Ce$_{3}$Ni$_{6}$Si$_{2}$ Structure: A3B6C2_cI44_229_e_h_c-001
| Prototype | Ce$_{3}$Ni$_{6}$Si$_{2}$ |
| AFLOW prototype label | A3B6C2_cI44_229_e_h_c-001 |
| ICSD | 25622 |
| Pearson symbol | cI44 |
| Space group number | 229 |
| Space group symbol | $Im\overline{3}m$ |
| AFLOW prototype command |
aflow --proto=A3B6C2_cI44_229_e_h_c-001
--params=$a, \allowbreak x_{2}, \allowbreak y_{3}$ |
Other compounds with this structure
Dy$_{3}$Ni$_{6}$Si$_{2}$, Er$_{3}$Ni$_{6}$Al$_{2}$, Er$_{3}$Ni$_{6}$Si$_{2}$, Eu$_{3}$Ni$_{6}$Si$_{2}$, Gd$_{3}$Ni$_{6}$Si$_{2}$, Ho$_{3}$Ni$_{6}$Si$_{2}$, Lu$_{3}$Ni$_{6}$Si$_{2}$, Nd$_{3}$Ni$_{6}$Si$_{2}$, Pr$_{3}$Ni$_{6}$Si$_{2}$, Sm$_{3}$Ni$_{6}$Si$_{2}$, Tb$_{3}$Ni$_{6}$Si$_{2}$, Tm$_{3}$Ni$_{6}$Si$_{2}$, U$_{3}$Ni$_{6}$Ge$_{2}$, U$_{3}$Ni$_{6}$Si$_{2}$, Yb$_{3}$Ni$_{6}$Si$_{2}$
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}a \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (8c) | Si I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}- \frac{1}{4}a \,\mathbf{\hat{z}}$ | (8c) | Si I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- \frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (8c) | Si I |
| $\mathbf{B_{4}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}$ | = | $- \frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (8c) | Si I |
| $\mathbf{B_{5}}$ | = | $x_{2} \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}$ | (12e) | Ce I |
| $\mathbf{B_{6}}$ | = | $- x_{2} \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}$ | (12e) | Ce I |
| $\mathbf{B_{7}}$ | = | $x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{y}}$ | (12e) | Ce I |
| $\mathbf{B_{8}}$ | = | $- x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{y}}$ | (12e) | Ce I |
| $\mathbf{B_{9}}$ | = | $x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}$ | = | $a x_{2} \,\mathbf{\hat{z}}$ | (12e) | Ce I |
| $\mathbf{B_{10}}$ | = | $- x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}$ | = | $- a x_{2} \,\mathbf{\hat{z}}$ | (12e) | Ce I |
| $\mathbf{B_{11}}$ | = | $2 y_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}+y_{3} \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{y}}+a y_{3} \,\mathbf{\hat{z}}$ | (24h) | Ni I |
| $\mathbf{B_{12}}$ | = | $y_{3} \, \mathbf{a}_{2}- y_{3} \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{y}}+a y_{3} \,\mathbf{\hat{z}}$ | (24h) | Ni I |
| $\mathbf{B_{13}}$ | = | $- y_{3} \, \mathbf{a}_{2}+y_{3} \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{y}}- a y_{3} \,\mathbf{\hat{z}}$ | (24h) | Ni I |
| $\mathbf{B_{14}}$ | = | $- 2 y_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}- y_{3} \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{y}}- a y_{3} \,\mathbf{\hat{z}}$ | (24h) | Ni I |
| $\mathbf{B_{15}}$ | = | $y_{3} \, \mathbf{a}_{1}+2 y_{3} \, \mathbf{a}_{2}+y_{3} \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{x}}+a y_{3} \,\mathbf{\hat{z}}$ | (24h) | Ni I |
| $\mathbf{B_{16}}$ | = | $- y_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{x}}- a y_{3} \,\mathbf{\hat{z}}$ | (24h) | Ni I |
| $\mathbf{B_{17}}$ | = | $y_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{x}}+a y_{3} \,\mathbf{\hat{z}}$ | (24h) | Ni I |
| $\mathbf{B_{18}}$ | = | $- y_{3} \, \mathbf{a}_{1}- 2 y_{3} \, \mathbf{a}_{2}- y_{3} \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{x}}- a y_{3} \,\mathbf{\hat{z}}$ | (24h) | Ni I |
| $\mathbf{B_{19}}$ | = | $y_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}+2 y_{3} \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{x}}+a y_{3} \,\mathbf{\hat{y}}$ | (24h) | Ni I |
| $\mathbf{B_{20}}$ | = | $y_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}$ | = | $- a y_{3} \,\mathbf{\hat{x}}+a y_{3} \,\mathbf{\hat{y}}$ | (24h) | Ni I |
| $\mathbf{B_{21}}$ | = | $- y_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}$ | = | $a y_{3} \,\mathbf{\hat{x}}- a y_{3} \,\mathbf{\hat{y}}$ | (24h) | Ni I |
| $\mathbf{B_{22}}$ | = | $- y_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}- 2 y_{3} \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{x}}- a y_{3} \,\mathbf{\hat{y}}$ | (24h) | Ni I |
References
- E. I. Hladyschewskyj, P. I. Krypiakewytsch, and O. I. Bodak, Die Kristallstruktur von Ce$_{3}$Ni$_{6}$Si$_{2}$ und verwandten Verbindungen, Z. Anorganische und Allgemeine Chemie 344, 95–101 (1966), doi:10.1002/zaac.19663440113.
Prototype Generator
aflow --proto=A3B6C2_cI44_229_e_h_c --params=$a,x_{2},y_{3}$