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Crystal Lab › Prototype structures › Hexagonal

BaMgSiO₄

Hexagonal · space group P63 (No. 173) · Pearson hP42

Symmetry elements and Wyckoff positions (interactive)

BaMgSiO₄ in P63

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

Unit cell

Lattice constants
a = 9.112 Å, b = 9.112 Å, c = 8.737 Å; α = 90.00°, β = 90.00°, γ = 120.00°
Cell volume
628.2 ų
Atoms in the conventional cell
42 (Ba 6, Mg 6, O 24, Si 6)
Formula units Z
6
Pearson symbol
hP42 — hexagonal / trigonal, primitive lattice, 42 atoms per conventional cell
Symmetry operations
6 per cell

Crystallographic sites

SiteElementWyckoffMultiplicityxyz
Ba1Ba2a20.00000.00000.2500
Ba2Ba2b20.33330.66670.2360
Ba3Ba2b20.33330.66670.7690
Mg4Mg6c60.67380.66800.5390
O5O6c60.76200.90250.5160
O6O6c60.46810.89800.4980
O7O6c60.76700.19180.4560
O8O6c60.70900.65810.7510
Si9Si6c60.65300.98300.4350

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 42 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_hP42_173_a2b_c_4c_c-001: the stoichiometry comes first (A, B, C… are the elements in alphabetical order of their site labels), then the Pearson symbol hP42, then the space-group number 173, then the Wyckoff letters occupied by each element in turn (Ba: 2a; Ba: 2b; Ba: 2b; Mg: 6c; O: 6c; O: 6c; O: 6c; O: 6c; Si: 6c). Two structures with the same label are the same arrangement with different cell parameters or coordinates.

Other compounds with this structure

BNaSiO₄, Ba(Ge, Zn)SiO₄, BaCoSiO₄, BaZnSiO₄, CaAl₂O₄, NaGaSiO₄ (sodalite), (Na_{0.7}K_{0.3}GaSiO₄, NaZnAsO₄, NaZnPO₄, SrAl₂O₄ <!--beginning with an

Source

Coordinates and cell from the AFLOW Encyclopedia of Crystallographic Prototypes, entry ABC4D_hP42_173_a2b_c_4c_c-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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