Crystal Lab › Prototype structures › Hexagonal
BaMgSiO₄
Hexagonal · space group P63 (No. 173) · Pearson hP42
Symmetry elements and Wyckoff positions (interactive)
BaMgSiO₄ in P63
SettingUnit 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
| Site | Element | Wyckoff | Multiplicity | x | y | z |
|---|---|---|---|---|---|---|
| Ba1 | Ba | 2a | 2 | 0.0000 | 0.0000 | 0.2500 |
| Ba2 | Ba | 2b | 2 | 0.3333 | 0.6667 | 0.2360 |
| Ba3 | Ba | 2b | 2 | 0.3333 | 0.6667 | 0.7690 |
| Mg4 | Mg | 6c | 6 | 0.6738 | 0.6680 | 0.5390 |
| O5 | O | 6c | 6 | 0.7620 | 0.9025 | 0.5160 |
| O6 | O | 6c | 6 | 0.4681 | 0.8980 | 0.4980 |
| O7 | O | 6c | 6 | 0.7670 | 0.1918 | 0.4560 |
| O8 | O | 6c | 6 | 0.7090 | 0.6581 | 0.7510 |
| Si9 | Si | 6c | 6 | 0.6530 | 0.9830 | 0.4350 |
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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