Rh$_{10}$Ga$_{17}$ Structure: A17B10_tP108_116_e8j_ad2g2h5i-001
| Prototype | Ga$_{17}$Rh$_{10}$ |
| AFLOW prototype label | A17B10_tP108_116_e8j_ad2g2h5i-001 |
| ICSD | 103949 |
| Pearson symbol | tP108 |
| Space group number | 116 |
| Space group symbol | $P\overline{4}c2$ |
| AFLOW prototype command |
aflow --proto=A17B10_tP108_116_e8j_ad2g2h5i-001
--params=$a, \allowbreak c/a, \allowbreak x_{3}, \allowbreak z_{4}, \allowbreak z_{5}, \allowbreak z_{6}, \allowbreak z_{7}, \allowbreak z_{8}, \allowbreak z_{9}, \allowbreak z_{10}, \allowbreak z_{11}, \allowbreak z_{12}, \allowbreak x_{13}, \allowbreak y_{13}, \allowbreak z_{13}, \allowbreak x_{14}, \allowbreak y_{14}, \allowbreak z_{14}, \allowbreak x_{15}, \allowbreak y_{15}, \allowbreak z_{15}, \allowbreak x_{16}, \allowbreak y_{16}, \allowbreak z_{16}, \allowbreak x_{17}, \allowbreak y_{17}, \allowbreak z_{17}, \allowbreak x_{18}, \allowbreak y_{18}, \allowbreak z_{18}, \allowbreak x_{19}, \allowbreak y_{19}, \allowbreak z_{19}, \allowbreak x_{20}, \allowbreak y_{20}, \allowbreak z_{20}$ |
- We have shifted the origin used by (Vollenkle, 1967) to place the Rh I atom on the (2a) site rather than the (2b) site.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}c \,\mathbf{\hat{z}}$ | (2a) | Rh I |
| $\mathbf{B_{2}}$ | = | $\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}c \,\mathbf{\hat{z}}$ | (2a) | Rh I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}$ | (2d) | Rh II |
| $\mathbf{B_{4}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (2d) | Rh II |
| $\mathbf{B_{5}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4e) | Ga I |
| $\mathbf{B_{6}}$ | = | $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4e) | Ga I |
| $\mathbf{B_{7}}$ | = | $x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (4e) | Ga I |
| $\mathbf{B_{8}}$ | = | $- x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (4e) | Ga I |
| $\mathbf{B_{9}}$ | = | $z_{4} \, \mathbf{a}_{3}$ | = | $c z_{4} \,\mathbf{\hat{z}}$ | (4g) | Rh III |
| $\mathbf{B_{10}}$ | = | $- z_{4} \, \mathbf{a}_{3}$ | = | $- c z_{4} \,\mathbf{\hat{z}}$ | (4g) | Rh III |
| $\mathbf{B_{11}}$ | = | $\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $c \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4g) | Rh III |
| $\mathbf{B_{12}}$ | = | $- \left(z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- c \left(z_{4} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4g) | Rh III |
| $\mathbf{B_{13}}$ | = | $z_{5} \, \mathbf{a}_{3}$ | = | $c z_{5} \,\mathbf{\hat{z}}$ | (4g) | Rh IV |
| $\mathbf{B_{14}}$ | = | $- z_{5} \, \mathbf{a}_{3}$ | = | $- c z_{5} \,\mathbf{\hat{z}}$ | (4g) | Rh IV |
| $\mathbf{B_{15}}$ | = | $\left(z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $c \left(z_{5} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4g) | Rh IV |
| $\mathbf{B_{16}}$ | = | $- \left(z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- c \left(z_{5} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4g) | Rh IV |
