γ-Fe$_{2}$O$_{3}$ ($D5_{7}$) Structure: A2B3_cP60_212_acd_bce-001
| Prototype | Fe$_{2}$O$_{3}$ |
| AFLOW prototype label | A2B3_cP60_212_acd_bce-001 |
| Strukturbericht designation | $D5_{7}$ |
| ICSD | none |
| Pearson symbol | cP60 |
| Space group number | 212 |
| Space group symbol | $P4_332$ |
| AFLOW prototype command |
aflow --proto=A2B3_cP60_212_acd_bce-001
--params=$a, \allowbreak x_{3}, \allowbreak x_{4}, \allowbreak y_{5}, \allowbreak x_{6}, \allowbreak y_{6}, \allowbreak z_{6}$ |
Other compounds with this structure
$\gamma$-Al$_{2}$O$_{3}$ ($\gamma$-corundum)
- (Hermann, 1937) gives $\gamma$–Al$_{2}$O$_{3}$ as the prototype for Strukturbericht $D5_{7}$, but states that the data for $\gamma$–Fe$_{2}$O$_{3}$ is more reliable and presents the data for the later compound, which we use as the prototype.
- More information about the Al$_{2}$O$_{3}$ compounds can be found on the corundum ($D5_{1}$) page.
- This is a rock-salt ($B1$) structure with defects.
- This structure can also be expressed in the enantiomorphic space group $P4_{1}32$ #213.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&a \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{8} \, \mathbf{a}_{1}+\frac{1}{8} \, \mathbf{a}_{2}+\frac{1}{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ | (4a) | Fe I |
| $\mathbf{B_{2}}$ | = | $\frac{3}{8} \, \mathbf{a}_{1}+\frac{7}{8} \, \mathbf{a}_{2}+\frac{5}{8} \, \mathbf{a}_{3}$ | = | $\frac{3}{8}a \,\mathbf{\hat{x}}+\frac{7}{8}a \,\mathbf{\hat{y}}+\frac{5}{8}a \,\mathbf{\hat{z}}$ | (4a) | Fe I |
| $\mathbf{B_{3}}$ | = | $\frac{7}{8} \, \mathbf{a}_{1}+\frac{5}{8} \, \mathbf{a}_{2}+\frac{3}{8} \, \mathbf{a}_{3}$ | = | $\frac{7}{8}a \,\mathbf{\hat{x}}+\frac{5}{8}a \,\mathbf{\hat{y}}+\frac{3}{8}a \,\mathbf{\hat{z}}$ | (4a) | Fe I |
| $\mathbf{B_{4}}$ | = | $\frac{5}{8} \, \mathbf{a}_{1}+\frac{3}{8} \, \mathbf{a}_{2}+\frac{7}{8} \, \mathbf{a}_{3}$ | = | $\frac{5}{8}a \,\mathbf{\hat{x}}+\frac{3}{8}a \,\mathbf{\hat{y}}+\frac{7}{8}a \,\mathbf{\hat{z}}$ | (4a) | Fe I |
| $\mathbf{B_{5}}$ | = | $\frac{5}{8} \, \mathbf{a}_{1}+\frac{5}{8} \, \mathbf{a}_{2}+\frac{5}{8} \, \mathbf{a}_{3}$ | = | $\frac{5}{8}a \,\mathbf{\hat{x}}+\frac{5}{8}a \,\mathbf{\hat{y}}+\frac{5}{8}a \,\mathbf{\hat{z}}$ | (4b) | O I |
| $\mathbf{B_{6}}$ | = | $\frac{7}{8} \, \mathbf{a}_{1}+\frac{3}{8} \, \mathbf{a}_{2}+\frac{1}{8} \, \mathbf{a}_{3}$ | = | $\frac{7}{8}a \,\mathbf{\hat{x}}+\frac{3}{8}a \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ | (4b) | O I |
| $\mathbf{B_{7}}$ | = | $\frac{3}{8} \, \mathbf{a}_{1}+\frac{1}{8} \, \mathbf{a}_{2}+\frac{7}{8} \, \mathbf{a}_{3}$ | = | $\frac{3}{8}a \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}+\frac{7}{8}a \,\mathbf{\hat{z}}$ | (4b) | O I |
| $\mathbf{B_{8}}$ | = | $\frac{1}{8} \, \mathbf{a}_{1}+\frac{7}{8} \, \mathbf{a}_{2}+\frac{3}{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}+\frac{7}{8}a \,\mathbf{\hat{y}}+\frac{3}{8}a \,\mathbf{\hat{z}}$ | (4b) | O I |
| $\mathbf{B_{9}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (8c) | Fe II |
| $\mathbf{B_{10}}$ | = | $- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}+a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8c) | Fe II |
| $\mathbf{B_{11}}$ | = | $- x_{3} \, \mathbf{a}_{1}+\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8c) | Fe II |
| $\mathbf{B_{12}}$ | = | $\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (8c) | Fe II |
| $\mathbf{B_{13}}$ | = | $\left(x_{3} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{3} + \frac{3}{4}\right) \, \mathbf{a}_{2}- \left(x_{3} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{3}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{3} - \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8c) | Fe II |
| $\mathbf{B_{14}}$ | = | $- \left(x_{3} - \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{3} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{3} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8c) | Fe II |
| $\mathbf{B_{15}}$ | = | $\left(x_{3} + \frac{3}{4}\right) \, \mathbf{a}_{1}- \left(x_{3} - \frac{3}{4}\right) \, \mathbf{a}_{2}+\left(x_{3} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{3}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{3}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8c) | Fe II |
| $\mathbf{B_{16}}$ | = | $- \left(x_{3} - \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(x_{3} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{3} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{3}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{3} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8c) | Fe II |
