Hypothetical Cubic SiO$_{2}$ Structure: A2B_cI72_211_hi_i-001
| Prototype | O$_{2}$Si |
| AFLOW prototype label | A2B_cI72_211_hi_i-001 |
| ICSD | 170506 |
| Pearson symbol | cI72 |
| Space group number | 211 |
| Space group symbol | $I432$ |
| AFLOW prototype command |
aflow --proto=A2B_cI72_211_hi_i-001
--params=$a, \allowbreak y_{1}, \allowbreak y_{2}, \allowbreak y_{3}$ |
- This is a hypothetical cubic structure for SiO$_{2}$. We use the data from the 1_158.cif file provided in the supplementary information of (Foster, 2004).
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}a \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $2 y_{1} \, \mathbf{a}_{1}+y_{1} \, \mathbf{a}_{2}+y_{1} \, \mathbf{a}_{3}$ | = | $a y_{1} \,\mathbf{\hat{y}}+a y_{1} \,\mathbf{\hat{z}}$ | (24h) | O I |
| $\mathbf{B_{2}}$ | = | $y_{1} \, \mathbf{a}_{2}- y_{1} \, \mathbf{a}_{3}$ | = | $- a y_{1} \,\mathbf{\hat{y}}+a y_{1} \,\mathbf{\hat{z}}$ | (24h) | O I |
| $\mathbf{B_{3}}$ | = | $- y_{1} \, \mathbf{a}_{2}+y_{1} \, \mathbf{a}_{3}$ | = | $a y_{1} \,\mathbf{\hat{y}}- a y_{1} \,\mathbf{\hat{z}}$ | (24h) | O I |
| $\mathbf{B_{4}}$ | = | $- 2 y_{1} \, \mathbf{a}_{1}- y_{1} \, \mathbf{a}_{2}- y_{1} \, \mathbf{a}_{3}$ | = | $- a y_{1} \,\mathbf{\hat{y}}- a y_{1} \,\mathbf{\hat{z}}$ | (24h) | O I |
| $\mathbf{B_{5}}$ | = | $y_{1} \, \mathbf{a}_{1}+2 y_{1} \, \mathbf{a}_{2}+y_{1} \, \mathbf{a}_{3}$ | = | $a y_{1} \,\mathbf{\hat{x}}+a y_{1} \,\mathbf{\hat{z}}$ | (24h) | O I |
| $\mathbf{B_{6}}$ | = | $- y_{1} \, \mathbf{a}_{1}+y_{1} \, \mathbf{a}_{3}$ | = | $a y_{1} \,\mathbf{\hat{x}}- a y_{1} \,\mathbf{\hat{z}}$ | (24h) | O I |
| $\mathbf{B_{7}}$ | = | $y_{1} \, \mathbf{a}_{1}- y_{1} \, \mathbf{a}_{3}$ | = | $- a y_{1} \,\mathbf{\hat{x}}+a y_{1} \,\mathbf{\hat{z}}$ | (24h) | O I |
| $\mathbf{B_{8}}$ | = | $- y_{1} \, \mathbf{a}_{1}- 2 y_{1} \, \mathbf{a}_{2}- y_{1} \, \mathbf{a}_{3}$ | = | $- a y_{1} \,\mathbf{\hat{x}}- a y_{1} \,\mathbf{\hat{z}}$ | (24h) | O I |
| $\mathbf{B_{9}}$ | = | $y_{1} \, \mathbf{a}_{1}+y_{1} \, \mathbf{a}_{2}+2 y_{1} \, \mathbf{a}_{3}$ | = | $a y_{1} \,\mathbf{\hat{x}}+a y_{1} \,\mathbf{\hat{y}}$ | (24h) | O I |
| $\mathbf{B_{10}}$ | = | $y_{1} \, \mathbf{a}_{1}- y_{1} \, \mathbf{a}_{2}$ | = | $- a y_{1} \,\mathbf{\hat{x}}+a y_{1} \,\mathbf{\hat{y}}$ | (24h) | O I |
| $\mathbf{B_{11}}$ | = | $- y_{1} \, \mathbf{a}_{1}+y_{1} \, \mathbf{a}_{2}$ | = | $a y_{1} \,\mathbf{\hat{x}}- a y_{1} \,\mathbf{\hat{y}}$ | (24h) | O I |
| $\mathbf{B_{12}}$ | = | $- y_{1} \, \mathbf{a}_{1}- y_{1} \, \mathbf{a}_{2}- 2 y_{1} \, \mathbf{a}_{3}$ | = | $- a y_{1} \,\mathbf{\hat{x}}- a y_{1} \,\mathbf{\hat{y}}$ | (24h) | O I |
| $\mathbf{B_{13}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- \left(y_{2} - \frac{3}{4}\right) \, \mathbf{a}_{2}+\left(y_{2} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+a y_{2} \,\mathbf{\hat{y}}- a \left(y_{2} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24i) | O II |
| $\mathbf{B_{14}}$ | = | $- \left(2 y_{2} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{2} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(y_{2} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- a \left(y_{2} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a y_{2} \,\mathbf{\hat{z}}$ | (24i) | O II |
| $\mathbf{B_{15}}$ | = | $\left(2 y_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{2} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(y_{2} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+a \left(y_{2} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a y_{2} \,\mathbf{\hat{z}}$ | (24i) | O II |
| $\mathbf{B_{16}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\left(y_{2} + \frac{3}{4}\right) \, \mathbf{a}_{2}- \left(y_{2} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- a y_{2} \,\mathbf{\hat{y}}+a \left(y_{2} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24i) | O II |
| $\mathbf{B_{17}}$ | = | $\left(y_{2} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}- \left(y_{2} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{2} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+a y_{2} \,\mathbf{\hat{z}}$ | (24i) | O II |
| $\mathbf{B_{18}}$ | = | $- \left(y_{2} - \frac{3}{4}\right) \, \mathbf{a}_{1}- \left(2 y_{2} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{2} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a y_{2} \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}- a \left(y_{2} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24i) | O II |
| $\mathbf{B_{19}}$ | = | $\left(y_{2} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(2 y_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{2} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a y_{2} \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+a \left(y_{2} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24i) | O II |
