β (high) Cristobalite AlPO$_{4}$ Structure: AB12C_cF56_216_a_h_c-001
| Prototype | AlO$_{4}$P |
| AFLOW prototype label | AB12C_cF56_216_a_h_c-001 |
| ICSD | 162669 |
| CCDC | 1678996 |
| Pearson symbol | cF56 |
| Space group number | 216 |
| Space group symbol | $F\overline{4}3m$ |
| AFLOW prototype command |
aflow --proto=AB12C_cF56_216_a_h_c-001
--params=$a, \allowbreak x_{3}, \allowbreak z_{3}$ |
- This is the AlPO$_{4}$ analog of $C9$ SiO$_{2}$ $\beta$ cristobalite. It transforms to the the orthorhombic $\alpha$ (low) structure at a temperature near 500K (Hatch, 1994).
- The oxygen (48h) sites are only 1/3 filled. If replaced them by an averaged (16e) (x,x,x) site with x ≈ 0.136 we would obtain the ideal structure analogous to $C9$ SiO$_{2}$, but the Al-O and P-O distances would be slightly too small.
- For more information, see our silica and aluminum phosphate page.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (4a) | Al I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (4c) | P I |
| $\mathbf{B_{3}}$ | = | $z_{3} \, \mathbf{a}_{1}+z_{3} \, \mathbf{a}_{2}+\left(2 x_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}+a z_{3} \,\mathbf{\hat{z}}$ | (48h) | O I |
| $\mathbf{B_{4}}$ | = | $z_{3} \, \mathbf{a}_{1}+z_{3} \, \mathbf{a}_{2}- \left(2 x_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}+a z_{3} \,\mathbf{\hat{z}}$ | (48h) | O I |
| $\mathbf{B_{5}}$ | = | $\left(2 x_{3} - z_{3}\right) \, \mathbf{a}_{1}- \left(2 x_{3} + z_{3}\right) \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}- a z_{3} \,\mathbf{\hat{z}}$ | (48h) | O I |
| $\mathbf{B_{6}}$ | = | $- \left(2 x_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(2 x_{3} - z_{3}\right) \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}- a z_{3} \,\mathbf{\hat{z}}$ | (48h) | O I |
| $\mathbf{B_{7}}$ | = | $\left(2 x_{3} - z_{3}\right) \, \mathbf{a}_{1}+z_{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $a z_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (48h) | O I |
| $\mathbf{B_{8}}$ | = | $- \left(2 x_{3} + z_{3}\right) \, \mathbf{a}_{1}+z_{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $a z_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (48h) | O I |
| $\mathbf{B_{9}}$ | = | $z_{3} \, \mathbf{a}_{1}+\left(2 x_{3} - z_{3}\right) \, \mathbf{a}_{2}- \left(2 x_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a z_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (48h) | O I |
| $\mathbf{B_{10}}$ | = | $z_{3} \, \mathbf{a}_{1}- \left(2 x_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(2 x_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a z_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (48h) | O I |
| $\mathbf{B_{11}}$ | = | $z_{3} \, \mathbf{a}_{1}+\left(2 x_{3} - z_{3}\right) \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a z_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (48h) | O I |
| $\mathbf{B_{12}}$ | = | $z_{3} \, \mathbf{a}_{1}- \left(2 x_{3} + z_{3}\right) \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+a z_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (48h) | O I |
| $\mathbf{B_{13}}$ | = | $- \left(2 x_{3} + z_{3}\right) \, \mathbf{a}_{1}+z_{3} \, \mathbf{a}_{2}+\left(2 x_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}- a z_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (48h) | O I |
| $\mathbf{B_{14}}$ | = | $\left(2 x_{3} - z_{3}\right) \, \mathbf{a}_{1}+z_{3} \, \mathbf{a}_{2}- \left(2 x_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a z_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (48h) | O I |
References
- B. L. Phillips, J. G. Thompson, Y. Xiao, and R. J. Kirkpatrick, Constraints on the structure and dynamics of the β-cristobalite polymorphs of SiO$_{2}$ and AlPO$_{4}$ from $^{31}$P, $^{27}$Al and $^{29}$Si NMR spectroscopy to 770 K, Phys. Chem. Minerals 20, 341–352 (1993), doi:10.1007/BF00215105.
Found in
- D. M. Hatch, S. Ghose, and J. L. Bjorkstam, The $\alpha$-$\beta$ phase transition in AlPO$_{4}$ cristobalite: Symmetry analysis, domain structure and transition dynamics, Phys. Chem. Minerals 21, 67–77 (1994), doi:10.1007/BF00205217.
First cited in
- N. Anderson, M. J. Mehl, H. Eckert, S. Divilov, X. Campilongo, S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 5. Submitted to Computational Materials Science (2026).
Geometry files
Prototype Generator
aflow --proto=AB12C_cF56_216_a_h_c --params=$a,x_{3},z_{3}$