| $\mathbf{B_{17}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (4h) | Rh V |
| $\mathbf{B_{18}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- c z_{6} \,\mathbf{\hat{z}}$ | (4h) | Rh V |
| $\mathbf{B_{19}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+c \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4h) | Rh V |
| $\mathbf{B_{20}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}- \left(z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- c \left(z_{6} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4h) | Rh V |
| $\mathbf{B_{21}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (4h) | Rh VI |
| $\mathbf{B_{22}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}- z_{7} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- c z_{7} \,\mathbf{\hat{z}}$ | (4h) | Rh VI |
| $\mathbf{B_{23}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\left(z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4h) | Rh VI |
| $\mathbf{B_{24}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}- \left(z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- c \left(z_{7} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4h) | Rh VI |
| $\mathbf{B_{25}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (4i) | Rh VII |
| $\mathbf{B_{26}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- z_{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- c z_{8} \,\mathbf{\hat{z}}$ | (4i) | Rh VII |
| $\mathbf{B_{27}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+\left(z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+c \left(z_{8} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4i) | Rh VII |
| $\mathbf{B_{28}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- \left(z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- c \left(z_{8} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4i) | Rh VII |
| $\mathbf{B_{29}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (4i) | Rh VIII |
| $\mathbf{B_{30}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- z_{9} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- c z_{9} \,\mathbf{\hat{z}}$ | (4i) | Rh VIII |
| $\mathbf{B_{31}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+\left(z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+c \left(z_{9} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4i) | Rh VIII |
| $\mathbf{B_{32}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- \left(z_{9} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- c \left(z_{9} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4i) | Rh VIII |
| $\mathbf{B_{33}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (4i) | Rh IX |
| $\mathbf{B_{34}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- z_{10} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- c z_{10} \,\mathbf{\hat{z}}$ | (4i) | Rh IX |
| $\mathbf{B_{35}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+\left(z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+c \left(z_{10} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4i) | Rh IX |
