Al$_{22}$Mo$_{5}$ Structure: A22B5_oF216_43_11b_a2b-001
| Prototype | Al$_{22}$Mo$_{5}$ |
| AFLOW prototype label | A22B5_oF216_43_11b_a2b-001 |
| ICSD | 400888 |
| Pearson symbol | oF216 |
| Space group number | 43 |
| Space group symbol | $Fdd2$ |
| AFLOW prototype command |
aflow --proto=A22B5_oF216_43_11b_a2b-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak z_{1}, \allowbreak x_{2}, \allowbreak y_{2}, \allowbreak z_{2}, \allowbreak x_{3}, \allowbreak y_{3}, \allowbreak z_{3}, \allowbreak x_{4}, \allowbreak y_{4}, \allowbreak z_{4}, \allowbreak x_{5}, \allowbreak y_{5}, \allowbreak z_{5}, \allowbreak x_{6}, \allowbreak y_{6}, \allowbreak z_{6}, \allowbreak x_{7}, \allowbreak y_{7}, \allowbreak z_{7}, \allowbreak x_{8}, \allowbreak y_{8}, \allowbreak z_{8}, \allowbreak x_{9}, \allowbreak y_{9}, \allowbreak z_{9}, \allowbreak x_{10}, \allowbreak y_{10}, \allowbreak z_{10}, \allowbreak x_{11}, \allowbreak y_{11}, \allowbreak z_{11}, \allowbreak x_{12}, \allowbreak y_{12}, \allowbreak z_{12}, \allowbreak x_{13}, \allowbreak y_{13}, \allowbreak z_{13}, \allowbreak x_{14}, \allowbreak y_{14}, \allowbreak z_{14}$ |
- Space group $Fdd2$ #43 allows an arbitrary choice of the origin of the $z$-axis. Here we follow (Grin, 1995) and set $z_{1} = 0$ for the Mo-I atom.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}b \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $z_{1} \, \mathbf{a}_{1}+z_{1} \, \mathbf{a}_{2}- z_{1} \, \mathbf{a}_{3}$ | = | $c z_{1} \,\mathbf{\hat{z}}$ | (8a) | Mo I |
| $\mathbf{B_{2}}$ | = | $\left(z_{1} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(z_{1} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(z_{1} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}+c \left(z_{1} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8a) | Mo I |
| $\mathbf{B_{3}}$ | = | $\left(- x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{1}+\left(x_{2} - y_{2} + z_{2}\right) \, \mathbf{a}_{2}+\left(x_{2} + y_{2} - z_{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}+b y_{2} \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (16b) | Al I |
| $\mathbf{B_{4}}$ | = | $\left(x_{2} - y_{2} + z_{2}\right) \, \mathbf{a}_{1}+\left(- x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{2}- \left(x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}- b y_{2} \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (16b) | Al I |
| $\mathbf{B_{5}}$ | = | $- \left(x_{2} + y_{2} - z_{2} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{2} + y_{2} + z_{2} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{2} - y_{2} - z_{2} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- b \left(y_{2} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | Al I |
| $\mathbf{B_{6}}$ | = | $\left(x_{2} + y_{2} + z_{2} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{2} + y_{2} - z_{2} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{2} - y_{2} + z_{2} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+b \left(y_{2} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | Al I |
| $\mathbf{B_{7}}$ | = | $\left(- x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(x_{3} + y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+b y_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (16b) | Al II |
| $\mathbf{B_{8}}$ | = | $\left(x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(- x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{2}- \left(x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- b y_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (16b) | Al II |
| $\mathbf{B_{9}}$ | = | $- \left(x_{3} + y_{3} - z_{3} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{3} + y_{3} + z_{3} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{3} - y_{3} - z_{3} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- b \left(y_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | Al II |
| $\mathbf{B_{10}}$ | = | $\left(x_{3} + y_{3} + z_{3} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{3} + y_{3} - z_{3} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{3} - y_{3} + z_{3} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+b \left(y_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | Al II |
| $\mathbf{B_{11}}$ | = | $\left(- x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+b y_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (16b) | Al III |
| $\mathbf{B_{12}}$ | = | $\left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(- x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{2}- \left(x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- b y_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (16b) | Al III |
| $\mathbf{B_{13}}$ | = | $- \left(x_{4} + y_{4} - z_{4} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{4} + y_{4} + z_{4} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{4} - y_{4} - z_{4} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- b \left(y_{4} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | Al III |
| $\mathbf{B_{14}}$ | = | $\left(x_{4} + y_{4} + z_{4} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{4} + y_{4} - z_{4} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{4} - y_{4} + z_{4} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+b \left(y_{4} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | Al III |
