YCd$_{6}$ Structure: A20B3_cI184_204_def3gh_g-001
| Prototype | Cd$_{6}$Y |
| AFLOW prototype label | A20B3_cI184_204_def3gh_g-001 |
| ICSD | 9148 |
| Pearson symbol | cI184 |
| Space group number | 204 |
| Space group symbol | $Im\overline{3}$ |
| AFLOW prototype command |
aflow --proto=A20B3_cI184_204_def3gh_g-001
--params=$a, \allowbreak x_{1}, \allowbreak x_{2}, \allowbreak x_{3}, \allowbreak y_{4}, \allowbreak z_{4}, \allowbreak y_{5}, \allowbreak z_{5}, \allowbreak y_{6}, \allowbreak z_{6}, \allowbreak y_{7}, \allowbreak z_{7}, \allowbreak x_{8}, \allowbreak y_{8}, \allowbreak z_{8}$ |
Other compounds with this structure
CeCd$_{6}$, DyCd$_{6}$, ErCd$_{6}$, EuCd$_{6}$, GdCd$_{6}$, HoCd$_{6}$, LuCd$_{6}$, NdCd$_{6}$, PrCd$_{6}$, PuCd$_{6}$, SmCd$_{6}$, TbCd$_{6}$, TmCd$_{6}$
- The site we label Cd-VI is occupied only 33.1% of the time. Removing this atom transforms this to the Ru$_{3}$Be$_{17}$ structure.
- (Armbrüster, 2000) found that what had previously been thought to be CeCd$_{6}$ was actually Ce$_{6}$Cd$_{37}$. This suggests that other XCd$_{6}$ structures may actually have different compositions.
- (Armbrüster, 2000) also give a structure for CeCd$_{6}$ which differs slightly from the one presented here.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}a \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $x_{1} \, \mathbf{a}_{2}+x_{1} \, \mathbf{a}_{3}$ | = | $a x_{1} \,\mathbf{\hat{x}}$ | (12d) | Cd I |
| $\mathbf{B_{2}}$ | = | $- x_{1} \, \mathbf{a}_{2}- x_{1} \, \mathbf{a}_{3}$ | = | $- a x_{1} \,\mathbf{\hat{x}}$ | (12d) | Cd I |
| $\mathbf{B_{3}}$ | = | $x_{1} \, \mathbf{a}_{1}+x_{1} \, \mathbf{a}_{3}$ | = | $a x_{1} \,\mathbf{\hat{y}}$ | (12d) | Cd I |
| $\mathbf{B_{4}}$ | = | $- x_{1} \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{3}$ | = | $- a x_{1} \,\mathbf{\hat{y}}$ | (12d) | Cd I |
| $\mathbf{B_{5}}$ | = | $x_{1} \, \mathbf{a}_{1}+x_{1} \, \mathbf{a}_{2}$ | = | $a x_{1} \,\mathbf{\hat{z}}$ | (12d) | Cd I |
| $\mathbf{B_{6}}$ | = | $- x_{1} \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{2}$ | = | $- a x_{1} \,\mathbf{\hat{z}}$ | (12d) | Cd I |
| $\mathbf{B_{7}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (12e) | Cd II |
| $\mathbf{B_{8}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (12e) | Cd II |
| $\mathbf{B_{9}}$ | = | $x_{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}$ | (12e) | Cd II |
| $\mathbf{B_{10}}$ | = | $- x_{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}$ | (12e) | Cd II |
| $\mathbf{B_{11}}$ | = | $\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+a x_{2} \,\mathbf{\hat{z}}$ | (12e) | Cd II |