| $\mathbf{B_{36}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- \left(z_{10} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- c \left(z_{10} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4i) | Rh IX |
| $\mathbf{B_{37}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ | (4i) | Rh X |
| $\mathbf{B_{38}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- z_{11} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- c z_{11} \,\mathbf{\hat{z}}$ | (4i) | Rh X |
| $\mathbf{B_{39}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+\left(z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+c \left(z_{11} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4i) | Rh X |
| $\mathbf{B_{40}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- \left(z_{11} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- c \left(z_{11} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4i) | Rh X |
| $\mathbf{B_{41}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+z_{12} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+c z_{12} \,\mathbf{\hat{z}}$ | (4i) | Rh XI |
| $\mathbf{B_{42}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- z_{12} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- c z_{12} \,\mathbf{\hat{z}}$ | (4i) | Rh XI |
| $\mathbf{B_{43}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+\left(z_{12} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+c \left(z_{12} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4i) | Rh XI |
| $\mathbf{B_{44}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- \left(z_{12} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- c \left(z_{12} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4i) | Rh XI |
| $\mathbf{B_{45}}$ | = | $x_{13} \, \mathbf{a}_{1}+y_{13} \, \mathbf{a}_{2}+z_{13} \, \mathbf{a}_{3}$ | = | $a x_{13} \,\mathbf{\hat{x}}+a y_{13} \,\mathbf{\hat{y}}+c z_{13} \,\mathbf{\hat{z}}$ | (8j) | Ga II |
| $\mathbf{B_{46}}$ | = | $- x_{13} \, \mathbf{a}_{1}- y_{13} \, \mathbf{a}_{2}+z_{13} \, \mathbf{a}_{3}$ | = | $- a x_{13} \,\mathbf{\hat{x}}- a y_{13} \,\mathbf{\hat{y}}+c z_{13} \,\mathbf{\hat{z}}$ | (8j) | Ga II |
| $\mathbf{B_{47}}$ | = | $y_{13} \, \mathbf{a}_{1}- x_{13} \, \mathbf{a}_{2}- z_{13} \, \mathbf{a}_{3}$ | = | $a y_{13} \,\mathbf{\hat{x}}- a x_{13} \,\mathbf{\hat{y}}- c z_{13} \,\mathbf{\hat{z}}$ | (8j) | Ga II |
| $\mathbf{B_{48}}$ | = | $- y_{13} \, \mathbf{a}_{1}+x_{13} \, \mathbf{a}_{2}- z_{13} \, \mathbf{a}_{3}$ | = | $- a y_{13} \,\mathbf{\hat{x}}+a x_{13} \,\mathbf{\hat{y}}- c z_{13} \,\mathbf{\hat{z}}$ | (8j) | Ga II |
| $\mathbf{B_{49}}$ | = | $x_{13} \, \mathbf{a}_{1}- y_{13} \, \mathbf{a}_{2}+\left(z_{13} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{13} \,\mathbf{\hat{x}}- a y_{13} \,\mathbf{\hat{y}}+c \left(z_{13} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8j) | Ga II |
| $\mathbf{B_{50}}$ | = | $- x_{13} \, \mathbf{a}_{1}+y_{13} \, \mathbf{a}_{2}+\left(z_{13} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{13} \,\mathbf{\hat{x}}+a y_{13} \,\mathbf{\hat{y}}+c \left(z_{13} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8j) | Ga II |