| $\mathbf{B_{15}}$ | = | $\left(- x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+b y_{5} \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (16b) | Al IV |
| $\mathbf{B_{16}}$ | = | $\left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(- x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{2}- \left(x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}- b y_{5} \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (16b) | Al IV |
| $\mathbf{B_{17}}$ | = | $- \left(x_{5} + y_{5} - z_{5} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{5} + y_{5} + z_{5} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{5} - y_{5} - z_{5} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{5} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- b \left(y_{5} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{5} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | Al IV |
| $\mathbf{B_{18}}$ | = | $\left(x_{5} + y_{5} + z_{5} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{5} + y_{5} - z_{5} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{5} - y_{5} + z_{5} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{5} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+b \left(y_{5} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{5} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | Al IV |
| $\mathbf{B_{19}}$ | = | $\left(- x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{1}+\left(x_{6} - y_{6} + z_{6}\right) \, \mathbf{a}_{2}+\left(x_{6} + y_{6} - z_{6}\right) \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}+b y_{6} \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (16b) | Al V |
| $\mathbf{B_{20}}$ | = | $\left(x_{6} - y_{6} + z_{6}\right) \, \mathbf{a}_{1}+\left(- x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{2}- \left(x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}- b y_{6} \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (16b) | Al V |
| $\mathbf{B_{21}}$ | = | $- \left(x_{6} + y_{6} - z_{6} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{6} + y_{6} + z_{6} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{6} - y_{6} - z_{6} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{6} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- b \left(y_{6} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{6} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | Al V |
| $\mathbf{B_{22}}$ | = | $\left(x_{6} + y_{6} + z_{6} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{6} + y_{6} - z_{6} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{6} - y_{6} + z_{6} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{6} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+b \left(y_{6} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{6} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | Al V |
| $\mathbf{B_{23}}$ | = | $\left(- x_{7} + y_{7} + z_{7}\right) \, \mathbf{a}_{1}+\left(x_{7} - y_{7} + z_{7}\right) \, \mathbf{a}_{2}+\left(x_{7} + y_{7} - z_{7}\right) \, \mathbf{a}_{3}$ | = | $a x_{7} \,\mathbf{\hat{x}}+b y_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (16b) | Al VI |
| $\mathbf{B_{24}}$ | = | $\left(x_{7} - y_{7} + z_{7}\right) \, \mathbf{a}_{1}+\left(- x_{7} + y_{7} + z_{7}\right) \, \mathbf{a}_{2}- \left(x_{7} + y_{7} + z_{7}\right) \, \mathbf{a}_{3}$ | = | $- a x_{7} \,\mathbf{\hat{x}}- b y_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (16b) | Al VI |
| $\mathbf{B_{25}}$ | = | $- \left(x_{7} + y_{7} - z_{7} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{7} + y_{7} + z_{7} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{7} - y_{7} - z_{7} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{7} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- b \left(y_{7} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | Al VI |
| $\mathbf{B_{26}}$ | = | $\left(x_{7} + y_{7} + z_{7} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{7} + y_{7} - z_{7} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{7} - y_{7} + z_{7} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{7} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+b \left(y_{7} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | Al VI |
| $\mathbf{B_{27}}$ | = | $\left(- x_{8} + y_{8} + z_{8}\right) \, \mathbf{a}_{1}+\left(x_{8} - y_{8} + z_{8}\right) \, \mathbf{a}_{2}+\left(x_{8} + y_{8} - z_{8}\right) \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}+b y_{8} \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (16b) | Al VII |
| $\mathbf{B_{28}}$ | = | $\left(x_{8} - y_{8} + z_{8}\right) \, \mathbf{a}_{1}+\left(- x_{8} + y_{8} + z_{8}\right) \, \mathbf{a}_{2}- \left(x_{8} + y_{8} + z_{8}\right) \, \mathbf{a}_{3}$ | = | $- a x_{8} \,\mathbf{\hat{x}}- b y_{8} \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (16b) | Al VII |