| $\mathbf{B_{12}}$ | = | $- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}- a x_{2} \,\mathbf{\hat{z}}$ | (12e) | Cd II |
| $\mathbf{B_{13}}$ | = | $2 x_{3} \, \mathbf{a}_{1}+2 x_{3} \, \mathbf{a}_{2}+2 x_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (16f) | Cd III |
| $\mathbf{B_{14}}$ | = | $- 2 x_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (16f) | Cd III |
| $\mathbf{B_{15}}$ | = | $- 2 x_{3} \, \mathbf{a}_{2}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (16f) | Cd III |
| $\mathbf{B_{16}}$ | = | $- 2 x_{3} \, \mathbf{a}_{1}$ | = | $a x_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (16f) | Cd III |
| $\mathbf{B_{17}}$ | = | $- 2 x_{3} \, \mathbf{a}_{1}- 2 x_{3} \, \mathbf{a}_{2}- 2 x_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (16f) | Cd III |
| $\mathbf{B_{18}}$ | = | $2 x_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (16f) | Cd III |
| $\mathbf{B_{19}}$ | = | $2 x_{3} \, \mathbf{a}_{2}$ | = | $a x_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (16f) | Cd III |
| $\mathbf{B_{20}}$ | = | $2 x_{3} \, \mathbf{a}_{1}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (16f) | Cd III |
| $\mathbf{B_{21}}$ | = | $\left(y_{4} + z_{4}\right) \, \mathbf{a}_{1}+z_{4} \, \mathbf{a}_{2}+y_{4} \, \mathbf{a}_{3}$ | = | $a y_{4} \,\mathbf{\hat{y}}+a z_{4} \,\mathbf{\hat{z}}$ | (24g) | Cd IV |
| $\mathbf{B_{22}}$ | = | $- \left(y_{4} - z_{4}\right) \, \mathbf{a}_{1}+z_{4} \, \mathbf{a}_{2}- y_{4} \, \mathbf{a}_{3}$ | = | $- a y_{4} \,\mathbf{\hat{y}}+a z_{4} \,\mathbf{\hat{z}}$ | (24g) | Cd IV |
| $\mathbf{B_{23}}$ | = | $\left(y_{4} - z_{4}\right) \, \mathbf{a}_{1}- z_{4} \, \mathbf{a}_{2}+y_{4} \, \mathbf{a}_{3}$ | = | $a y_{4} \,\mathbf{\hat{y}}- a z_{4} \,\mathbf{\hat{z}}$ | (24g) | Cd IV |
| $\mathbf{B_{24}}$ | = | $- \left(y_{4} + z_{4}\right) \, \mathbf{a}_{1}- z_{4} \, \mathbf{a}_{2}- y_{4} \, \mathbf{a}_{3}$ | = | $- a y_{4} \,\mathbf{\hat{y}}- a z_{4} \,\mathbf{\hat{z}}$ | (24g) | Cd IV |
| $\mathbf{B_{25}}$ | = | $y_{4} \, \mathbf{a}_{1}+\left(y_{4} + z_{4}\right) \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $a z_{4} \,\mathbf{\hat{x}}+a y_{4} \,\mathbf{\hat{z}}$ | (24g) | Cd IV |
| $\mathbf{B_{26}}$ | = | $- y_{4} \, \mathbf{a}_{1}- \left(y_{4} - z_{4}\right) \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $a z_{4} \,\mathbf{\hat{x}}- a y_{4} \,\mathbf{\hat{z}}$ | (24g) | Cd IV |
| $\mathbf{B_{27}}$ | = | $y_{4} \, \mathbf{a}_{1}+\left(y_{4} - z_{4}\right) \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $- a z_{4} \,\mathbf{\hat{x}}+a y_{4} \,\mathbf{\hat{z}}$ | (24g) | Cd IV |