| $\mathbf{B_{17}}$ | = | $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (8c) | O II |
| $\mathbf{B_{18}}$ | = | $- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}+a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8c) | O II |
| $\mathbf{B_{19}}$ | = | $- x_{4} \, \mathbf{a}_{1}+\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8c) | O II |
| $\mathbf{B_{20}}$ | = | $\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ | = | $a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (8c) | O II |
| $\mathbf{B_{21}}$ | = | $\left(x_{4} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{4} + \frac{3}{4}\right) \, \mathbf{a}_{2}- \left(x_{4} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{4} + \frac{3}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{4} - \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8c) | O II |
| $\mathbf{B_{22}}$ | = | $- \left(x_{4} - \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{4} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{4} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8c) | O II |
| $\mathbf{B_{23}}$ | = | $\left(x_{4} + \frac{3}{4}\right) \, \mathbf{a}_{1}- \left(x_{4} - \frac{3}{4}\right) \, \mathbf{a}_{2}+\left(x_{4} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{4} + \frac{3}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{4} - \frac{3}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8c) | O II |
| $\mathbf{B_{24}}$ | = | $- \left(x_{4} - \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(x_{4} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{4} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{4} - \frac{3}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{4} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8c) | O II |
| $\mathbf{B_{25}}$ | = | $\frac{1}{8} \, \mathbf{a}_{1}+y_{5} \, \mathbf{a}_{2}- \left(y_{5} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}+a y_{5} \,\mathbf{\hat{y}}- a \left(y_{5} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (12d) | Fe III |
| $\mathbf{B_{26}}$ | = | $\frac{3}{8} \, \mathbf{a}_{1}- y_{5} \, \mathbf{a}_{2}- \left(y_{5} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{3}{8}a \,\mathbf{\hat{x}}- a y_{5} \,\mathbf{\hat{y}}- a \left(y_{5} - \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (12d) | Fe III |
| $\mathbf{B_{27}}$ | = | $\frac{7}{8} \, \mathbf{a}_{1}+\left(y_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{5} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{7}{8}a \,\mathbf{\hat{x}}+a \left(y_{5} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(y_{5} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (12d) | Fe III |
| $\mathbf{B_{28}}$ | = | $\frac{5}{8} \, \mathbf{a}_{1}- \left(y_{5} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{5} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{5}{8}a \,\mathbf{\hat{x}}- a \left(y_{5} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(y_{5} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (12d) | Fe III |
| $\mathbf{B_{29}}$ | = | $- \left(y_{5} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\frac{1}{8} \, \mathbf{a}_{2}+y_{5} \, \mathbf{a}_{3}$ | = | $- a \left(y_{5} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}+a y_{5} \,\mathbf{\hat{z}}$ | (12d) | Fe III |
| $\mathbf{B_{30}}$ | = | $- \left(y_{5} - \frac{3}{4}\right) \, \mathbf{a}_{1}+\frac{3}{8} \, \mathbf{a}_{2}- y_{5} \, \mathbf{a}_{3}$ | = | $- a \left(y_{5} - \frac{3}{4}\right) \,\mathbf{\hat{x}}+\frac{3}{8}a \,\mathbf{\hat{y}}- a y_{5} \,\mathbf{\hat{z}}$ | (12d) | Fe III |
| $\mathbf{B_{31}}$ | = | $\left(y_{5} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\frac{7}{8} \, \mathbf{a}_{2}+\left(y_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{5} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{7}{8}a \,\mathbf{\hat{y}}+a \left(y_{5} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12d) | Fe III |
| $\mathbf{B_{32}}$ | = | $\left(y_{5} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\frac{5}{8} \, \mathbf{a}_{2}- \left(y_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{5} + \frac{3}{4}\right) \,\mathbf{\hat{x}}+\frac{5}{8}a \,\mathbf{\hat{y}}- a \left(y_{5} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12d) | Fe III |
| $\mathbf{B_{33}}$ | = | $y_{5} \, \mathbf{a}_{1}- \left(y_{5} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\frac{1}{8} \, \mathbf{a}_{3}$ | = | $a y_{5} \,\mathbf{\hat{x}}- a \left(y_{5} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ | (12d) | Fe III |