| $\mathbf{B_{51}}$ | = | $y_{13} \, \mathbf{a}_{1}+x_{13} \, \mathbf{a}_{2}- \left(z_{13} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{13} \,\mathbf{\hat{x}}+a x_{13} \,\mathbf{\hat{y}}- c \left(z_{13} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8j) | Ga II |
| $\mathbf{B_{52}}$ | = | $- y_{13} \, \mathbf{a}_{1}- x_{13} \, \mathbf{a}_{2}- \left(z_{13} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{13} \,\mathbf{\hat{x}}- a x_{13} \,\mathbf{\hat{y}}- c \left(z_{13} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8j) | Ga II |
| $\mathbf{B_{53}}$ | = | $x_{14} \, \mathbf{a}_{1}+y_{14} \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ | = | $a x_{14} \,\mathbf{\hat{x}}+a y_{14} \,\mathbf{\hat{y}}+c z_{14} \,\mathbf{\hat{z}}$ | (8j) | Ga III |
| $\mathbf{B_{54}}$ | = | $- x_{14} \, \mathbf{a}_{1}- y_{14} \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ | = | $- a x_{14} \,\mathbf{\hat{x}}- a y_{14} \,\mathbf{\hat{y}}+c z_{14} \,\mathbf{\hat{z}}$ | (8j) | Ga III |
| $\mathbf{B_{55}}$ | = | $y_{14} \, \mathbf{a}_{1}- x_{14} \, \mathbf{a}_{2}- z_{14} \, \mathbf{a}_{3}$ | = | $a y_{14} \,\mathbf{\hat{x}}- a x_{14} \,\mathbf{\hat{y}}- c z_{14} \,\mathbf{\hat{z}}$ | (8j) | Ga III |
| $\mathbf{B_{56}}$ | = | $- y_{14} \, \mathbf{a}_{1}+x_{14} \, \mathbf{a}_{2}- z_{14} \, \mathbf{a}_{3}$ | = | $- a y_{14} \,\mathbf{\hat{x}}+a x_{14} \,\mathbf{\hat{y}}- c z_{14} \,\mathbf{\hat{z}}$ | (8j) | Ga III |
| $\mathbf{B_{57}}$ | = | $x_{14} \, \mathbf{a}_{1}- y_{14} \, \mathbf{a}_{2}+\left(z_{14} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{14} \,\mathbf{\hat{x}}- a y_{14} \,\mathbf{\hat{y}}+c \left(z_{14} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8j) | Ga III |
| $\mathbf{B_{58}}$ | = | $- x_{14} \, \mathbf{a}_{1}+y_{14} \, \mathbf{a}_{2}+\left(z_{14} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{14} \,\mathbf{\hat{x}}+a y_{14} \,\mathbf{\hat{y}}+c \left(z_{14} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8j) | Ga III |
| $\mathbf{B_{59}}$ | = | $y_{14} \, \mathbf{a}_{1}+x_{14} \, \mathbf{a}_{2}- \left(z_{14} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{14} \,\mathbf{\hat{x}}+a x_{14} \,\mathbf{\hat{y}}- c \left(z_{14} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8j) | Ga III |
| $\mathbf{B_{60}}$ | = | $- y_{14} \, \mathbf{a}_{1}- x_{14} \, \mathbf{a}_{2}- \left(z_{14} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{14} \,\mathbf{\hat{x}}- a x_{14} \,\mathbf{\hat{y}}- c \left(z_{14} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8j) | Ga III |
| $\mathbf{B_{61}}$ | = | $x_{15} \, \mathbf{a}_{1}+y_{15} \, \mathbf{a}_{2}+z_{15} \, \mathbf{a}_{3}$ | = | $a x_{15} \,\mathbf{\hat{x}}+a y_{15} \,\mathbf{\hat{y}}+c z_{15} \,\mathbf{\hat{z}}$ | (8j) | Ga IV |
