Rb$_{3}$AsSe$_{16}$ Structure: AB3C16_cF160_203_a_bc_eg-001
| Prototype | AsRb$_{3}$Se$_{16}$ |
| AFLOW prototype label | AB3C16_cF160_203_a_bc_eg-001 |
| ICSD | 405959 |
| Pearson symbol | cF160 |
| Space group number | 203 |
| Space group symbol | $Fd\overline{3}$ |
| AFLOW prototype command |
aflow --proto=AB3C16_cF160_203_a_bc_eg-001
--params=$a, \allowbreak x_{4}, \allowbreak x_{5}, \allowbreak y_{5}, \allowbreak z_{5}$ |
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{8} \, \mathbf{a}_{1}+\frac{1}{8} \, \mathbf{a}_{2}+\frac{1}{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ | (8a) | As I |
| $\mathbf{B_{2}}$ | = | $\frac{7}{8} \, \mathbf{a}_{1}+\frac{7}{8} \, \mathbf{a}_{2}+\frac{7}{8} \, \mathbf{a}_{3}$ | = | $\frac{7}{8}a \,\mathbf{\hat{x}}+\frac{7}{8}a \,\mathbf{\hat{y}}+\frac{7}{8}a \,\mathbf{\hat{z}}$ | (8a) | As I |
| $\mathbf{B_{3}}$ | = | $\frac{5}{8} \, \mathbf{a}_{1}+\frac{5}{8} \, \mathbf{a}_{2}+\frac{5}{8} \, \mathbf{a}_{3}$ | = | $\frac{5}{8}a \,\mathbf{\hat{x}}+\frac{5}{8}a \,\mathbf{\hat{y}}+\frac{5}{8}a \,\mathbf{\hat{z}}$ | (8b) | Rb I |
| $\mathbf{B_{4}}$ | = | $\frac{3}{8} \, \mathbf{a}_{1}+\frac{3}{8} \, \mathbf{a}_{2}+\frac{3}{8} \, \mathbf{a}_{3}$ | = | $\frac{3}{8}a \,\mathbf{\hat{x}}+\frac{3}{8}a \,\mathbf{\hat{y}}+\frac{3}{8}a \,\mathbf{\hat{z}}$ | (8b) | Rb I |
| $\mathbf{B_{5}}$ | = | $0$ | = | $0$ | (16c) | Rb II |
| $\mathbf{B_{6}}$ | = | $\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}$ | (16c) | Rb II |
| $\mathbf{B_{7}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (16c) | Rb II |
| $\mathbf{B_{8}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}$ | = | $\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (16c) | Rb II |
| $\mathbf{B_{9}}$ | = | $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (32e) | Se I |
| $\mathbf{B_{10}}$ | = | $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}- \left(3 x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (32e) | Se I |
| $\mathbf{B_{11}}$ | = | $x_{4} \, \mathbf{a}_{1}- \left(3 x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32e) | Se I |
| $\mathbf{B_{12}}$ | = | $- \left(3 x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32e) | Se I |
| $\mathbf{B_{13}}$ | = | $- x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (32e) | Se I |
| $\mathbf{B_{14}}$ | = | $- x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+\left(3 x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (32e) | Se I |
| $\mathbf{B_{15}}$ | = | $- x_{4} \, \mathbf{a}_{1}+\left(3 x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ | = | $a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}+a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32e) | Se I |
| $\mathbf{B_{16}}$ | = | $\left(3 x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32e) | Se I |
| $\mathbf{B_{17}}$ | = | $\left(- x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+a y_{5} \,\mathbf{\hat{y}}+a z_{5} \,\mathbf{\hat{z}}$ | (96g) | Se II |
| $\mathbf{B_{18}}$ | = | $\left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(- x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{2}- \left(x_{5} + y_{5} + z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{5} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(y_{5} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a z_{5} \,\mathbf{\hat{z}}$ | (96g) | Se II |
| $\mathbf{B_{19}}$ | = | $\left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} + y_{5} + z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(- x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{5} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a y_{5} \,\mathbf{\hat{y}}- a \left(z_{5} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | Se II |
| $\mathbf{B_{20}}$ | = | $- \left(x_{5} + y_{5} + z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}- a \left(y_{5} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{5} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | Se II |
| $\mathbf{B_{21}}$ | = | $\left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{1}+\left(- x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $a z_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}+a y_{5} \,\mathbf{\hat{z}}$ | (96g) | Se II |
| $\mathbf{B_{22}}$ | = | $- \left(x_{5} + y_{5} + z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(- x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $a z_{5} \,\mathbf{\hat{x}}- a \left(x_{5} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(y_{5} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | Se II |
| $\mathbf{B_{23}}$ | = | $\left(- x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{2}- \left(x_{5} + y_{5} + z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{5} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{5} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a y_{5} \,\mathbf{\hat{z}}$ | (96g) | Se II |
| $\mathbf{B_{24}}$ | = | $\left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} + y_{5} + z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{5} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}- a \left(y_{5} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | Se II |
| $\mathbf{B_{25}}$ | = | $\left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{2}+\left(- x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $a y_{5} \,\mathbf{\hat{x}}+a z_{5} \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (96g) | Se II |
