom x

x = 0.10, y = 0.17, z = 0.08

Unit cell

Lattice constants: a = 19.500 Å, b = 19.500 Å, c = 10.300 Å; α = 90.00°, β = 90.00°, γ = 120.00°
Cell volume: 3391.9 Å³
Atoms in the conventional cell: 136 (Ta 84, Te 52)
Formula units Z: 4
Pearson symbol: hP136 — hexagonal / trigonal, primitive lattice, 136 atoms per conventional cell
Symmetry operations: 12 per cell

Crystallographic sites

Site	Element	Wyckoff	Multiplicity	x	y	z
Ta1	Ta	1a	1	0.0000	0.0000	0.6770
Te15	Te	1a	1	0.0000	0.0000	0.9400
Te16	Te	1a	1	0.0000	0.0000	0.4200
Ta2	Ta	2b	2	0.3333	0.6667	0.4840
Te17	Te	2b	2	0.3333	0.6667	0.9400
Ta3	Ta	3c	3	0.5000	0.0000	0.3940
Ta4	Ta	6d	6	0.7350	0.0000	0.5990
Ta5	Ta	6d	6	0.8550	0.0000	0.8040
Ta6	Ta	6d	6	0.5710	0.0000	0.6420
Te18	Te	6d	6	0.6800	0.0000	0.8440
Te19	Te	6d	6	0.5960	0.0000	0.1860
Te20	Te	6d	6	0.7980	0.0000	0.3670
Ta10	Ta	6e	6	0.9170	0.0830	0.5720
Ta11	Ta	6e	6	0.8380	0.1620	0.4900
Ta12	Ta	6e	6	0.7500	0.2500	0.4620
Ta7	Ta	6e	6	0.5780	0.4220	0.5540
Ta8	Ta	6e	6	0.7140	0.2860	0.7210
Ta9	Ta	6e	6	0.8550	0.1450	0.7610
Te21	Te	6e	6	0.8870	0.1130	0.0110
Te22	Te	6e	6	0.7780	0.2220	0.9090
Te23	Te	6e	6	0.5670	0.4330	0.8170
Te24	Te	6e	6	0.8020	0.1980	0.2480
Te25	Te	6e	6	0.6050	0.3950	0.3000
Ta13	Ta	12f	12	0.2840	0.4280	0.6810
Ta14	Ta	12f	12	0.3310	0.4150	0.4190

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 136 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

A21B13_hP136_183_abc3d6e2f_2ab3d5e-001: the stoichiometry comes first (A, B, C… are the elements in alphabetical order of their site labels), then the Pearson symbol hP136, then the space-group number 183, then the Wyckoff letters occupied by each element in turn (Ta: 1a; Te: 1a; Te: 1a; Ta: 2b; Te: 2b; Ta: 3c; Ta: 6d; Ta: 6d; Ta: 6d; Te: 6d; Te: 6d; Te: 6d; Ta: 6e; Ta: 6e; Ta: 6e; Ta: 6e; Ta: 6e; Ta: 6e; Te: 6e; Te: 6e; Te: 6e; Te: 6e; Te: 6e; Ta: 12f; Ta: 12f). Two structures with the same label are the same arrangement with different cell parameters or coordinates.

Note: Approx. quasicrystal.

Source

Coordinates and cell from the AFLOW Encyclopedia of Crystallographic Prototypes, entry A21B13_hP136_183_abc3d6e2f_2ab3d5e-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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