| $\mathbf{B_{62}}$ | = | $- x_{15} \, \mathbf{a}_{1}- y_{15} \, \mathbf{a}_{2}+z_{15} \, \mathbf{a}_{3}$ | = | $- a x_{15} \,\mathbf{\hat{x}}- a y_{15} \,\mathbf{\hat{y}}+c z_{15} \,\mathbf{\hat{z}}$ | (8j) | Ga IV |
| $\mathbf{B_{63}}$ | = | $y_{15} \, \mathbf{a}_{1}- x_{15} \, \mathbf{a}_{2}- z_{15} \, \mathbf{a}_{3}$ | = | $a y_{15} \,\mathbf{\hat{x}}- a x_{15} \,\mathbf{\hat{y}}- c z_{15} \,\mathbf{\hat{z}}$ | (8j) | Ga IV |
| $\mathbf{B_{64}}$ | = | $- y_{15} \, \mathbf{a}_{1}+x_{15} \, \mathbf{a}_{2}- z_{15} \, \mathbf{a}_{3}$ | = | $- a y_{15} \,\mathbf{\hat{x}}+a x_{15} \,\mathbf{\hat{y}}- c z_{15} \,\mathbf{\hat{z}}$ | (8j) | Ga IV |
| $\mathbf{B_{65}}$ | = | $x_{15} \, \mathbf{a}_{1}- y_{15} \, \mathbf{a}_{2}+\left(z_{15} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{15} \,\mathbf{\hat{x}}- a y_{15} \,\mathbf{\hat{y}}+c \left(z_{15} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8j) | Ga IV |
| $\mathbf{B_{66}}$ | = | $- x_{15} \, \mathbf{a}_{1}+y_{15} \, \mathbf{a}_{2}+\left(z_{15} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{15} \,\mathbf{\hat{x}}+a y_{15} \,\mathbf{\hat{y}}+c \left(z_{15} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8j) | Ga IV |
| $\mathbf{B_{67}}$ | = | $y_{15} \, \mathbf{a}_{1}+x_{15} \, \mathbf{a}_{2}- \left(z_{15} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{15} \,\mathbf{\hat{x}}+a x_{15} \,\mathbf{\hat{y}}- c \left(z_{15} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8j) | Ga IV |
| $\mathbf{B_{68}}$ | = | $- y_{15} \, \mathbf{a}_{1}- x_{15} \, \mathbf{a}_{2}- \left(z_{15} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{15} \,\mathbf{\hat{x}}- a x_{15} \,\mathbf{\hat{y}}- c \left(z_{15} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8j) | Ga IV |
| $\mathbf{B_{69}}$ | = | $x_{16} \, \mathbf{a}_{1}+y_{16} \, \mathbf{a}_{2}+z_{16} \, \mathbf{a}_{3}$ | = | $a x_{16} \,\mathbf{\hat{x}}+a y_{16} \,\mathbf{\hat{y}}+c z_{16} \,\mathbf{\hat{z}}$ | (8j) | Ga V |
| $\mathbf{B_{70}}$ | = | $- x_{16} \, \mathbf{a}_{1}- y_{16} \, \mathbf{a}_{2}+z_{16} \, \mathbf{a}_{3}$ | = | $- a x_{16} \,\mathbf{\hat{x}}- a y_{16} \,\mathbf{\hat{y}}+c z_{16} \,\mathbf{\hat{z}}$ | (8j) | Ga V |
| $\mathbf{B_{71}}$ | = | $y_{16} \, \mathbf{a}_{1}- x_{16} \, \mathbf{a}_{2}- z_{16} \, \mathbf{a}_{3}$ | = | $a y_{16} \,\mathbf{\hat{x}}- a x_{16} \,\mathbf{\hat{y}}- c z_{16} \,\mathbf{\hat{z}}$ | (8j) | Ga V |
| $\mathbf{B_{72}}$ | = | $- y_{16} \, \mathbf{a}_{1}+x_{16} \, \mathbf{a}_{2}- z_{16} \, \mathbf{a}_{3}$ | = | $- a y_{16} \,\mathbf{\hat{x}}+a x_{16} \,\mathbf{\hat{y}}- c z_{16} \,\mathbf{\hat{z}}$ | (8j) | Ga V |
| $\mathbf{B_{73}}$ | = | $x_{16} \, \mathbf{a}_{1}- y_{16} \, \mathbf{a}_{2}+\left(z_{16} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{16} \,\mathbf{\hat{x}}- a y_{16} \,\mathbf{\hat{y}}+c \left(z_{16} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8j) | Ga V |
| $\mathbf{B_{74}}$ | = | $- x_{16} \, \mathbf{a}_{1}+y_{16} \, \mathbf{a}_{2}+\left(z_{16} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{16} \,\mathbf{\hat{x}}+a y_{16} \,\mathbf{\hat{y}}+c \left(z_{16} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8j) | Ga V |
