Langbeinite [K₂Mg₂(SO₄)₃]

Unit cell

Lattice constants

a = 9.919 Å, b = 9.919 Å, c = 9.919 Å; α = 90.00°, β = 90.00°, γ = 90.00°

Cell volume

975.9 ų

Atoms in the conventional cell

76 (K 8, Mg 8, O 48, S 12)

Formula units Z

4

Pearson symbol

cP76 — cubic, primitive lattice, 76 atoms per conventional cell

Symmetry operations

12 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 76 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

A2B2C12D3_cP76_198_2a_2a_4b_b-001: the stoichiometry comes first (A, B, C… are the elements in alphabetical order of their site labels), then the Pearson symbol cP76, then the space-group number 198, then the Wyckoff letters occupied by each element in turn (K: 4a; K: 4a; Mg: 4a; Mg: 4a; O: 12b; O: 12b; O: 12b; O: 12b; S: 12b). Two structures with the same label are the same arrangement with different cell parameters or coordinates.

Other compounds with this structure

K₂Ca₂(SO₄)₃), K₂Fe₂(SO₄)₃), K₂Mn₂(SO₄)₃), (K, Ba)Cr₂(PO₄)₃), (NH₄)₂Mg₂(SO₄)₃) <!--beginning with an

Note: Langbeinite.

Source

Coordinates and cell from the AFLOW Encyclopedia of Crystallographic Prototypes, entry A2B2C12D3_cP76_198_2a_2a_4b_b-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.