Mg$_{2}$Zn$_{11}$ ($D8_{c}$) Structure: A2B11_cP39_200_f_begik-001
| Prototype | Mg$_{2}$Zn$_{11}$ |
| AFLOW prototype label | A2B11_cP39_200_f_begik-001 |
| Strukturbericht designation | $D8_{c}$ |
| ICSD | 104898 |
| Pearson symbol | cP39 |
| Space group number | 200 |
| Space group symbol | $Pm\overline{3}$ |
| AFLOW prototype command |
aflow --proto=A2B11_cP39_200_f_begik-001
--params=$a, \allowbreak x_{2}, \allowbreak x_{3}, \allowbreak x_{4}, \allowbreak x_{5}, \allowbreak y_{6}, \allowbreak z_{6}$ |
Other compounds with this structure
Na$_{2}$Cd$_{11}$, Mg$_{2}$Cu$_{6}$Al$_{5}$, Mg$_{2}$Cu$_{6}$Ga$_{5}$, Na$_{2}$Au$_{6}$In$_{5}$, Sc$_{2}$Co$_{7}$Ga$_{4}$, K$_{6}$Na$_{14}$CdTl$_{18}$, K$_{6}$Na$_{14}$HgTl$_{18}$, K$_{6}$Na$_{14}$MgTl$_{18}$, K$_{6}$Na$_{14}$ZnTl$_{18}$
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&a \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (1b) | Zn I |
| $\mathbf{B_{2}}$ | = | $x_{2} \, \mathbf{a}_{1}$ | = | $a x_{2} \,\mathbf{\hat{x}}$ | (6e) | Zn II |
| $\mathbf{B_{3}}$ | = | $- x_{2} \, \mathbf{a}_{1}$ | = | $- a x_{2} \,\mathbf{\hat{x}}$ | (6e) | Zn II |
| $\mathbf{B_{4}}$ | = | $x_{2} \, \mathbf{a}_{2}$ | = | $a x_{2} \,\mathbf{\hat{y}}$ | (6e) | Zn II |
| $\mathbf{B_{5}}$ | = | $- x_{2} \, \mathbf{a}_{2}$ | = | $- a x_{2} \,\mathbf{\hat{y}}$ | (6e) | Zn II |
| $\mathbf{B_{6}}$ | = | $x_{2} \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{z}}$ | (6e) | Zn II |
| $\mathbf{B_{7}}$ | = | $- x_{2} \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{z}}$ | (6e) | Zn II |
| $\mathbf{B_{8}}$ | = | $x_{3} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (6f) | Mg I |
| $\mathbf{B_{9}}$ | = | $- x_{3} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (6f) | Mg I |
| $\mathbf{B_{10}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}$ | (6f) | Mg I |
| $\mathbf{B_{11}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}$ | (6f) | Mg I |
| $\mathbf{B_{12}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (6f) | Mg I |
| $\mathbf{B_{13}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (6f) | Mg I |
| $\mathbf{B_{14}}$ | = | $x_{4} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $a x_{4} \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}$ | (6g) | Zn III |
| $\mathbf{B_{15}}$ | = | $- x_{4} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}$ | (6g) | Zn III |
| $\mathbf{B_{16}}$ | = | $x_{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (6g) | Zn III |
| $\mathbf{B_{17}}$ | = | $- x_{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (6g) | Zn III |
| $\mathbf{B_{18}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{z}}$ | (6g) | Zn III |
| $\mathbf{B_{19}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{z}}$ | (6g) | Zn III |
| $\mathbf{B_{20}}$ | = | $x_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (8i) | Zn IV |
| $\mathbf{B_{21}}$ | = | $- x_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (8i) | Zn IV |
| $\mathbf{B_{22}}$ | = | $- x_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}- x_{5} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (8i) | Zn IV |
| $\mathbf{B_{23}}$ | = | $x_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}- x_{5} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (8i) | Zn IV |
| $\mathbf{B_{24}}$ | = | $- x_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}- x_{5} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (8i) | Zn IV |
| $\mathbf{B_{25}}$ | = | $x_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}- x_{5} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (8i) | Zn IV |
| $\mathbf{B_{26}}$ | = | $x_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (8i) | Zn IV |
| $\mathbf{B_{27}}$ | = | $- x_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (8i) | Zn IV |
| $\mathbf{B_{28}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+y_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+a y_{6} \,\mathbf{\hat{y}}+a z_{6} \,\mathbf{\hat{z}}$ | (12k) | Zn V |
| $\mathbf{B_{29}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- y_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- a y_{6} \,\mathbf{\hat{y}}+a z_{6} \,\mathbf{\hat{z}}$ | (12k) | Zn V |
| $\mathbf{B_{30}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+y_{6} \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+a y_{6} \,\mathbf{\hat{y}}- a z_{6} \,\mathbf{\hat{z}}$ | (12k) | Zn V |
| $\mathbf{B_{31}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- y_{6} \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- a y_{6} \,\mathbf{\hat{y}}- a z_{6} \,\mathbf{\hat{z}}$ | (12k) | Zn V |
| $\mathbf{B_{32}}$ | = | $z_{6} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+y_{6} \, \mathbf{a}_{3}$ | = | $a z_{6} \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+a y_{6} \,\mathbf{\hat{z}}$ | (12k) | Zn V |
| $\mathbf{B_{33}}$ | = | $z_{6} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}- y_{6} \, \mathbf{a}_{3}$ | = | $a z_{6} \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- a y_{6} \,\mathbf{\hat{z}}$ | (12k) | Zn V |
| $\mathbf{B_{34}}$ | = | $- z_{6} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+y_{6} \, \mathbf{a}_{3}$ | = | $- a z_{6} \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+a y_{6} \,\mathbf{\hat{z}}$ | (12k) | Zn V |
| $\mathbf{B_{35}}$ | = | $- z_{6} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}- y_{6} \, \mathbf{a}_{3}$ | = | $- a z_{6} \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- a y_{6} \,\mathbf{\hat{z}}$ | (12k) | Zn V |
| $\mathbf{B_{36}}$ | = | $y_{6} \, \mathbf{a}_{1}+z_{6} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a y_{6} \,\mathbf{\hat{x}}+a z_{6} \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (12k) | Zn V |
| $\mathbf{B_{37}}$ | = | $- y_{6} \, \mathbf{a}_{1}+z_{6} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a y_{6} \,\mathbf{\hat{x}}+a z_{6} \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (12k) | Zn V |
| $\mathbf{B_{38}}$ | = | $y_{6} \, \mathbf{a}_{1}- z_{6} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a y_{6} \,\mathbf{\hat{x}}- a z_{6} \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (12k) | Zn V |
| $\mathbf{B_{39}}$ | = | $- y_{6} \, \mathbf{a}_{1}- z_{6} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a y_{6} \,\mathbf{\hat{x}}- a z_{6} \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (12k) | Zn V |
References
- S. Samson, Die Kristallstruktur von Mg$_{2}$Zn$_{11}$, Acta Chem. Scand. 3, 835–843 (1949), doi:10.3891/acta.chem.scand.03-0835.
Prototype Generator
aflow --proto=A2B11_cP39_200_f_begik --params=$a,x_{2},x_{3},x_{4},x_{5},y_{6},z_{6}$