Cr$_{23}$C$_{6}$ ($D8_{4}$) Structure: A6B23_cF116_225_e_acfh-001
| Prototype | C$_{6}$Cr$_{23}$ |
| AFLOW prototype label | A6B23_cF116_225_e_acfh-001 |
| Strukturbericht designation | $D8_{4}$ |
| ICSD | 2837 |
| Pearson symbol | cF116 |
| Space group number | 225 |
| Space group symbol | $Fm\overline{3}m$ |
| AFLOW prototype command |
aflow --proto=A6B23_cF116_225_e_acfh-001
--params=$a, \allowbreak x_{3}, \allowbreak x_{4}, \allowbreak y_{5}$ |
Other compounds with this structure
Mn$_{23}$C$_{6}$, Co$_{21}$Sn$_{2}$B$_{6}$, Fe$_{21}$Mo$_{2}$C$_{6}$, Fe$_{21}$W$_{2}$C$_{6}$, Ni$_{20}$Mg$_{3}$B$_{6}$, Ni$_{21}$In$_{2}$B$_{6}$, Ni$_{21}$Sn$_{2}$B$_{6}$
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (4a) | Cr I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (8c) | Cr II |
| $\mathbf{B_{3}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}+\frac{3}{4}a \,\mathbf{\hat{z}}$ | (8c) | Cr II |
| $\mathbf{B_{4}}$ | = | $- x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}$ | (24e) | C I |
| $\mathbf{B_{5}}$ | = | $x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}$ | (24e) | C I |
| $\mathbf{B_{6}}$ | = | $x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{y}}$ | (24e) | C I |
| $\mathbf{B_{7}}$ | = | $- x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{y}}$ | (24e) | C I |
| $\mathbf{B_{8}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{z}}$ | (24e) | C I |
| $\mathbf{B_{9}}$ | = | $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{z}}$ | (24e) | C I |
| $\mathbf{B_{10}}$ | = | $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (32f) | Cr III |
| $\mathbf{B_{11}}$ | = | $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}- 3 x_{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (32f) | Cr III |
| $\mathbf{B_{12}}$ | = | $x_{4} \, \mathbf{a}_{1}- 3 x_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (32f) | Cr III |
| $\mathbf{B_{13}}$ | = | $- 3 x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (32f) | Cr III |
| $\mathbf{B_{14}}$ | = | $- x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+3 x_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (32f) | Cr III |
| $\mathbf{B_{15}}$ | = | $- x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (32f) | Cr III |
| $\mathbf{B_{16}}$ | = | $- x_{4} \, \mathbf{a}_{1}+3 x_{4} \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (32f) | Cr III |
| $\mathbf{B_{17}}$ | = | $3 x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (32f) | Cr III |
| $\mathbf{B_{18}}$ | = | $2 y_{5} \, \mathbf{a}_{1}$ | = | $a y_{5} \,\mathbf{\hat{y}}+a y_{5} \,\mathbf{\hat{z}}$ | (48h) | Cr IV |
| $\mathbf{B_{19}}$ | = | $2 y_{5} \, \mathbf{a}_{2}- 2 y_{5} \, \mathbf{a}_{3}$ | = | $- a y_{5} \,\mathbf{\hat{y}}+a y_{5} \,\mathbf{\hat{z}}$ | (48h) | Cr IV |
| $\mathbf{B_{20}}$ | = | $- 2 y_{5} \, \mathbf{a}_{2}+2 y_{5} \, \mathbf{a}_{3}$ | = | $a y_{5} \,\mathbf{\hat{y}}- a y_{5} \,\mathbf{\hat{z}}$ | (48h) | Cr IV |
| $\mathbf{B_{21}}$ | = | $- 2 y_{5} \, \mathbf{a}_{1}$ | = | $- a y_{5} \,\mathbf{\hat{y}}- a y_{5} \,\mathbf{\hat{z}}$ | (48h) | Cr IV |
| $\mathbf{B_{22}}$ | = | $2 y_{5} \, \mathbf{a}_{2}$ | = | $a y_{5} \,\mathbf{\hat{x}}+a y_{5} \,\mathbf{\hat{z}}$ | (48h) | Cr IV |
| $\mathbf{B_{23}}$ | = | $- 2 y_{5} \, \mathbf{a}_{1}+2 y_{5} \, \mathbf{a}_{3}$ | = | $a y_{5} \,\mathbf{\hat{x}}- a y_{5} \,\mathbf{\hat{z}}$ | (48h) | Cr IV |
| $\mathbf{B_{24}}$ | = | $2 y_{5} \, \mathbf{a}_{1}- 2 y_{5} \, \mathbf{a}_{3}$ | = | $- a y_{5} \,\mathbf{\hat{x}}+a y_{5} \,\mathbf{\hat{z}}$ | (48h) | Cr IV |
| $\mathbf{B_{25}}$ | = | $- 2 y_{5} \, \mathbf{a}_{2}$ | = | $- a y_{5} \,\mathbf{\hat{x}}- a y_{5} \,\mathbf{\hat{z}}$ | (48h) | Cr IV |
| $\mathbf{B_{26}}$ | = | $2 y_{5} \, \mathbf{a}_{3}$ | = | $a y_{5} \,\mathbf{\hat{x}}+a y_{5} \,\mathbf{\hat{y}}$ | (48h) | Cr IV |
| $\mathbf{B_{27}}$ | = | $2 y_{5} \, \mathbf{a}_{1}- 2 y_{5} \, \mathbf{a}_{2}$ | = | $- a y_{5} \,\mathbf{\hat{x}}+a y_{5} \,\mathbf{\hat{y}}$ | (48h) | Cr IV |
| $\mathbf{B_{28}}$ | = | $- 2 y_{5} \, \mathbf{a}_{1}+2 y_{5} \, \mathbf{a}_{2}$ | = | $a y_{5} \,\mathbf{\hat{x}}- a y_{5} \,\mathbf{\hat{y}}$ | (48h) | Cr IV |
| $\mathbf{B_{29}}$ | = | $- 2 y_{5} \, \mathbf{a}_{3}$ | = | $- a y_{5} \,\mathbf{\hat{x}}- a y_{5} \,\mathbf{\hat{y}}$ | (48h) | Cr IV |
References
- A. L. Bowman, G. P. Arnold, E. K. Storms, and N. G. Nereson, The crystal structure of Cr$_{23}$C$_6$, Acta Crystallogr. Sect. B 28, 3102–3103 (1972), doi:10.1107/S0567740872007526.
Prototype Generator
aflow --proto=A6B23_cF116_225_e_acfh --params=$a,x_{3},x_{4},y_{5}$