| $\mathbf{B_{28}}$ | = | $- y_{4} \, \mathbf{a}_{1}- \left(y_{4} + z_{4}\right) \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $- a z_{4} \,\mathbf{\hat{x}}- a y_{4} \,\mathbf{\hat{z}}$ | (24g) | Cd IV |
| $\mathbf{B_{29}}$ | = | $z_{4} \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{2}+\left(y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $a y_{4} \,\mathbf{\hat{x}}+a z_{4} \,\mathbf{\hat{y}}$ | (24g) | Cd IV |
| $\mathbf{B_{30}}$ | = | $z_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}- \left(y_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a y_{4} \,\mathbf{\hat{x}}+a z_{4} \,\mathbf{\hat{y}}$ | (24g) | Cd IV |
| $\mathbf{B_{31}}$ | = | $- z_{4} \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{2}+\left(y_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $a y_{4} \,\mathbf{\hat{x}}- a z_{4} \,\mathbf{\hat{y}}$ | (24g) | Cd IV |
| $\mathbf{B_{32}}$ | = | $- z_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}- \left(y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a y_{4} \,\mathbf{\hat{x}}- a z_{4} \,\mathbf{\hat{y}}$ | (24g) | Cd IV |
| $\mathbf{B_{33}}$ | = | $\left(y_{5} + z_{5}\right) \, \mathbf{a}_{1}+z_{5} \, \mathbf{a}_{2}+y_{5} \, \mathbf{a}_{3}$ | = | $a y_{5} \,\mathbf{\hat{y}}+a z_{5} \,\mathbf{\hat{z}}$ | (24g) | Cd V |
| $\mathbf{B_{34}}$ | = | $- \left(y_{5} - z_{5}\right) \, \mathbf{a}_{1}+z_{5} \, \mathbf{a}_{2}- y_{5} \, \mathbf{a}_{3}$ | = | $- a y_{5} \,\mathbf{\hat{y}}+a z_{5} \,\mathbf{\hat{z}}$ | (24g) | Cd V |
| $\mathbf{B_{35}}$ | = | $\left(y_{5} - z_{5}\right) \, \mathbf{a}_{1}- z_{5} \, \mathbf{a}_{2}+y_{5} \, \mathbf{a}_{3}$ | = | $a y_{5} \,\mathbf{\hat{y}}- a z_{5} \,\mathbf{\hat{z}}$ | (24g) | Cd V |
| $\mathbf{B_{36}}$ | = | $- \left(y_{5} + z_{5}\right) \, \mathbf{a}_{1}- z_{5} \, \mathbf{a}_{2}- y_{5} \, \mathbf{a}_{3}$ | = | $- a y_{5} \,\mathbf{\hat{y}}- a z_{5} \,\mathbf{\hat{z}}$ | (24g) | Cd V |
| $\mathbf{B_{37}}$ | = | $y_{5} \, \mathbf{a}_{1}+\left(y_{5} + z_{5}\right) \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $a z_{5} \,\mathbf{\hat{x}}+a y_{5} \,\mathbf{\hat{z}}$ | (24g) | Cd V |
| $\mathbf{B_{38}}$ | = | $- y_{5} \, \mathbf{a}_{1}- \left(y_{5} - z_{5}\right) \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $a z_{5} \,\mathbf{\hat{x}}- a y_{5} \,\mathbf{\hat{z}}$ | (24g) | Cd V |
| $\mathbf{B_{39}}$ | = | $y_{5} \, \mathbf{a}_{1}+\left(y_{5} - z_{5}\right) \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}$ | = | $- a z_{5} \,\mathbf{\hat{x}}+a y_{5} \,\mathbf{\hat{z}}$ | (24g) | Cd V |
| $\mathbf{B_{40}}$ | = | $- y_{5} \, \mathbf{a}_{1}- \left(y_{5} + z_{5}\right) \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}$ | = | $- a z_{5} \,\mathbf{\hat{x}}- a y_{5} \,\mathbf{\hat{z}}$ | (24g) | Cd V |