| $\mathbf{B_{75}}$ | = | $y_{16} \, \mathbf{a}_{1}+x_{16} \, \mathbf{a}_{2}- \left(z_{16} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{16} \,\mathbf{\hat{x}}+a x_{16} \,\mathbf{\hat{y}}- c \left(z_{16} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8j) | Ga V |
| $\mathbf{B_{76}}$ | = | $- y_{16} \, \mathbf{a}_{1}- x_{16} \, \mathbf{a}_{2}- \left(z_{16} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{16} \,\mathbf{\hat{x}}- a x_{16} \,\mathbf{\hat{y}}- c \left(z_{16} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8j) | Ga V |
| $\mathbf{B_{77}}$ | = | $x_{17} \, \mathbf{a}_{1}+y_{17} \, \mathbf{a}_{2}+z_{17} \, \mathbf{a}_{3}$ | = | $a x_{17} \,\mathbf{\hat{x}}+a y_{17} \,\mathbf{\hat{y}}+c z_{17} \,\mathbf{\hat{z}}$ | (8j) | Ga VI |
| $\mathbf{B_{78}}$ | = | $- x_{17} \, \mathbf{a}_{1}- y_{17} \, \mathbf{a}_{2}+z_{17} \, \mathbf{a}_{3}$ | = | $- a x_{17} \,\mathbf{\hat{x}}- a y_{17} \,\mathbf{\hat{y}}+c z_{17} \,\mathbf{\hat{z}}$ | (8j) | Ga VI |
| $\mathbf{B_{79}}$ | = | $y_{17} \, \mathbf{a}_{1}- x_{17} \, \mathbf{a}_{2}- z_{17} \, \mathbf{a}_{3}$ | = | $a y_{17} \,\mathbf{\hat{x}}- a x_{17} \,\mathbf{\hat{y}}- c z_{17} \,\mathbf{\hat{z}}$ | (8j) | Ga VI |
| $\mathbf{B_{80}}$ | = | $- y_{17} \, \mathbf{a}_{1}+x_{17} \, \mathbf{a}_{2}- z_{17} \, \mathbf{a}_{3}$ | = | $- a y_{17} \,\mathbf{\hat{x}}+a x_{17} \,\mathbf{\hat{y}}- c z_{17} \,\mathbf{\hat{z}}$ | (8j) | Ga VI |
| $\mathbf{B_{81}}$ | = | $x_{17} \, \mathbf{a}_{1}- y_{17} \, \mathbf{a}_{2}+\left(z_{17} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{17} \,\mathbf{\hat{x}}- a y_{17} \,\mathbf{\hat{y}}+c \left(z_{17} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8j) | Ga VI |
| $\mathbf{B_{82}}$ | = | $- x_{17} \, \mathbf{a}_{1}+y_{17} \, \mathbf{a}_{2}+\left(z_{17} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{17} \,\mathbf{\hat{x}}+a y_{17} \,\mathbf{\hat{y}}+c \left(z_{17} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8j) | Ga VI |
| $\mathbf{B_{83}}$ | = | $y_{17} \, \mathbf{a}_{1}+x_{17} \, \mathbf{a}_{2}- \left(z_{17} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{17} \,\mathbf{\hat{x}}+a x_{17} \,\mathbf{\hat{y}}- c \left(z_{17} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8j) | Ga VI |
| $\mathbf{B_{84}}$ | = | $- y_{17} \, \mathbf{a}_{1}- x_{17} \, \mathbf{a}_{2}- \left(z_{17} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{17} \,\mathbf{\hat{x}}- a x_{17} \,\mathbf{\hat{y}}- c \left(z_{17} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8j) | Ga VI |
| $\mathbf{B_{85}}$ | = | $x_{18} \, \mathbf{a}_{1}+y_{18} \, \mathbf{a}_{2}+z_{18} \, \mathbf{a}_{3}$ | = | $a x_{18} \,\mathbf{\hat{x}}+a y_{18} \,\mathbf{\hat{y}}+c z_{18} \,\mathbf{\hat{z}}$ | (8j) | Ga VII |
| $\mathbf{B_{86}}$ | = | $- x_{18} \, \mathbf{a}_{1}- y_{18} \, \mathbf{a}_{2}+z_{18} \, \mathbf{a}_{3}$ | = | $- a x_{18} \,\mathbf{\hat{x}}- a y_{18} \,\mathbf{\hat{y}}+c z_{18} \,\mathbf{\hat{z}}$ | (8j) | Ga VII |