| $\mathbf{B_{34}}$ | = | $- y_{5} \, \mathbf{a}_{1}- \left(y_{5} - \frac{3}{4}\right) \, \mathbf{a}_{2}+\frac{3}{8} \, \mathbf{a}_{3}$ | = | $- a y_{5} \,\mathbf{\hat{x}}- a \left(y_{5} - \frac{3}{4}\right) \,\mathbf{\hat{y}}+\frac{3}{8}a \,\mathbf{\hat{z}}$ | (12d) | Fe III |
| $\mathbf{B_{35}}$ | = | $\left(y_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{5} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\frac{7}{8} \, \mathbf{a}_{3}$ | = | $a \left(y_{5} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{5} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{7}{8}a \,\mathbf{\hat{z}}$ | (12d) | Fe III |
| $\mathbf{B_{36}}$ | = | $- \left(y_{5} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{5} + \frac{3}{4}\right) \, \mathbf{a}_{2}+\frac{5}{8} \, \mathbf{a}_{3}$ | = | $- a \left(y_{5} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{5} + \frac{3}{4}\right) \,\mathbf{\hat{y}}+\frac{5}{8}a \,\mathbf{\hat{z}}$ | (12d) | Fe III |
| $\mathbf{B_{37}}$ | = | $x_{6} \, \mathbf{a}_{1}+y_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}+a y_{6} \,\mathbf{\hat{y}}+a z_{6} \,\mathbf{\hat{z}}$ | (24e) | O III |
| $\mathbf{B_{38}}$ | = | $- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{6} \, \mathbf{a}_{2}+\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a y_{6} \,\mathbf{\hat{y}}+a \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24e) | O III |
| $\mathbf{B_{39}}$ | = | $- x_{6} \, \mathbf{a}_{1}+\left(y_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}+a \left(y_{6} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(z_{6} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24e) | O III |
| $\mathbf{B_{40}}$ | = | $\left(x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{6} - \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $a \left(x_{6} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{6} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a z_{6} \,\mathbf{\hat{z}}$ | (24e) | O III |
| $\mathbf{B_{41}}$ | = | $z_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}+y_{6} \, \mathbf{a}_{3}$ | = | $a z_{6} \,\mathbf{\hat{x}}+a x_{6} \,\mathbf{\hat{y}}+a y_{6} \,\mathbf{\hat{z}}$ | (24e) | O III |
| $\mathbf{B_{42}}$ | = | $\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{2}- y_{6} \, \mathbf{a}_{3}$ | = | $a \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a y_{6} \,\mathbf{\hat{z}}$ | (24e) | O III |
| $\mathbf{B_{43}}$ | = | $- \left(z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}+\left(y_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{6} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{6} \,\mathbf{\hat{y}}+a \left(y_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24e) | O III |
| $\mathbf{B_{44}}$ | = | $- z_{6} \, \mathbf{a}_{1}+\left(x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a z_{6} \,\mathbf{\hat{x}}+a \left(x_{6} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(y_{6} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24e) | O III |
| $\mathbf{B_{45}}$ | = | $y_{6} \, \mathbf{a}_{1}+z_{6} \, \mathbf{a}_{2}+x_{6} \, \mathbf{a}_{3}$ | = | $a y_{6} \,\mathbf{\hat{x}}+a z_{6} \,\mathbf{\hat{y}}+a x_{6} \,\mathbf{\hat{z}}$ | (24e) | O III |
| $\mathbf{B_{46}}$ | = | $- y_{6} \, \mathbf{a}_{1}+\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{6} \,\mathbf{\hat{x}}+a \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24e) | O III |
| $\mathbf{B_{47}}$ | = | $\left(y_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{2}- x_{6} \, \mathbf{a}_{3}$ | = | $a \left(y_{6} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(z_{6} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a x_{6} \,\mathbf{\hat{z}}$ | (24e) | O III |
| $\mathbf{B_{48}}$ | = | $- \left(y_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{6} \, \mathbf{a}_{2}+\left(x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{6} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a z_{6} \,\mathbf{\hat{y}}+a \left(x_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24e) | O III |
| $\mathbf{B_{49}}$ | = | $\left(y_{6} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{6} + \frac{3}{4}\right) \, \mathbf{a}_{2}- \left(z_{6} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{6} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{6} + \frac{3}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{6} - \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (24e) | O III |