| $\mathbf{B_{41}}$ | = | $z_{5} \, \mathbf{a}_{1}+y_{5} \, \mathbf{a}_{2}+\left(y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $a y_{5} \,\mathbf{\hat{x}}+a z_{5} \,\mathbf{\hat{y}}$ | (24g) | Cd V |
| $\mathbf{B_{42}}$ | = | $z_{5} \, \mathbf{a}_{1}- y_{5} \, \mathbf{a}_{2}- \left(y_{5} - z_{5}\right) \, \mathbf{a}_{3}$ | = | $- a y_{5} \,\mathbf{\hat{x}}+a z_{5} \,\mathbf{\hat{y}}$ | (24g) | Cd V |
| $\mathbf{B_{43}}$ | = | $- z_{5} \, \mathbf{a}_{1}+y_{5} \, \mathbf{a}_{2}+\left(y_{5} - z_{5}\right) \, \mathbf{a}_{3}$ | = | $a y_{5} \,\mathbf{\hat{x}}- a z_{5} \,\mathbf{\hat{y}}$ | (24g) | Cd V |
| $\mathbf{B_{44}}$ | = | $- z_{5} \, \mathbf{a}_{1}- y_{5} \, \mathbf{a}_{2}- \left(y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $- a y_{5} \,\mathbf{\hat{x}}- a z_{5} \,\mathbf{\hat{y}}$ | (24g) | Cd V |
| $\mathbf{B_{45}}$ | = | $\left(y_{6} + z_{6}\right) \, \mathbf{a}_{1}+z_{6} \, \mathbf{a}_{2}+y_{6} \, \mathbf{a}_{3}$ | = | $a y_{6} \,\mathbf{\hat{y}}+a z_{6} \,\mathbf{\hat{z}}$ | (24g) | Cd VI |
| $\mathbf{B_{46}}$ | = | $- \left(y_{6} - z_{6}\right) \, \mathbf{a}_{1}+z_{6} \, \mathbf{a}_{2}- y_{6} \, \mathbf{a}_{3}$ | = | $- a y_{6} \,\mathbf{\hat{y}}+a z_{6} \,\mathbf{\hat{z}}$ | (24g) | Cd VI |
| $\mathbf{B_{47}}$ | = | $\left(y_{6} - z_{6}\right) \, \mathbf{a}_{1}- z_{6} \, \mathbf{a}_{2}+y_{6} \, \mathbf{a}_{3}$ | = | $a y_{6} \,\mathbf{\hat{y}}- a z_{6} \,\mathbf{\hat{z}}$ | (24g) | Cd VI |
| $\mathbf{B_{48}}$ | = | $- \left(y_{6} + z_{6}\right) \, \mathbf{a}_{1}- z_{6} \, \mathbf{a}_{2}- y_{6} \, \mathbf{a}_{3}$ | = | $- a y_{6} \,\mathbf{\hat{y}}- a z_{6} \,\mathbf{\hat{z}}$ | (24g) | Cd VI |
| $\mathbf{B_{49}}$ | = | $y_{6} \, \mathbf{a}_{1}+\left(y_{6} + z_{6}\right) \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $a z_{6} \,\mathbf{\hat{x}}+a y_{6} \,\mathbf{\hat{z}}$ | (24g) | Cd VI |
| $\mathbf{B_{50}}$ | = | $- y_{6} \, \mathbf{a}_{1}- \left(y_{6} - z_{6}\right) \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $a z_{6} \,\mathbf{\hat{x}}- a y_{6} \,\mathbf{\hat{z}}$ | (24g) | Cd VI |
| $\mathbf{B_{51}}$ | = | $y_{6} \, \mathbf{a}_{1}+\left(y_{6} - z_{6}\right) \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $- a z_{6} \,\mathbf{\hat{x}}+a y_{6} \,\mathbf{\hat{z}}$ | (24g) | Cd VI |
| $\mathbf{B_{52}}$ | = | $- y_{6} \, \mathbf{a}_{1}- \left(y_{6} + z_{6}\right) \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $- a z_{6} \,\mathbf{\hat{x}}- a y_{6} \,\mathbf{\hat{z}}$ | (24g) | Cd VI |
