β-Alumina (D5₆, Al₂O₃)

Unit cell

Lattice constants

a = 5.560 Å, b = 5.560 Å, c = 22.550 Å; α = 90.00°, β = 90.00°, γ = 120.00°

Cell volume

603.7 ų

Atoms in the conventional cell

60 (O 36, Al 24)

Formula units Z

12

Pearson symbol

hP60 — hexagonal / trigonal, primitive lattice, 60 atoms per conventional cell

Symmetry operations

24 per cell

Crystallographic sites

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 60 atoms drawn above are these sites multiplied by all 24 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

A2B3_hP60_194_3fk_cdef2k-001: the stoichiometry comes first (A, B, C… are the elements in alphabetical order of their site labels), then the Pearson symbol hP60, then the space-group number 194, then the Wyckoff letters occupied by each element in turn (O: 2c; O: 2d; O: 4e; Al: 4f; Al: 4f; Al: 4f; O: 4f; Al: 12k; O: 12k; O: 12k). Two structures with the same label are the same arrangement with different cell parameters or coordinates.

Note: D5₆, \beta-Alumina.

Source

Coordinates and cell from the AFLOW Encyclopedia of Crystallographic Prototypes, entry A2B3_hP60_194_3fk_cdef2k-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.