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Hexagonal Trinepheline (NaAlSiO₄)

Hexagonal · space group P61 (No. 169) · Pearson hP168 · mineral: trinepheline

Symmetry elements and Wyckoff positions (interactive)

Hexagonal Trinepheline (NaAlSiO₄) in P61

Setting

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Model atom x

x = 0.10, y = 0.17, z = 0.08

Unit cell

Lattice constants: a = 9.995 Å, b = 9.995 Å, c = 24.797 Å; α = 90.00°, β = 90.00°, γ = 120.00°
Cell volume: 2145.3 Å³
Atoms in the conventional cell: 168 (Al 24, Na 24, O 96, Si 24)
Formula units Z: 24
Pearson symbol: hP168 — hexagonal / trigonal, primitive lattice, 168 atoms per conventional cell
Symmetry operations: 6 per cell

Crystallographic sites

Site	Element	Wyckoff	Multiplicity	x	y	z
Al1	Al	6a	6	0.3266	0.0980	0.0864
Al2	Al	6a	6	0.8807	0.2456	0.0917
Al3	Al	6a	6	0.8111	0.7080	0.0954
Al4	Al	6a	6	0.3308	0.6452	0.0906
Na5	Na	6a	6	0.0205	0.5648	0.0356
Na6	Na	6a	6	0.4735	0.4421	0.0303
Na7	Na	6a	6	0.5183	0.5574	0.1864
Na8	Na	6a	6	0.0043	0.0149	0.0280
O10	O	6a	6	0.0584	0.3363	0.9259
O11	O	6a	6	0.0281	0.2729	0.1362
O12	O	6a	6	0.2765	0.3131	0.1869
O13	O	6a	6	0.0581	0.7541	0.1950
O14	O	6a	6	0.1918	0.1587	0.0955
O15	O	6a	6	0.6810	0.5348	0.1264
O16	O	6a	6	0.8617	0.0543	0.9606
O17	O	6a	6	0.9600	0.2904	0.0271
O18	O	6a	6	0.7696	0.2587	0.9493
O19	O	6a	6	0.1799	0.6454	0.1262
O20	O	6a	6	0.5167	0.2485	0.0918
O21	O	6a	6	0.2881	0.9467	0.1303
O22	O	6a	6	0.3024	0.6774	0.0239
O23	O	6a	6	0.0045	0.7562	0.0920
O24	O	6a	6	0.8212	0.3766	0.1086
O9	O	6a	6	0.3137	0.4629	0.0967
Si25	Si	6a	6	0.2024	0.3036	0.1279
Si26	Si	6a	6	0.3637	0.7023	0.9626
Si27	Si	6a	6	0.9122	0.2364	0.9650
Si28	Si	6a	6	0.1334	0.7782	0.1358

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 168 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

ABC4D_hP168_169_4a_4a_16a_4a-001: the stoichiometry comes first (A, B, C… are the elements in alphabetical order of their site labels), then the Pearson symbol hP168, then the space-group number 169, then the Wyckoff letters occupied by each element in turn (Al: 6a; Al: 6a; Al: 6a; Al: 6a; Na: 6a; Na: 6a; Na: 6a; Na: 6a; O: 6a; O: 6a; O: 6a; O: 6a; O: 6a; O: 6a; O: 6a; O: 6a; O: 6a; O: 6a; O: 6a; O: 6a; O: 6a; O: 6a; O: 6a; O: 6a; Si: 6a; Si: 6a; Si: 6a; Si: 6a). Two structures with the same label are the same arrangement with different cell parameters or coordinates.

Note: Trinepheline.

Source

Coordinates and cell from the AFLOW Encyclopedia of Crystallographic Prototypes, entry ABC4D_hP168_169_4a_4a_16a_4a-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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