| $\mathbf{B_{53}}$ | = | $z_{6} \, \mathbf{a}_{1}+y_{6} \, \mathbf{a}_{2}+\left(y_{6} + z_{6}\right) \, \mathbf{a}_{3}$ | = | $a y_{6} \,\mathbf{\hat{x}}+a z_{6} \,\mathbf{\hat{y}}$ | (24g) | Cd VI |
| $\mathbf{B_{54}}$ | = | $z_{6} \, \mathbf{a}_{1}- y_{6} \, \mathbf{a}_{2}- \left(y_{6} - z_{6}\right) \, \mathbf{a}_{3}$ | = | $- a y_{6} \,\mathbf{\hat{x}}+a z_{6} \,\mathbf{\hat{y}}$ | (24g) | Cd VI |
| $\mathbf{B_{55}}$ | = | $- z_{6} \, \mathbf{a}_{1}+y_{6} \, \mathbf{a}_{2}+\left(y_{6} - z_{6}\right) \, \mathbf{a}_{3}$ | = | $a y_{6} \,\mathbf{\hat{x}}- a z_{6} \,\mathbf{\hat{y}}$ | (24g) | Cd VI |
| $\mathbf{B_{56}}$ | = | $- z_{6} \, \mathbf{a}_{1}- y_{6} \, \mathbf{a}_{2}- \left(y_{6} + z_{6}\right) \, \mathbf{a}_{3}$ | = | $- a y_{6} \,\mathbf{\hat{x}}- a z_{6} \,\mathbf{\hat{y}}$ | (24g) | Cd VI |
| $\mathbf{B_{57}}$ | = | $\left(y_{7} + z_{7}\right) \, \mathbf{a}_{1}+z_{7} \, \mathbf{a}_{2}+y_{7} \, \mathbf{a}_{3}$ | = | $a y_{7} \,\mathbf{\hat{y}}+a z_{7} \,\mathbf{\hat{z}}$ | (24g) | Y I |
| $\mathbf{B_{58}}$ | = | $- \left(y_{7} - z_{7}\right) \, \mathbf{a}_{1}+z_{7} \, \mathbf{a}_{2}- y_{7} \, \mathbf{a}_{3}$ | = | $- a y_{7} \,\mathbf{\hat{y}}+a z_{7} \,\mathbf{\hat{z}}$ | (24g) | Y I |
| $\mathbf{B_{59}}$ | = | $\left(y_{7} - z_{7}\right) \, \mathbf{a}_{1}- z_{7} \, \mathbf{a}_{2}+y_{7} \, \mathbf{a}_{3}$ | = | $a y_{7} \,\mathbf{\hat{y}}- a z_{7} \,\mathbf{\hat{z}}$ | (24g) | Y I |
| $\mathbf{B_{60}}$ | = | $- \left(y_{7} + z_{7}\right) \, \mathbf{a}_{1}- z_{7} \, \mathbf{a}_{2}- y_{7} \, \mathbf{a}_{3}$ | = | $- a y_{7} \,\mathbf{\hat{y}}- a z_{7} \,\mathbf{\hat{z}}$ | (24g) | Y I |
| $\mathbf{B_{61}}$ | = | $y_{7} \, \mathbf{a}_{1}+\left(y_{7} + z_{7}\right) \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $a z_{7} \,\mathbf{\hat{x}}+a y_{7} \,\mathbf{\hat{z}}$ | (24g) | Y I |
| $\mathbf{B_{62}}$ | = | $- y_{7} \, \mathbf{a}_{1}- \left(y_{7} - z_{7}\right) \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $a z_{7} \,\mathbf{\hat{x}}- a y_{7} \,\mathbf{\hat{z}}$ | (24g) | Y I |
| $\mathbf{B_{63}}$ | = | $y_{7} \, \mathbf{a}_{1}+\left(y_{7} - z_{7}\right) \, \mathbf{a}_{2}- z_{7} \, \mathbf{a}_{3}$ | = | $- a z_{7} \,\mathbf{\hat{x}}+a y_{7} \,\mathbf{\hat{z}}$ | (24g) | Y I |
| $\mathbf{B_{64}}$ | = | $- y_{7} \, \mathbf{a}_{1}- \left(y_{7} + z_{7}\right) \, \mathbf{a}_{2}- z_{7} \, \mathbf{a}_{3}$ | = | $- a z_{7} \,\mathbf{\hat{x}}- a y_{7} \,\mathbf{\hat{z}}$ | (24g) | Y I |
| $\mathbf{B_{65}}$ | = | $z_{7} \, \mathbf{a}_{1}+y_{7} \, \mathbf{a}_{2}+\left(y_{7} + z_{7}\right) \, \mathbf{a}_{3}$ | = | $a y_{7} \,\mathbf{\hat{x}}+a z_{7} \,\mathbf{\hat{y}}$ | (24g) | Y I |