| $\mathbf{B_{87}}$ | = | $y_{18} \, \mathbf{a}_{1}- x_{18} \, \mathbf{a}_{2}- z_{18} \, \mathbf{a}_{3}$ | = | $a y_{18} \,\mathbf{\hat{x}}- a x_{18} \,\mathbf{\hat{y}}- c z_{18} \,\mathbf{\hat{z}}$ | (8j) | Ga VII |
| $\mathbf{B_{88}}$ | = | $- y_{18} \, \mathbf{a}_{1}+x_{18} \, \mathbf{a}_{2}- z_{18} \, \mathbf{a}_{3}$ | = | $- a y_{18} \,\mathbf{\hat{x}}+a x_{18} \,\mathbf{\hat{y}}- c z_{18} \,\mathbf{\hat{z}}$ | (8j) | Ga VII |
| $\mathbf{B_{89}}$ | = | $x_{18} \, \mathbf{a}_{1}- y_{18} \, \mathbf{a}_{2}+\left(z_{18} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{18} \,\mathbf{\hat{x}}- a y_{18} \,\mathbf{\hat{y}}+c \left(z_{18} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8j) | Ga VII |
| $\mathbf{B_{90}}$ | = | $- x_{18} \, \mathbf{a}_{1}+y_{18} \, \mathbf{a}_{2}+\left(z_{18} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{18} \,\mathbf{\hat{x}}+a y_{18} \,\mathbf{\hat{y}}+c \left(z_{18} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8j) | Ga VII |
| $\mathbf{B_{91}}$ | = | $y_{18} \, \mathbf{a}_{1}+x_{18} \, \mathbf{a}_{2}- \left(z_{18} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{18} \,\mathbf{\hat{x}}+a x_{18} \,\mathbf{\hat{y}}- c \left(z_{18} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8j) | Ga VII |
| $\mathbf{B_{92}}$ | = | $- y_{18} \, \mathbf{a}_{1}- x_{18} \, \mathbf{a}_{2}- \left(z_{18} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{18} \,\mathbf{\hat{x}}- a x_{18} \,\mathbf{\hat{y}}- c \left(z_{18} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8j) | Ga VII |
| $\mathbf{B_{93}}$ | = | $x_{19} \, \mathbf{a}_{1}+y_{19} \, \mathbf{a}_{2}+z_{19} \, \mathbf{a}_{3}$ | = | $a x_{19} \,\mathbf{\hat{x}}+a y_{19} \,\mathbf{\hat{y}}+c z_{19} \,\mathbf{\hat{z}}$ | (8j) | Ga VIII |
| $\mathbf{B_{94}}$ | = | $- x_{19} \, \mathbf{a}_{1}- y_{19} \, \mathbf{a}_{2}+z_{19} \, \mathbf{a}_{3}$ | = | $- a x_{19} \,\mathbf{\hat{x}}- a y_{19} \,\mathbf{\hat{y}}+c z_{19} \,\mathbf{\hat{z}}$ | (8j) | Ga VIII |
| $\mathbf{B_{95}}$ | = | $y_{19} \, \mathbf{a}_{1}- x_{19} \, \mathbf{a}_{2}- z_{19} \, \mathbf{a}_{3}$ | = | $a y_{19} \,\mathbf{\hat{x}}- a x_{19} \,\mathbf{\hat{y}}- c z_{19} \,\mathbf{\hat{z}}$ | (8j) | Ga VIII |
| $\mathbf{B_{96}}$ | = | $- y_{19} \, \mathbf{a}_{1}+x_{19} \, \mathbf{a}_{2}- z_{19} \, \mathbf{a}_{3}$ | = | $- a y_{19} \,\mathbf{\hat{x}}+a x_{19} \,\mathbf{\hat{y}}- c z_{19} \,\mathbf{\hat{z}}$ | (8j) | Ga VIII |
| $\mathbf{B_{97}}$ | = | $x_{19} \, \mathbf{a}_{1}- y_{19} \, \mathbf{a}_{2}+\left(z_{19} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{19} \,\mathbf{\hat{x}}- a y_{19} \,\mathbf{\hat{y}}+c \left(z_{19} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8j) | Ga VIII |
| $\mathbf{B_{98}}$ | = | $- x_{19} \, \mathbf{a}_{1}+y_{19} \, \mathbf{a}_{2}+\left(z_{19} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{19} \,\mathbf{\hat{x}}+a y_{19} \,\mathbf{\hat{y}}+c \left(z_{19} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8j) | Ga VIII |