| $\mathbf{B_{29}}$ | = | $- \left(x_{8} + y_{8} - z_{8} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{8} + y_{8} + z_{8} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{8} - y_{8} - z_{8} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{8} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- b \left(y_{8} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{8} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | Al VII |
| $\mathbf{B_{30}}$ | = | $\left(x_{8} + y_{8} + z_{8} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{8} + y_{8} - z_{8} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{8} - y_{8} + z_{8} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{8} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+b \left(y_{8} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{8} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | Al VII |
| $\mathbf{B_{31}}$ | = | $\left(- x_{9} + y_{9} + z_{9}\right) \, \mathbf{a}_{1}+\left(x_{9} - y_{9} + z_{9}\right) \, \mathbf{a}_{2}+\left(x_{9} + y_{9} - z_{9}\right) \, \mathbf{a}_{3}$ | = | $a x_{9} \,\mathbf{\hat{x}}+b y_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (16b) | Al VIII |
| $\mathbf{B_{32}}$ | = | $\left(x_{9} - y_{9} + z_{9}\right) \, \mathbf{a}_{1}+\left(- x_{9} + y_{9} + z_{9}\right) \, \mathbf{a}_{2}- \left(x_{9} + y_{9} + z_{9}\right) \, \mathbf{a}_{3}$ | = | $- a x_{9} \,\mathbf{\hat{x}}- b y_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (16b) | Al VIII |
| $\mathbf{B_{33}}$ | = | $- \left(x_{9} + y_{9} - z_{9} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{9} + y_{9} + z_{9} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{9} - y_{9} - z_{9} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{9} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- b \left(y_{9} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{9} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | Al VIII |
| $\mathbf{B_{34}}$ | = | $\left(x_{9} + y_{9} + z_{9} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{9} + y_{9} - z_{9} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{9} - y_{9} + z_{9} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{9} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+b \left(y_{9} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{9} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | Al VIII |
| $\mathbf{B_{35}}$ | = | $\left(- x_{10} + y_{10} + z_{10}\right) \, \mathbf{a}_{1}+\left(x_{10} - y_{10} + z_{10}\right) \, \mathbf{a}_{2}+\left(x_{10} + y_{10} - z_{10}\right) \, \mathbf{a}_{3}$ | = | $a x_{10} \,\mathbf{\hat{x}}+b y_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (16b) | Al IX |
| $\mathbf{B_{36}}$ | = | $\left(x_{10} - y_{10} + z_{10}\right) \, \mathbf{a}_{1}+\left(- x_{10} + y_{10} + z_{10}\right) \, \mathbf{a}_{2}- \left(x_{10} + y_{10} + z_{10}\right) \, \mathbf{a}_{3}$ | = | $- a x_{10} \,\mathbf{\hat{x}}- b y_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (16b) | Al IX |
| $\mathbf{B_{37}}$ | = | $- \left(x_{10} + y_{10} - z_{10} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{10} + y_{10} + z_{10} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{10} - y_{10} - z_{10} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{10} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- b \left(y_{10} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{10} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | Al IX |
| $\mathbf{B_{38}}$ | = | $\left(x_{10} + y_{10} + z_{10} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{10} + y_{10} - z_{10} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{10} - y_{10} + z_{10} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{10} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+b \left(y_{10} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{10} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | Al IX |
| $\mathbf{B_{39}}$ | = | $\left(- x_{11} + y_{11} + z_{11}\right) \, \mathbf{a}_{1}+\left(x_{11} - y_{11} + z_{11}\right) \, \mathbf{a}_{2}+\left(x_{11} + y_{11} - z_{11}\right) \, \mathbf{a}_{3}$ | = | $a x_{11} \,\mathbf{\hat{x}}+b y_{11} \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ | (16b) | Al X |
| $\mathbf{B_{40}}$ | = | $\left(x_{11} - y_{11} + z_{11}\right) \, \mathbf{a}_{1}+\left(- x_{11} + y_{11} + z_{11}\right) \, \mathbf{a}_{2}- \left(x_{11} + y_{11} + z_{11}\right) \, \mathbf{a}_{3}$ | = | $- a x_{11} \,\mathbf{\hat{x}}- b y_{11} \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ | (16b) | Al X |
| $\mathbf{B_{41}}$ | = | $- \left(x_{11} + y_{11} - z_{11} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{11} + y_{11} + z_{11} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{11} - y_{11} - z_{11} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{11} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- b \left(y_{11} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{11} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | Al X |
| $\mathbf{B_{42}}$ | = | $\left(x_{11} + y_{11} + z_{11} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{11} + y_{11} - z_{11} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{11} - y_{11} + z_{11} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{11} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+b \left(y_{11} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{11} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | Al X |