| $\mathbf{B_{66}}$ | = | $z_{7} \, \mathbf{a}_{1}- y_{7} \, \mathbf{a}_{2}- \left(y_{7} - z_{7}\right) \, \mathbf{a}_{3}$ | = | $- a y_{7} \,\mathbf{\hat{x}}+a z_{7} \,\mathbf{\hat{y}}$ | (24g) | Y I |
| $\mathbf{B_{67}}$ | = | $- z_{7} \, \mathbf{a}_{1}+y_{7} \, \mathbf{a}_{2}+\left(y_{7} - z_{7}\right) \, \mathbf{a}_{3}$ | = | $a y_{7} \,\mathbf{\hat{x}}- a z_{7} \,\mathbf{\hat{y}}$ | (24g) | Y I |
| $\mathbf{B_{68}}$ | = | $- z_{7} \, \mathbf{a}_{1}- y_{7} \, \mathbf{a}_{2}- \left(y_{7} + z_{7}\right) \, \mathbf{a}_{3}$ | = | $- a y_{7} \,\mathbf{\hat{x}}- a z_{7} \,\mathbf{\hat{y}}$ | (24g) | Y I |
| $\mathbf{B_{69}}$ | = | $\left(y_{8} + z_{8}\right) \, \mathbf{a}_{1}+\left(x_{8} + z_{8}\right) \, \mathbf{a}_{2}+\left(x_{8} + y_{8}\right) \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}+a y_{8} \,\mathbf{\hat{y}}+a z_{8} \,\mathbf{\hat{z}}$ | (48h) | Cd VII |
| $\mathbf{B_{70}}$ | = | $- \left(y_{8} - z_{8}\right) \, \mathbf{a}_{1}- \left(x_{8} - z_{8}\right) \, \mathbf{a}_{2}- \left(x_{8} + y_{8}\right) \, \mathbf{a}_{3}$ | = | $- a x_{8} \,\mathbf{\hat{x}}- a y_{8} \,\mathbf{\hat{y}}+a z_{8} \,\mathbf{\hat{z}}$ | (48h) | Cd VII |
| $\mathbf{B_{71}}$ | = | $\left(y_{8} - z_{8}\right) \, \mathbf{a}_{1}- \left(x_{8} + z_{8}\right) \, \mathbf{a}_{2}- \left(x_{8} - y_{8}\right) \, \mathbf{a}_{3}$ | = | $- a x_{8} \,\mathbf{\hat{x}}+a y_{8} \,\mathbf{\hat{y}}- a z_{8} \,\mathbf{\hat{z}}$ | (48h) | Cd VII |
| $\mathbf{B_{72}}$ | = | $- \left(y_{8} + z_{8}\right) \, \mathbf{a}_{1}+\left(x_{8} - z_{8}\right) \, \mathbf{a}_{2}+\left(x_{8} - y_{8}\right) \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}- a y_{8} \,\mathbf{\hat{y}}- a z_{8} \,\mathbf{\hat{z}}$ | (48h) | Cd VII |
| $\mathbf{B_{73}}$ | = | $\left(x_{8} + y_{8}\right) \, \mathbf{a}_{1}+\left(y_{8} + z_{8}\right) \, \mathbf{a}_{2}+\left(x_{8} + z_{8}\right) \, \mathbf{a}_{3}$ | = | $a z_{8} \,\mathbf{\hat{x}}+a x_{8} \,\mathbf{\hat{y}}+a y_{8} \,\mathbf{\hat{z}}$ | (48h) | Cd VII |
| $\mathbf{B_{74}}$ | = | $- \left(x_{8} + y_{8}\right) \, \mathbf{a}_{1}- \left(y_{8} - z_{8}\right) \, \mathbf{a}_{2}- \left(x_{8} - z_{8}\right) \, \mathbf{a}_{3}$ | = | $a z_{8} \,\mathbf{\hat{x}}- a x_{8} \,\mathbf{\hat{y}}- a y_{8} \,\mathbf{\hat{z}}$ | (48h) | Cd VII |
| $\mathbf{B_{75}}$ | = | $- \left(x_{8} - y_{8}\right) \, \mathbf{a}_{1}+\left(y_{8} - z_{8}\right) \, \mathbf{a}_{2}- \left(x_{8} + z_{8}\right) \, \mathbf{a}_{3}$ | = | $- a z_{8} \,\mathbf{\hat{x}}- a x_{8} \,\mathbf{\hat{y}}+a y_{8} \,\mathbf{\hat{z}}$ | (48h) | Cd VII |
| $\mathbf{B_{76}}$ | = | $\left(x_{8} - y_{8}\right) \, \mathbf{a}_{1}- \left(y_{8} + z_{8}\right) \, \mathbf{a}_{2}+\left(x_{8} - z_{8}\right) \, \mathbf{a}_{3}$ | = | $- a z_{8} \,\mathbf{\hat{x}}+a x_{8} \,\mathbf{\hat{y}}- a y_{8} \,\mathbf{\hat{z}}$ | (48h) | Cd VII |
