KGe Structure: AB_cP64_218_ei_ei-001
| Prototype | GeK |
| AFLOW prototype label | AB_cP64_218_ei_ei-001 |
| ICSD | 43515 |
| Pearson symbol | cP64 |
| Space group number | 218 |
| Space group symbol | $P\overline{4}3n$ |
| AFLOW prototype command |
aflow --proto=AB_cP64_218_ei_ei-001
--params=$a, \allowbreak x_{1}, \allowbreak x_{2}, \allowbreak x_{3}, \allowbreak y_{3}, \allowbreak z_{3}, \allowbreak x_{4}, \allowbreak y_{4}, \allowbreak z_{4}$ |
Other compounds with this structure
CsGe, CsSi, KSi, RbGe, RbSi
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&a \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $x_{1} \, \mathbf{a}_{1}+x_{1} \, \mathbf{a}_{2}+x_{1} \, \mathbf{a}_{3}$ | = | $a x_{1} \,\mathbf{\hat{x}}+a x_{1} \,\mathbf{\hat{y}}+a x_{1} \,\mathbf{\hat{z}}$ | (8e) | Ge I |
| $\mathbf{B_{2}}$ | = | $- x_{1} \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{2}+x_{1} \, \mathbf{a}_{3}$ | = | $- a x_{1} \,\mathbf{\hat{x}}- a x_{1} \,\mathbf{\hat{y}}+a x_{1} \,\mathbf{\hat{z}}$ | (8e) | Ge I |
| $\mathbf{B_{3}}$ | = | $- x_{1} \, \mathbf{a}_{1}+x_{1} \, \mathbf{a}_{2}- x_{1} \, \mathbf{a}_{3}$ | = | $- a x_{1} \,\mathbf{\hat{x}}+a x_{1} \,\mathbf{\hat{y}}- a x_{1} \,\mathbf{\hat{z}}$ | (8e) | Ge I |
| $\mathbf{B_{4}}$ | = | $x_{1} \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{2}- x_{1} \, \mathbf{a}_{3}$ | = | $a x_{1} \,\mathbf{\hat{x}}- a x_{1} \,\mathbf{\hat{y}}- a x_{1} \,\mathbf{\hat{z}}$ | (8e) | Ge I |
| $\mathbf{B_{5}}$ | = | $\left(x_{1} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{1} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{1} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{1} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{1} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(x_{1} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8e) | Ge I |
| $\mathbf{B_{6}}$ | = | $- \left(x_{1} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{1} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{1} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{1} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{1} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(x_{1} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8e) | Ge I |
| $\mathbf{B_{7}}$ | = | $\left(x_{1} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{1} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{1} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{1} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{1} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{1} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8e) | Ge I |
| $\mathbf{B_{8}}$ | = | $- \left(x_{1} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{1} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{1} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{1} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{1} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{1} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8e) | Ge I |
| $\mathbf{B_{9}}$ | = | $x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}+a x_{2} \,\mathbf{\hat{z}}$ | (8e) | K I |
| $\mathbf{B_{10}}$ | = | $- x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}+a x_{2} \,\mathbf{\hat{z}}$ | (8e) | K I |
| $\mathbf{B_{11}}$ | = | $- x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}- a x_{2} \,\mathbf{\hat{z}}$ | (8e) | K I |
| $\mathbf{B_{12}}$ | = | $x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}- a x_{2} \,\mathbf{\hat{z}}$ | (8e) | K I |
| $\mathbf{B_{13}}$ | = | $\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8e) | K I |
| $\mathbf{B_{14}}$ | = | $- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8e) | K I |
| $\mathbf{B_{15}}$ | = | $\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8e) | K I |
| $\mathbf{B_{16}}$ | = | $- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8e) | K I |
| $\mathbf{B_{17}}$ | = | $x_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a y_{3} \,\mathbf{\hat{y}}+a z_{3} \,\mathbf{\hat{z}}$ | (24i) | Ge II |
| $\mathbf{B_{18}}$ | = | $- x_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a y_{3} \,\mathbf{\hat{y}}+a z_{3} \,\mathbf{\hat{z}}$ | (24i) | Ge II |
