Crystal Lab › Prototype structures › Cubic
Ca₃Al₂O₆
Cubic · space group Pa-3 (No. 205) · Pearson cP264
Symmetry elements and Wyckoff positions (interactive)
Ca₃Al₂O₆ in Pa-3
SettingUnit cell
- Lattice constants
- a = 15.263 Å, b = 15.263 Å, c = 15.263 Å; α = 90.00°, β = 90.00°, γ = 90.00°
- Cell volume
- 3555.7 ų
- Atoms in the conventional cell
- 264 (Ca 72, Al 48, O 144)
- Formula units Z
- 24
- Pearson symbol
- cP264 — cubic, primitive lattice, 264 atoms per conventional cell
- Symmetry operations
- 24 per cell
Crystallographic sites
| Site | Element | Wyckoff | Multiplicity | x | y | z |
|---|---|---|---|---|---|---|
| Ca3 | Ca | 4a | 4 | 0.0000 | 0.0000 | 0.0000 |
| Ca4 | Ca | 4b | 4 | 0.5000 | 0.5000 | 0.5000 |
| Ca5 | Ca | 8c | 8 | 0.2561 | 0.2561 | 0.2561 |
| Ca6 | Ca | 8c | 8 | 0.3750 | 0.3750 | 0.3750 |
| Al1 | Al | 24d | 24 | 0.2526 | 0.0133 | 0.0197 |
| Al2 | Al | 24d | 24 | 0.2444 | 0.2335 | 0.0046 |
| Ca7 | Ca | 24d | 24 | 0.1386 | 0.3763 | 0.1272 |
| Ca8 | Ca | 24d | 24 | 0.3800 | 0.3838 | 0.1209 |
| O10 | O | 24d | 24 | 0.4835 | 0.1315 | 0.2536 |
| O11 | O | 24d | 24 | 0.2664 | 0.2841 | 0.1049 |
| O12 | O | 24d | 24 | 0.2350 | 0.4047 | 0.2921 |
| O13 | O | 24d | 24 | 0.3491 | 0.9615 | 0.8926 |
| O14 | O | 24d | 24 | 0.1509 | 0.9896 | 0.9758 |
| O9 | O | 24d | 24 | 0.2777 | 0.1241 | 0.0103 |
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 264 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
A2B3C6_cP264_205_2d_ab2c2d_6d-001: the stoichiometry comes first (A, B, C… are the elements in alphabetical order of their site labels), then the Pearson symbol cP264, then the space-group number 205, then the Wyckoff letters occupied by each element in turn (Ca: 4a; Ca: 4b; Ca: 8c; Ca: 8c; Al: 24d; Al: 24d; Ca: 24d; Ca: 24d; O: 24d; O: 24d; O: 24d; O: 24d; O: 24d; O: 24d). Two structures with the same label are the same arrangement with different cell parameters or coordinates.
Source
Coordinates and cell from the AFLOW Encyclopedia of Crystallographic Prototypes, entry A2B3C6_cP264_205_2d_ab2c2d_6d-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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