| $\mathbf{B_{99}}$ | = | $y_{19} \, \mathbf{a}_{1}+x_{19} \, \mathbf{a}_{2}- \left(z_{19} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{19} \,\mathbf{\hat{x}}+a x_{19} \,\mathbf{\hat{y}}- c \left(z_{19} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8j) | Ga VIII |
| $\mathbf{B_{100}}$ | = | $- y_{19} \, \mathbf{a}_{1}- x_{19} \, \mathbf{a}_{2}- \left(z_{19} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{19} \,\mathbf{\hat{x}}- a x_{19} \,\mathbf{\hat{y}}- c \left(z_{19} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8j) | Ga VIII |
| $\mathbf{B_{101}}$ | = | $x_{20} \, \mathbf{a}_{1}+y_{20} \, \mathbf{a}_{2}+z_{20} \, \mathbf{a}_{3}$ | = | $a x_{20} \,\mathbf{\hat{x}}+a y_{20} \,\mathbf{\hat{y}}+c z_{20} \,\mathbf{\hat{z}}$ | (8j) | Ga IX |
| $\mathbf{B_{102}}$ | = | $- x_{20} \, \mathbf{a}_{1}- y_{20} \, \mathbf{a}_{2}+z_{20} \, \mathbf{a}_{3}$ | = | $- a x_{20} \,\mathbf{\hat{x}}- a y_{20} \,\mathbf{\hat{y}}+c z_{20} \,\mathbf{\hat{z}}$ | (8j) | Ga IX |
| $\mathbf{B_{103}}$ | = | $y_{20} \, \mathbf{a}_{1}- x_{20} \, \mathbf{a}_{2}- z_{20} \, \mathbf{a}_{3}$ | = | $a y_{20} \,\mathbf{\hat{x}}- a x_{20} \,\mathbf{\hat{y}}- c z_{20} \,\mathbf{\hat{z}}$ | (8j) | Ga IX |
| $\mathbf{B_{104}}$ | = | $- y_{20} \, \mathbf{a}_{1}+x_{20} \, \mathbf{a}_{2}- z_{20} \, \mathbf{a}_{3}$ | = | $- a y_{20} \,\mathbf{\hat{x}}+a x_{20} \,\mathbf{\hat{y}}- c z_{20} \,\mathbf{\hat{z}}$ | (8j) | Ga IX |
| $\mathbf{B_{105}}$ | = | $x_{20} \, \mathbf{a}_{1}- y_{20} \, \mathbf{a}_{2}+\left(z_{20} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{20} \,\mathbf{\hat{x}}- a y_{20} \,\mathbf{\hat{y}}+c \left(z_{20} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8j) | Ga IX |
| $\mathbf{B_{106}}$ | = | $- x_{20} \, \mathbf{a}_{1}+y_{20} \, \mathbf{a}_{2}+\left(z_{20} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{20} \,\mathbf{\hat{x}}+a y_{20} \,\mathbf{\hat{y}}+c \left(z_{20} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8j) | Ga IX |
| $\mathbf{B_{107}}$ | = | $y_{20} \, \mathbf{a}_{1}+x_{20} \, \mathbf{a}_{2}- \left(z_{20} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{20} \,\mathbf{\hat{x}}+a x_{20} \,\mathbf{\hat{y}}- c \left(z_{20} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8j) | Ga IX |
| $\mathbf{B_{108}}$ | = | $- y_{20} \, \mathbf{a}_{1}- x_{20} \, \mathbf{a}_{2}- \left(z_{20} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{20} \,\mathbf{\hat{x}}- a x_{20} \,\mathbf{\hat{y}}- c \left(z_{20} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8j) | Ga IX |
References
- H. Völlenkle, A. Wittmann, and H. Nowotny, Die Kristallstrukturen von Rh$_{10}$Ga$_{17}$ und Ir$_{3}$Ga$_{5}$, Monatsh. Chem 98, 176–183 (1967), doi:10.1007/BF00901115.
Prototype Generator
aflow --proto=A17B10_tP108_116_e8j_ad2g2h5i --params=$a,c/a,x_{3},z_{4},z_{5},z_{6},z_{7},z_{8},z_{9},z_{10},z_{11},z_{12},x_{13},y_{13},z_{13},x_{14},y_{14},z_{14},x_{15},y_{15},z_{15},x_{16},y_{16},z_{16},x_{17},y_{17},z_{17},x_{18},y_{18},z_{18},x_{19},y_{19},z_{19},x_{20},y_{20},z_{20}$