| $\mathbf{B_{77}}$ | = | $\left(x_{8} + z_{8}\right) \, \mathbf{a}_{1}+\left(x_{8} + y_{8}\right) \, \mathbf{a}_{2}+\left(y_{8} + z_{8}\right) \, \mathbf{a}_{3}$ | = | $a y_{8} \,\mathbf{\hat{x}}+a z_{8} \,\mathbf{\hat{y}}+a x_{8} \,\mathbf{\hat{z}}$ | (48h) | Cd VII |
| $\mathbf{B_{78}}$ | = | $- \left(x_{8} - z_{8}\right) \, \mathbf{a}_{1}- \left(x_{8} + y_{8}\right) \, \mathbf{a}_{2}- \left(y_{8} - z_{8}\right) \, \mathbf{a}_{3}$ | = | $- a y_{8} \,\mathbf{\hat{x}}+a z_{8} \,\mathbf{\hat{y}}- a x_{8} \,\mathbf{\hat{z}}$ | (48h) | Cd VII |
| $\mathbf{B_{79}}$ | = | $- \left(x_{8} + z_{8}\right) \, \mathbf{a}_{1}- \left(x_{8} - y_{8}\right) \, \mathbf{a}_{2}+\left(y_{8} - z_{8}\right) \, \mathbf{a}_{3}$ | = | $a y_{8} \,\mathbf{\hat{x}}- a z_{8} \,\mathbf{\hat{y}}- a x_{8} \,\mathbf{\hat{z}}$ | (48h) | Cd VII |
| $\mathbf{B_{80}}$ | = | $\left(x_{8} - z_{8}\right) \, \mathbf{a}_{1}+\left(x_{8} - y_{8}\right) \, \mathbf{a}_{2}- \left(y_{8} + z_{8}\right) \, \mathbf{a}_{3}$ | = | $- a y_{8} \,\mathbf{\hat{x}}- a z_{8} \,\mathbf{\hat{y}}+a x_{8} \,\mathbf{\hat{z}}$ | (48h) | Cd VII |
| $\mathbf{B_{81}}$ | = | $- \left(y_{8} + z_{8}\right) \, \mathbf{a}_{1}- \left(x_{8} + z_{8}\right) \, \mathbf{a}_{2}- \left(x_{8} + y_{8}\right) \, \mathbf{a}_{3}$ | = | $- a x_{8} \,\mathbf{\hat{x}}- a y_{8} \,\mathbf{\hat{y}}- a z_{8} \,\mathbf{\hat{z}}$ | (48h) | Cd VII |
| $\mathbf{B_{82}}$ | = | $\left(y_{8} - z_{8}\right) \, \mathbf{a}_{1}+\left(x_{8} - z_{8}\right) \, \mathbf{a}_{2}+\left(x_{8} + y_{8}\right) \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}+a y_{8} \,\mathbf{\hat{y}}- a z_{8} \,\mathbf{\hat{z}}$ | (48h) | Cd VII |
| $\mathbf{B_{83}}$ | = | $- \left(y_{8} - z_{8}\right) \, \mathbf{a}_{1}+\left(x_{8} + z_{8}\right) \, \mathbf{a}_{2}+\left(x_{8} - y_{8}\right) \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}- a y_{8} \,\mathbf{\hat{y}}+a z_{8} \,\mathbf{\hat{z}}$ | (48h) | Cd VII |
| $\mathbf{B_{84}}$ | = | $\left(y_{8} + z_{8}\right) \, \mathbf{a}_{1}- \left(x_{8} - z_{8}\right) \, \mathbf{a}_{2}- \left(x_{8} - y_{8}\right) \, \mathbf{a}_{3}$ | = | $- a x_{8} \,\mathbf{\hat{x}}+a y_{8} \,\mathbf{\hat{y}}+a z_{8} \,\mathbf{\hat{z}}$ | (48h) | Cd VII |
| $\mathbf{B_{85}}$ | = | $- \left(x_{8} + y_{8}\right) \, \mathbf{a}_{1}- \left(y_{8} + z_{8}\right) \, \mathbf{a}_{2}- \left(x_{8} + z_{8}\right) \, \mathbf{a}_{3}$ | = | $- a z_{8} \,\mathbf{\hat{x}}- a x_{8} \,\mathbf{\hat{y}}- a y_{8} \,\mathbf{\hat{z}}$ | (48h) | Cd VII |