| $\mathbf{B_{19}}$ | = | $- x_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+a y_{3} \,\mathbf{\hat{y}}- a z_{3} \,\mathbf{\hat{z}}$ | (24i) | Ge II |
| $\mathbf{B_{20}}$ | = | $x_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}- a y_{3} \,\mathbf{\hat{y}}- a z_{3} \,\mathbf{\hat{z}}$ | (24i) | Ge II |
| $\mathbf{B_{21}}$ | = | $z_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+y_{3} \, \mathbf{a}_{3}$ | = | $a z_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}+a y_{3} \,\mathbf{\hat{z}}$ | (24i) | Ge II |
| $\mathbf{B_{22}}$ | = | $z_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- y_{3} \, \mathbf{a}_{3}$ | = | $a z_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}- a y_{3} \,\mathbf{\hat{z}}$ | (24i) | Ge II |
| $\mathbf{B_{23}}$ | = | $- z_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+y_{3} \, \mathbf{a}_{3}$ | = | $- a z_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}+a y_{3} \,\mathbf{\hat{z}}$ | (24i) | Ge II |
| $\mathbf{B_{24}}$ | = | $- z_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}- y_{3} \, \mathbf{a}_{3}$ | = | $- a z_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}- a y_{3} \,\mathbf{\hat{z}}$ | (24i) | Ge II |
| $\mathbf{B_{25}}$ | = | $y_{3} \, \mathbf{a}_{1}+z_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{x}}+a z_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (24i) | Ge II |
| $\mathbf{B_{26}}$ | = | $- y_{3} \, \mathbf{a}_{1}+z_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{x}}+a z_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (24i) | Ge II |
| $\mathbf{B_{27}}$ | = | $y_{3} \, \mathbf{a}_{1}- z_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{x}}- a z_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (24i) | Ge II |
| $\mathbf{B_{28}}$ | = | $- y_{3} \, \mathbf{a}_{1}- z_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{x}}- a z_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (24i) | Ge II |
| $\mathbf{B_{29}}$ | = | $\left(y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24i) | Ge II |
| $\mathbf{B_{30}}$ | = | $- \left(y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24i) | Ge II |
| $\mathbf{B_{31}}$ | = | $\left(y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(z_{3} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24i) | Ge II |
| $\mathbf{B_{32}}$ | = | $- \left(y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(z_{3} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24i) | Ge II |
| $\mathbf{B_{33}}$ | = | $\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24i) | Ge II |
| $\mathbf{B_{34}}$ | = | $- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24i) | Ge II |
| $\mathbf{B_{35}}$ | = | $- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(z_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24i) | Ge II |
| $\mathbf{B_{36}}$ | = | $\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(z_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24i) | Ge II |
| $\mathbf{B_{37}}$ | = | $\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24i) | Ge II |
| $\mathbf{B_{38}}$ | = | $\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24i) | Ge II |
| $\mathbf{B_{39}}$ | = | $- \left(z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24i) | Ge II |
| $\mathbf{B_{40}}$ | = | $- \left(z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24i) | Ge II |
| $\mathbf{B_{41}}$ | = | $x_{4} \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a y_{4} \,\mathbf{\hat{y}}+a z_{4} \,\mathbf{\hat{z}}$ | (24i) | K II |
| $\mathbf{B_{42}}$ | = | $- x_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- a y_{4} \,\mathbf{\hat{y}}+a z_{4} \,\mathbf{\hat{z}}$ | (24i) | K II |
| $\mathbf{B_{43}}$ | = | $- x_{4} \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+a y_{4} \,\mathbf{\hat{y}}- a z_{4} \,\mathbf{\hat{z}}$ | (24i) | K II |
| $\mathbf{B_{44}}$ | = | $x_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}- a y_{4} \,\mathbf{\hat{y}}- a z_{4} \,\mathbf{\hat{z}}$ | (24i) | K II |
| $\mathbf{B_{45}}$ | = | $z_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+y_{4} \, \mathbf{a}_{3}$ | = | $a z_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}+a y_{4} \,\mathbf{\hat{z}}$ | (24i) | K II |