| $\mathbf{B_{26}}$ | = | $\left(- x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} + y_{5} + z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{5} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a z_{5} \,\mathbf{\hat{y}}- a \left(x_{5} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | Se II |
| $\mathbf{B_{27}}$ | = | $- \left(x_{5} + y_{5} + z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{3}$ | = | $a y_{5} \,\mathbf{\hat{x}}- a \left(z_{5} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{5} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | Se II |
| $\mathbf{B_{28}}$ | = | $\left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{2}- \left(x_{5} + y_{5} + z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{5} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{5} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (96g) | Se II |
| $\mathbf{B_{29}}$ | = | $\left(x_{5} - y_{5} - z_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{2}- \left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}- a y_{5} \,\mathbf{\hat{y}}- a z_{5} \,\mathbf{\hat{z}}$ | (96g) | Se II |
| $\mathbf{B_{30}}$ | = | $- \left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} - y_{5} - z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} + y_{5} + z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{5} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(y_{5} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a z_{5} \,\mathbf{\hat{z}}$ | (96g) | Se II |
| $\mathbf{B_{31}}$ | = | $- \left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} + y_{5} + z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{5} - y_{5} - z_{5}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{5} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a y_{5} \,\mathbf{\hat{y}}+a \left(z_{5} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | Se II |
| $\mathbf{B_{32}}$ | = | $\left(x_{5} + y_{5} + z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{2}- \left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}+a \left(y_{5} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{5} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | Se II |
| $\mathbf{B_{33}}$ | = | $- \left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} - y_{5} - z_{5}\right) \, \mathbf{a}_{2}- \left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $- a z_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}- a y_{5} \,\mathbf{\hat{z}}$ | (96g) | Se II |
| $\mathbf{B_{34}}$ | = | $\left(x_{5} + y_{5} + z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} - y_{5} - z_{5}\right) \, \mathbf{a}_{3}$ | = | $- a z_{5} \,\mathbf{\hat{x}}+a \left(x_{5} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(y_{5} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | Se II |
| $\mathbf{B_{35}}$ | = | $\left(x_{5} - y_{5} - z_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} + y_{5} + z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{5} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{5} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a y_{5} \,\mathbf{\hat{z}}$ | (96g) | Se II |
| $\mathbf{B_{36}}$ | = | $- \left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} + y_{5} + z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{5} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}+a \left(y_{5} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | Se II |
| $\mathbf{B_{37}}$ | = | $- \left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} - y_{5} - z_{5}\right) \, \mathbf{a}_{3}$ | = | $- a y_{5} \,\mathbf{\hat{x}}- a z_{5} \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (96g) | Se II |
| $\mathbf{B_{38}}$ | = | $\left(x_{5} - y_{5} - z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} + y_{5} + z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{5} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a z_{5} \,\mathbf{\hat{y}}+a \left(x_{5} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | Se II |
| $\mathbf{B_{39}}$ | = | $\left(x_{5} + y_{5} + z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{5} - y_{5} - z_{5}\right) \, \mathbf{a}_{2}- \left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{3}$ | = | $- a y_{5} \,\mathbf{\hat{x}}+a \left(z_{5} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{5} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | Se II |
| $\mathbf{B_{40}}$ | = | $- \left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} + y_{5} + z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{5} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{5} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (96g) | Se II |
References
- M. Wachhold and W. S. Sheldrick, Methanolothermale Synthese von Rb$_{3}$AsSe$_{4}$ $\cdot$ 2Se$_{6}$ und Cs$_{3}$AsSe$_{4}$ $\cdot$ 2Cs$_{2}$As$_{2}$Se$_{4}$ $\cdot$ 6Te$_{4}$Se$_{2}$, zwei Selenidoarsenate mit sechsgliedrigen Chalkogenringen, Z. Naturforsch. B 52, 169–175 (1997), doi:10.1515/znb-1997-0204.
Found in
- P. Villars and K. Cenzual, Pearson's Crystal Data – Crystal Structure Database for Inorganic Compounds (2013). ASM International.
Prototype Generator
aflow --proto=AB3C16_cF160_203_a_bc_eg --params=$a,x_{4},x_{5},y_{5},z_{5}$