| $\mathbf{B_{86}}$ | = | $\left(x_{8} + y_{8}\right) \, \mathbf{a}_{1}+\left(y_{8} - z_{8}\right) \, \mathbf{a}_{2}+\left(x_{8} - z_{8}\right) \, \mathbf{a}_{3}$ | = | $- a z_{8} \,\mathbf{\hat{x}}+a x_{8} \,\mathbf{\hat{y}}+a y_{8} \,\mathbf{\hat{z}}$ | (48h) | Cd VII |
| $\mathbf{B_{87}}$ | = | $\left(x_{8} - y_{8}\right) \, \mathbf{a}_{1}- \left(y_{8} - z_{8}\right) \, \mathbf{a}_{2}+\left(x_{8} + z_{8}\right) \, \mathbf{a}_{3}$ | = | $a z_{8} \,\mathbf{\hat{x}}+a x_{8} \,\mathbf{\hat{y}}- a y_{8} \,\mathbf{\hat{z}}$ | (48h) | Cd VII |
| $\mathbf{B_{88}}$ | = | $- \left(x_{8} - y_{8}\right) \, \mathbf{a}_{1}+\left(y_{8} + z_{8}\right) \, \mathbf{a}_{2}- \left(x_{8} - z_{8}\right) \, \mathbf{a}_{3}$ | = | $a z_{8} \,\mathbf{\hat{x}}- a x_{8} \,\mathbf{\hat{y}}+a y_{8} \,\mathbf{\hat{z}}$ | (48h) | Cd VII |
| $\mathbf{B_{89}}$ | = | $- \left(x_{8} + z_{8}\right) \, \mathbf{a}_{1}- \left(x_{8} + y_{8}\right) \, \mathbf{a}_{2}- \left(y_{8} + z_{8}\right) \, \mathbf{a}_{3}$ | = | $- a y_{8} \,\mathbf{\hat{x}}- a z_{8} \,\mathbf{\hat{y}}- a x_{8} \,\mathbf{\hat{z}}$ | (48h) | Cd VII |
| $\mathbf{B_{90}}$ | = | $\left(x_{8} - z_{8}\right) \, \mathbf{a}_{1}+\left(x_{8} + y_{8}\right) \, \mathbf{a}_{2}+\left(y_{8} - z_{8}\right) \, \mathbf{a}_{3}$ | = | $a y_{8} \,\mathbf{\hat{x}}- a z_{8} \,\mathbf{\hat{y}}+a x_{8} \,\mathbf{\hat{z}}$ | (48h) | Cd VII |
| $\mathbf{B_{91}}$ | = | $\left(x_{8} + z_{8}\right) \, \mathbf{a}_{1}+\left(x_{8} - y_{8}\right) \, \mathbf{a}_{2}- \left(y_{8} - z_{8}\right) \, \mathbf{a}_{3}$ | = | $- a y_{8} \,\mathbf{\hat{x}}+a z_{8} \,\mathbf{\hat{y}}+a x_{8} \,\mathbf{\hat{z}}$ | (48h) | Cd VII |
| $\mathbf{B_{92}}$ | = | $- \left(x_{8} - z_{8}\right) \, \mathbf{a}_{1}- \left(x_{8} - y_{8}\right) \, \mathbf{a}_{2}+\left(y_{8} + z_{8}\right) \, \mathbf{a}_{3}$ | = | $a y_{8} \,\mathbf{\hat{x}}+a z_{8} \,\mathbf{\hat{y}}- a x_{8} \,\mathbf{\hat{z}}$ | (48h) | Cd VII |
References
- A. C. Larson and D. T. Cromer, The Crystal Structure of YCd$_{6}$, Acta Crystallogr. Sect. B 27, 1875–1879 (1971), doi:10.1107/S0567740871005028.
- M. Armbrüster and S. Lidin, Reassessing the compound CeCd$_{6}$: the structure of Ce$_{6}$Cd$_{37}$, J. Alloys Compd. 307, 141–148 (2000), doi:10.1016/S0925-8388(00)00881-1.
Found in
- P. Villars, H. Okamoto, and K. Cenzual, eds., ASM Alloy Phase Diagram Database (ASM International, 2018), chap. Alloy Phase Diagram Database Cadmium-Yttrium Binary Phase Diagram (1990 Gschneidner K.A. Jr.). Copyright © 2006-2018 ASM International.
Prototype Generator
aflow --proto=A20B3_cI184_204_def3gh_g --params=$a,x_{1},x_{2},x_{3},y_{4},z_{4},y_{5},z_{5},y_{6},z_{6},y_{7},z_{7},x_{8},y_{8},z_{8}$