| $\mathbf{B_{43}}$ | = | $\left(- x_{12} + y_{12} + z_{12}\right) \, \mathbf{a}_{1}+\left(x_{12} - y_{12} + z_{12}\right) \, \mathbf{a}_{2}+\left(x_{12} + y_{12} - z_{12}\right) \, \mathbf{a}_{3}$ | = | $a x_{12} \,\mathbf{\hat{x}}+b y_{12} \,\mathbf{\hat{y}}+c z_{12} \,\mathbf{\hat{z}}$ | (16b) | Al XI |
| $\mathbf{B_{44}}$ | = | $\left(x_{12} - y_{12} + z_{12}\right) \, \mathbf{a}_{1}+\left(- x_{12} + y_{12} + z_{12}\right) \, \mathbf{a}_{2}- \left(x_{12} + y_{12} + z_{12}\right) \, \mathbf{a}_{3}$ | = | $- a x_{12} \,\mathbf{\hat{x}}- b y_{12} \,\mathbf{\hat{y}}+c z_{12} \,\mathbf{\hat{z}}$ | (16b) | Al XI |
| $\mathbf{B_{45}}$ | = | $- \left(x_{12} + y_{12} - z_{12} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{12} + y_{12} + z_{12} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{12} - y_{12} - z_{12} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{12} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- b \left(y_{12} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{12} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | Al XI |
| $\mathbf{B_{46}}$ | = | $\left(x_{12} + y_{12} + z_{12} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{12} + y_{12} - z_{12} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{12} - y_{12} + z_{12} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{12} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+b \left(y_{12} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{12} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | Al XI |
| $\mathbf{B_{47}}$ | = | $\left(- x_{13} + y_{13} + z_{13}\right) \, \mathbf{a}_{1}+\left(x_{13} - y_{13} + z_{13}\right) \, \mathbf{a}_{2}+\left(x_{13} + y_{13} - z_{13}\right) \, \mathbf{a}_{3}$ | = | $a x_{13} \,\mathbf{\hat{x}}+b y_{13} \,\mathbf{\hat{y}}+c z_{13} \,\mathbf{\hat{z}}$ | (16b) | Mo II |
| $\mathbf{B_{48}}$ | = | $\left(x_{13} - y_{13} + z_{13}\right) \, \mathbf{a}_{1}+\left(- x_{13} + y_{13} + z_{13}\right) \, \mathbf{a}_{2}- \left(x_{13} + y_{13} + z_{13}\right) \, \mathbf{a}_{3}$ | = | $- a x_{13} \,\mathbf{\hat{x}}- b y_{13} \,\mathbf{\hat{y}}+c z_{13} \,\mathbf{\hat{z}}$ | (16b) | Mo II |
| $\mathbf{B_{49}}$ | = | $- \left(x_{13} + y_{13} - z_{13} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{13} + y_{13} + z_{13} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{13} - y_{13} - z_{13} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{13} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- b \left(y_{13} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{13} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | Mo II |
| $\mathbf{B_{50}}$ | = | $\left(x_{13} + y_{13} + z_{13} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{13} + y_{13} - z_{13} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{13} - y_{13} + z_{13} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{13} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+b \left(y_{13} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{13} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | Mo II |
| $\mathbf{B_{51}}$ | = | $\left(- x_{14} + y_{14} + z_{14}\right) \, \mathbf{a}_{1}+\left(x_{14} - y_{14} + z_{14}\right) \, \mathbf{a}_{2}+\left(x_{14} + y_{14} - z_{14}\right) \, \mathbf{a}_{3}$ | = | $a x_{14} \,\mathbf{\hat{x}}+b y_{14} \,\mathbf{\hat{y}}+c z_{14} \,\mathbf{\hat{z}}$ | (16b) | Mo III |
| $\mathbf{B_{52}}$ | = | $\left(x_{14} - y_{14} + z_{14}\right) \, \mathbf{a}_{1}+\left(- x_{14} + y_{14} + z_{14}\right) \, \mathbf{a}_{2}- \left(x_{14} + y_{14} + z_{14}\right) \, \mathbf{a}_{3}$ | = | $- a x_{14} \,\mathbf{\hat{x}}- b y_{14} \,\mathbf{\hat{y}}+c z_{14} \,\mathbf{\hat{z}}$ | (16b) | Mo III |
| $\mathbf{B_{53}}$ | = | $- \left(x_{14} + y_{14} - z_{14} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{14} + y_{14} + z_{14} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{14} - y_{14} - z_{14} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{14} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- b \left(y_{14} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{14} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | Mo III |
| $\mathbf{B_{54}}$ | = | $\left(x_{14} + y_{14} + z_{14} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{14} + y_{14} - z_{14} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{14} - y_{14} + z_{14} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{14} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+b \left(y_{14} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{14} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | Mo III |
References
- Y. N. Grin, M. Ellner, K. Peters, and J. C. Schuster, The crystal structures of Mo$_{4}$Al$_{17}$ and Mo$_{5}$Al$_{22}$, Z. Kristallogr. 210, 96–99 (1995), doi:10.1524/zkri.1995.210.2.96.
Prototype Generator
aflow --proto=A22B5_oF216_43_11b_a2b --params=$a,b/a,c/a,z_{1},x_{2},y_{2},z_{2},x_{3},y_{3},z_{3},x_{4},y_{4},z_{4},x_{5},y_{5},z_{5},x_{6},y_{6},z_{6},x_{7},y_{7},z_{7},x_{8},y_{8},z_{8},x_{9},y_{9},z_{9},x_{10},y_{10},z_{10},x_{11},y_{11},z_{11},x_{12},y_{12},z_{12},x_{13},y_{13},z_{13},x_{14},y_{14},z_{14}$