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Crystal Lab › Prototype structures › Trigonal

KAl(MoO₄)₂: ABC2D8_hP12_164_a_b_d_di-001

Trigonal · space group P-3m1 (No. 164) · Pearson hP12

Symmetry elements and Wyckoff positions (interactive)

KAl(MoO₄)₂: ABC2D8_hP12_164_a_b_d_di-001 in P-3m1

Setting
Loading the group…
x = 0.10, y = 0.17, z = 0.08

Unit cell

Lattice constants
a = 5.545 Å, b = 5.545 Å, c = 7.070 Å; α = 90.00°, β = 90.00°, γ = 120.00°
Cell volume
188.3 ų
Atoms in the conventional cell
12 (Al 1, K 1, Mo 2, O 8)
Formula units Z
1
Pearson symbol
hP12 — hexagonal / trigonal, primitive lattice, 12 atoms per conventional cell
Symmetry operations
12 per cell

Crystallographic sites

SiteElementWyckoffMultiplicityxyz
Al1Al1a10.00000.00000.0000
K2K1b10.00000.00000.5000
Mo3Mo2d20.33330.66670.2349
O4O2d20.33330.66670.4645
O5O6i60.15500.31000.1561

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 12 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

ABC2D8_hP12_164_a_b_d_di-001: the stoichiometry comes first (A, B, C… are the elements in alphabetical order of their site labels), then the Pearson symbol hP12, then the space-group number 164, then the Wyckoff letters occupied by each element in turn (Al: 1a; K: 1b; Mo: 2d; O: 2d; O: 6i). Two structures with the same label are the same arrangement with different cell parameters or coordinates.

Other compounds with this structure

BaFe(MgD₄)₂, BaZr(PO₄)₂, Cd₂(MoO₄)₂, CsAl(MoO₄)₂, CsCr(MoO₄)₂, CsFe(MoO₄)₂, CsV(MoO₄)₂, KFe(MoO₄)₂, KSc(MoO₄)₂, RbAl(MoO₄)₂, RbFe(MoO₄)₂, RbIn(MoO₄)₂, RbIn(WO₄)₂, SrFe(MgD₄)₂, TlAl(MoO₄)₂, TlSc(MoO₄)₂ <!--beginning with an

Source

Coordinates and cell from the AFLOW Encyclopedia of Crystallographic Prototypes, entry ABC2D8_hP12_164_a_b_d_di-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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