| $\mathbf{B_{50}}$ | = | $- \left(y_{6} - \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{6} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(z_{6} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{6} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{6} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{6} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (24e) | O III |
| $\mathbf{B_{51}}$ | = | $\left(y_{6} + \frac{3}{4}\right) \, \mathbf{a}_{1}- \left(x_{6} - \frac{3}{4}\right) \, \mathbf{a}_{2}+\left(z_{6} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{6} + \frac{3}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{6} - \frac{3}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{6} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (24e) | O III |
| $\mathbf{B_{52}}$ | = | $- \left(y_{6} - \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(x_{6} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(z_{6} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{6} - \frac{3}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{6} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{6} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (24e) | O III |
| $\mathbf{B_{53}}$ | = | $\left(x_{6} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(z_{6} + \frac{3}{4}\right) \, \mathbf{a}_{2}- \left(y_{6} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{6} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{6} + \frac{3}{4}\right) \,\mathbf{\hat{y}}- a \left(y_{6} - \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (24e) | O III |
| $\mathbf{B_{54}}$ | = | $- \left(x_{6} - \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(z_{6} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(y_{6} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{6} - \frac{3}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{6} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(y_{6} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (24e) | O III |
| $\mathbf{B_{55}}$ | = | $- \left(x_{6} - \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(z_{6} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(y_{6} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{6} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{6} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(y_{6} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (24e) | O III |
| $\mathbf{B_{56}}$ | = | $\left(x_{6} + \frac{3}{4}\right) \, \mathbf{a}_{1}- \left(z_{6} - \frac{3}{4}\right) \, \mathbf{a}_{2}+\left(y_{6} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{6} + \frac{3}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{6} - \frac{3}{4}\right) \,\mathbf{\hat{y}}+a \left(y_{6} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (24e) | O III |
| $\mathbf{B_{57}}$ | = | $\left(z_{6} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(y_{6} + \frac{3}{4}\right) \, \mathbf{a}_{2}- \left(x_{6} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{6} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(y_{6} + \frac{3}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{6} - \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (24e) | O III |
| $\mathbf{B_{58}}$ | = | $\left(z_{6} + \frac{3}{4}\right) \, \mathbf{a}_{1}- \left(y_{6} - \frac{3}{4}\right) \, \mathbf{a}_{2}+\left(x_{6} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{6} + \frac{3}{4}\right) \,\mathbf{\hat{x}}- a \left(y_{6} - \frac{3}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{6} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (24e) | O III |
| $\mathbf{B_{59}}$ | = | $- \left(z_{6} - \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(y_{6} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{6} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{6} - \frac{3}{4}\right) \,\mathbf{\hat{x}}+a \left(y_{6} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{6} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (24e) | O III |
| $\mathbf{B_{60}}$ | = | $- \left(z_{6} - \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(y_{6} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{6} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{6} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(y_{6} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{6} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (24e) | O III |
References
- J. Thewils, The structure of ferromagnetic ferric oxide, Philos. Mag. 12, 1089–1106 (1931), doi:10.1080/14786443109461890.
Found in
- C. Hermann, O. Lohrmann, and H. Philipp, eds., Strukturbericht Band II 1928-1932 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1937).
Prototype Generator
aflow --proto=A2B3_cP60_212_acd_bce --params=$a,x_{3},x_{4},y_{5},x_{6},y_{6},z_{6}$