| $\mathbf{B_{20}}$ | = | $- \left(y_{2} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\left(y_{2} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{2} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}- a y_{2} \,\mathbf{\hat{z}}$ | (24i) | O II |
| $\mathbf{B_{21}}$ | = | $- \left(y_{2} - \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(y_{2} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a y_{2} \,\mathbf{\hat{x}}- a \left(y_{2} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24i) | O II |
| $\mathbf{B_{22}}$ | = | $- \left(y_{2} - \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(y_{2} - \frac{3}{4}\right) \, \mathbf{a}_{2}- \left(2 y_{2} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{2} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a y_{2} \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24i) | O II |
| $\mathbf{B_{23}}$ | = | $\left(y_{2} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(y_{2} + \frac{3}{4}\right) \, \mathbf{a}_{2}+\left(2 y_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{2} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a y_{2} \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24i) | O II |
| $\mathbf{B_{24}}$ | = | $\left(y_{2} + \frac{3}{4}\right) \, \mathbf{a}_{1}- \left(y_{2} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a y_{2} \,\mathbf{\hat{x}}+a \left(y_{2} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24i) | O II |
| $\mathbf{B_{25}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- \left(y_{3} - \frac{3}{4}\right) \, \mathbf{a}_{2}+\left(y_{3} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+a y_{3} \,\mathbf{\hat{y}}- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24i) | Si I |
| $\mathbf{B_{26}}$ | = | $- \left(2 y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{3} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(y_{3} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a y_{3} \,\mathbf{\hat{z}}$ | (24i) | Si I |
| $\mathbf{B_{27}}$ | = | $\left(2 y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{3} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(y_{3} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a y_{3} \,\mathbf{\hat{z}}$ | (24i) | Si I |
| $\mathbf{B_{28}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\left(y_{3} + \frac{3}{4}\right) \, \mathbf{a}_{2}- \left(y_{3} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- a y_{3} \,\mathbf{\hat{y}}+a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24i) | Si I |
| $\mathbf{B_{29}}$ | = | $\left(y_{3} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}- \left(y_{3} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+a y_{3} \,\mathbf{\hat{z}}$ | (24i) | Si I |
| $\mathbf{B_{30}}$ | = | $- \left(y_{3} - \frac{3}{4}\right) \, \mathbf{a}_{1}- \left(2 y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{3} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24i) | Si I |
| $\mathbf{B_{31}}$ | = | $\left(y_{3} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(2 y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{3} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24i) | Si I |
| $\mathbf{B_{32}}$ | = | $- \left(y_{3} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\left(y_{3} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}- a y_{3} \,\mathbf{\hat{z}}$ | (24i) | Si I |
| $\mathbf{B_{33}}$ | = | $- \left(y_{3} - \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(y_{3} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{x}}- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24i) | Si I |
| $\mathbf{B_{34}}$ | = | $- \left(y_{3} - \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(y_{3} - \frac{3}{4}\right) \, \mathbf{a}_{2}- \left(2 y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a y_{3} \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24i) | Si I |
| $\mathbf{B_{35}}$ | = | $\left(y_{3} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(y_{3} + \frac{3}{4}\right) \, \mathbf{a}_{2}+\left(2 y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a y_{3} \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24i) | Si I |
| $\mathbf{B_{36}}$ | = | $\left(y_{3} + \frac{3}{4}\right) \, \mathbf{a}_{1}- \left(y_{3} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{x}}+a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24i) | Si I |
References
- M. D. Foster, O. D. Friedrichs, R. G. Bell, F. A. A. Paz, and J. Klinowski, Chemical Evaluation of Hypothetical Uninodal Zeolites, J. Am. Chem. Soc. 126, 9769–9775 (2004), doi:10.1021/ja037334j.
Prototype Generator
aflow --proto=A2B_cI72_211_hi_i --params=$a,y_{1},y_{2},y_{3}$