Crystal Lab › Prototype structures › Tetragonal

Deltalumite (δ-alumina, Al₂O₃)

Tetragonal · space group P-4m2 (No. 115) · Pearson tP84 · mineral: deltalumite

Symmetry elements and Wyckoff positions (interactive)

Deltalumite (δ-alumina, Al₂O₃) in P-4m2

Setting

Loading the group…

Model atom x

x = 0.10, y = 0.17, z = 0.08

Unit cell

Lattice constants: a = 5.599 Å, b = 5.599 Å, c = 23.657 Å; α = 90.00°, β = 90.00°, γ = 90.00°
Cell volume: 741.6 Å³
Atoms in the conventional cell: 84 (Al 36, O 48)
Formula units Z: 12
Pearson symbol: tP84 — tetragonal, primitive lattice, 84 atoms per conventional cell
Symmetry operations: 8 per cell

Crystallographic sites

Site	Element	Wyckoff	Multiplicity	x	y	z
Al1	Al	1a	1	0.0000	0.0000	0.0000
Al2	Al	1c	1	0.5000	0.5000	0.5000
Al3	Al	2e	2	0.0000	0.0000	0.3333
Al4	Al	2f	2	0.5000	0.5000	0.1667
Al5	Al	2g	2	0.0000	0.5000	0.2550
Al6	Al	2g	2	0.0000	0.5000	0.5899
Al7	Al	2g	2	0.0000	0.5000	0.9190
Al10	Al	4j	4	0.2604	0.0000	0.8681
Al8	Al	4j	4	0.2608	0.0000	0.2148
Al9	Al	4j	4	0.2708	0.0000	0.5480
O14	O	4j	4	0.2689	0.0000	0.1288
O15	O	4j	4	0.2951	0.0000	0.2986
O16	O	4j	4	0.2595	0.0000	0.4601
O17	O	4j	4	0.2822	0.0000	0.6259
O18	O	4j	4	0.2437	0.0000	0.7856
O19	O	4j	4	0.2381	0.0000	0.9479
Al11	Al	4k	4	0.2689	0.5000	0.0476
Al12	Al	4k	4	0.2722	0.5000	0.3704
Al13	Al	4k	4	0.2603	0.5000	0.7090
O20	O	4k	4	0.2332	0.5000	0.1250
O21	O	4k	4	0.2707	0.5000	0.2917
O22	O	4k	4	0.2515	0.5000	0.4569
O23	O	4k	4	0.2755	0.5000	0.6328
O24	O	4k	4	0.2400	0.5000	0.7900
O25	O	4k	4	0.2755	0.5000	0.9606

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 84 atoms drawn above are these sites multiplied by all 8 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

A3B4_tP84_115_acef3g3j3k_6j6k-001: the stoichiometry comes first (A, B, C… are the elements in alphabetical order of their site labels), then the Pearson symbol tP84, then the space-group number 115, then the Wyckoff letters occupied by each element in turn (Al: 1a; Al: 1c; Al: 2e; Al: 2f; Al: 2g; Al: 2g; Al: 2g; Al: 4j; Al: 4j; Al: 4j; O: 4j; O: 4j; O: 4j; O: 4j; O: 4j; O: 4j; Al: 4k; Al: 4k; Al: 4k; O: 4k; O: 4k; O: 4k; O: 4k; O: 4k; O: 4k). Two structures with the same label are the same arrangement with different cell parameters or coordinates.

Note: \delta-alumina/Deltalumite.

Source

Coordinates and cell from the AFLOW Encyclopedia of Crystallographic Prototypes, entry A3B4_tP84_115_acef3g3j3k_6j6k-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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