UB$_{12}$ ($D2_{f}$) Structure: A12B_cF52_225_h_b-001
| Prototype | B$_{12}$U |
| AFLOW prototype label | A12B_cF52_225_h_b-001 |
| Strukturbericht designation | $D2_{f}$ |
| ICSD | 24705 |
| Pearson symbol | cF52 |
| Space group number | 225 |
| Space group symbol | $Fm\overline{3}m$ |
| AFLOW prototype command |
aflow --proto=A12B_cF52_225_h_b-001
--params=$a, \allowbreak y_{2}$ |
Other compounds with this structure
DyB$_{12}$, ErB$_{12}$, LuB$_{12}$, ThB$_{12}$, TmB$_{12}$, YB$_{12}$, YbB$_{12}$, ZrB$_{12}$, (Th$_{0.93}$Zr$_{0.07}$)B$_{12}$
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (4b) | U I |
| $\mathbf{B_{2}}$ | = | $2 y_{2} \, \mathbf{a}_{1}$ | = | $a y_{2} \,\mathbf{\hat{y}}+a y_{2} \,\mathbf{\hat{z}}$ | (48h) | B I |
| $\mathbf{B_{3}}$ | = | $2 y_{2} \, \mathbf{a}_{2}- 2 y_{2} \, \mathbf{a}_{3}$ | = | $- a y_{2} \,\mathbf{\hat{y}}+a y_{2} \,\mathbf{\hat{z}}$ | (48h) | B I |
| $\mathbf{B_{4}}$ | = | $- 2 y_{2} \, \mathbf{a}_{2}+2 y_{2} \, \mathbf{a}_{3}$ | = | $a y_{2} \,\mathbf{\hat{y}}- a y_{2} \,\mathbf{\hat{z}}$ | (48h) | B I |
| $\mathbf{B_{5}}$ | = | $- 2 y_{2} \, \mathbf{a}_{1}$ | = | $- a y_{2} \,\mathbf{\hat{y}}- a y_{2} \,\mathbf{\hat{z}}$ | (48h) | B I |
| $\mathbf{B_{6}}$ | = | $2 y_{2} \, \mathbf{a}_{2}$ | = | $a y_{2} \,\mathbf{\hat{x}}+a y_{2} \,\mathbf{\hat{z}}$ | (48h) | B I |
| $\mathbf{B_{7}}$ | = | $- 2 y_{2} \, \mathbf{a}_{1}+2 y_{2} \, \mathbf{a}_{3}$ | = | $a y_{2} \,\mathbf{\hat{x}}- a y_{2} \,\mathbf{\hat{z}}$ | (48h) | B I |
| $\mathbf{B_{8}}$ | = | $2 y_{2} \, \mathbf{a}_{1}- 2 y_{2} \, \mathbf{a}_{3}$ | = | $- a y_{2} \,\mathbf{\hat{x}}+a y_{2} \,\mathbf{\hat{z}}$ | (48h) | B I |
| $\mathbf{B_{9}}$ | = | $- 2 y_{2} \, \mathbf{a}_{2}$ | = | $- a y_{2} \,\mathbf{\hat{x}}- a y_{2} \,\mathbf{\hat{z}}$ | (48h) | B I |
| $\mathbf{B_{10}}$ | = | $2 y_{2} \, \mathbf{a}_{3}$ | = | $a y_{2} \,\mathbf{\hat{x}}+a y_{2} \,\mathbf{\hat{y}}$ | (48h) | B I |
| $\mathbf{B_{11}}$ | = | $2 y_{2} \, \mathbf{a}_{1}- 2 y_{2} \, \mathbf{a}_{2}$ | = | $- a y_{2} \,\mathbf{\hat{x}}+a y_{2} \,\mathbf{\hat{y}}$ | (48h) | B I |
| $\mathbf{B_{12}}$ | = | $- 2 y_{2} \, \mathbf{a}_{1}+2 y_{2} \, \mathbf{a}_{2}$ | = | $a y_{2} \,\mathbf{\hat{x}}- a y_{2} \,\mathbf{\hat{y}}$ | (48h) | B I |
| $\mathbf{B_{13}}$ | = | $- 2 y_{2} \, \mathbf{a}_{3}$ | = | $- a y_{2} \,\mathbf{\hat{x}}- a y_{2} \,\mathbf{\hat{y}}$ | (48h) | B I |
References
- P. Blum and F. Bertaut, Contribution à l'Étude des Borures à Teneur Élevée en Bore, Acta Cryst. 7, 81–86 (1954), doi:10.1107/S0365110X54000151.
Found in
- W. B. Pearson, The Crystal Chemistry and Physics of Metals and Alloys (Wiley Interscience, New York, London, Sydney, Tornoto, 1972).
Prototype Generator
aflow --proto=A12B_cF52_225_h_b --params=$a,y_{2}$