| $\mathbf{B_{46}}$ | = | $z_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}- y_{4} \, \mathbf{a}_{3}$ | = | $a z_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}- a y_{4} \,\mathbf{\hat{z}}$ | (24i) | K II |
| $\mathbf{B_{47}}$ | = | $- z_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+y_{4} \, \mathbf{a}_{3}$ | = | $- a z_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}+a y_{4} \,\mathbf{\hat{z}}$ | (24i) | K II |
| $\mathbf{B_{48}}$ | = | $- z_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}- y_{4} \, \mathbf{a}_{3}$ | = | $- a z_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}- a y_{4} \,\mathbf{\hat{z}}$ | (24i) | K II |
| $\mathbf{B_{49}}$ | = | $y_{4} \, \mathbf{a}_{1}+z_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $a y_{4} \,\mathbf{\hat{x}}+a z_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (24i) | K II |
| $\mathbf{B_{50}}$ | = | $- y_{4} \, \mathbf{a}_{1}+z_{4} \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ | = | $- a y_{4} \,\mathbf{\hat{x}}+a z_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (24i) | K II |
| $\mathbf{B_{51}}$ | = | $y_{4} \, \mathbf{a}_{1}- z_{4} \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ | = | $a y_{4} \,\mathbf{\hat{x}}- a z_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (24i) | K II |
| $\mathbf{B_{52}}$ | = | $- y_{4} \, \mathbf{a}_{1}- z_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $- a y_{4} \,\mathbf{\hat{x}}- a z_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (24i) | K II |
| $\mathbf{B_{53}}$ | = | $\left(y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{4} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24i) | K II |
| $\mathbf{B_{54}}$ | = | $- \left(y_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{4} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24i) | K II |
| $\mathbf{B_{55}}$ | = | $\left(y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{4} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(z_{4} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24i) | K II |
| $\mathbf{B_{56}}$ | = | $- \left(y_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{4} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(z_{4} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24i) | K II |
| $\mathbf{B_{57}}$ | = | $\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(y_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24i) | K II |
| $\mathbf{B_{58}}$ | = | $- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(y_{4} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24i) | K II |
| $\mathbf{B_{59}}$ | = | $- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(z_{4} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(y_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24i) | K II |
| $\mathbf{B_{60}}$ | = | $\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(z_{4} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(y_{4} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24i) | K II |
| $\mathbf{B_{61}}$ | = | $\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{4} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24i) | K II |
| $\mathbf{B_{62}}$ | = | $\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{4} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24i) | K II |
| $\mathbf{B_{63}}$ | = | $- \left(z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{4} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{4} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24i) | K II |
| $\mathbf{B_{64}}$ | = | $- \left(z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{4} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{4} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24i) | K II |
References
- E. Busmann, Das Verhalten der Alkalimetalle zu Halbmetallen. X. Die Kristallstrukturen von KSi, RbSi, CsSi, KGe, RbGe und CsGe, Z. Anorganische und Allgemeine Chemie 313, 90–106 (1961), doi:10.1002/zaac.19613130108.
Found in
- W. B. Pearson, A Handbook of Lattice Spacings and Structures of Metals and Alloys, Volume 2, International Series of Monographs on Metal Physics and Physical Metallurgy, vol. 8 (Pergamon Press, Oxford, London, Edinburgh, New York, Toronto, Sydney, Paris, Braunschweig, 1967).
Prototype Generator
aflow --proto=AB_cP64_218_ei_ei --params=$a,x_{1},x_{2},x_{3},y_{3},z_{3},x_{4},y_{4},z_{4}$