Ideal β-Cristobalite (SiO$_{2}$, $C9$) Structure: A2B_cF24_227_c_a-001
| Prototype | O$_{2}$Si |
| AFLOW prototype label | A2B_cF24_227_c_a-001 |
| Strukturbericht designation | $C9$ |
| Mineral name | cristobalite |
| ICSD | 35536 |
| Pearson symbol | cF24 |
| Space group number | 227 |
| Space group symbol | $Fd\overline{3}m$ |
| AFLOW prototype command |
aflow --proto=A2B_cF24_227_c_a-001
--params=$a$ |
Other compounds with this structure
BeF$_{2}$, AlPO$_{4}$
- This is an idealized version of the high-temperature phase of $\alpha$-cristobalite originally proposed by (Wyckoff, 1925).
- (Peacor, 1973) concludes that the oxygen atoms partially occupy the (96g) positions in the space group $Fd\overline{3}m$ #227. We average those positions to put the oxygen on the (16c) sites and return to the original structure.
- $\beta$-cristobalite is also known as
high
cristobalite.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{8} \, \mathbf{a}_{1}+\frac{1}{8} \, \mathbf{a}_{2}+\frac{1}{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ | (8a) | Si I |
| $\mathbf{B_{2}}$ | = | $\frac{7}{8} \, \mathbf{a}_{1}+\frac{7}{8} \, \mathbf{a}_{2}+\frac{7}{8} \, \mathbf{a}_{3}$ | = | $\frac{7}{8}a \,\mathbf{\hat{x}}+\frac{7}{8}a \,\mathbf{\hat{y}}+\frac{7}{8}a \,\mathbf{\hat{z}}$ | (8a) | Si I |
| $\mathbf{B_{3}}$ | = | $0$ | = | $0$ | (16c) | O I |
| $\mathbf{B_{4}}$ | = | $\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}$ | (16c) | O I |
| $\mathbf{B_{5}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (16c) | O I |
| $\mathbf{B_{6}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}$ | = | $\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (16c) | O I |
References
- R. W. G. Wyckoff, The crystal structure of the high temperature form of cristobalite (SiO$_{2}$, Am. J. Science 9, 448–459 (1925).
- D. R. Peacor, High-temperature single-crystal study of the cristobalite inversion, Z. Krystallogr. 138, 274–298 (1973), doi:10.1524/zkri.1973.138.1-4.274.
Found in
- R. T. Downs and M. Hall-Wallace, The American Mineralogist Crystal Structure Database, Am. Mineral. 88, 247–250 (2003).
Prototype Generator
aflow --proto=A2B_cF24_227_c_a --params=$a$