CaB$_{6}$ ($D2_{1}$) Structure: A6B_cP7_221_e_b-001
| Prototype | B$_{6}$Ca |
| AFLOW prototype label | A6B_cP7_221_e_b-001 |
| Strukturbericht designation | $D2_{1}$ |
| ICSD | 26753 |
| Pearson symbol | cP7 |
| Space group number | 221 |
| Space group symbol | $Pm\overline{3}m$ |
| AFLOW prototype command |
aflow --proto=A6B_cP7_221_e_b-001
--params=$a, \allowbreak x_{2}$ |
Other compounds with this structure
BaB$_{6}$, CeB$_{6}$, DyB$_{6}$, ErB$_{6}$, EuB$_{6}$, GdB$_{6}$, HoB$_{6}$, LaB$_{6}$, LuB$_{6}$, NaB$_{6}$, NdB$_{6}$, PrB$_{6}$, PuB$_{6}$, ScB$_{6}$, SiB$_{6}$, SmB$_{6}$, SrB$_{6}$, TbB$_{6}$, ThB$_{6}$, TmB$_{6}$, YB$_{6}$, YbB$_{6}$, (Ca, Sm)B$_{6}$, (Ce, La)B$_{6}$
- The internal parameter is chosen to match the intraoctalhedral boron-boron distance of 1.755\AA{} found in (Yahia, 1990). The ICSD entry is from (Pauling, 1934).
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&a \,\mathbf{\hat{z}}
\end{array}\]
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) | Ca I |
| $\mathbf{B_{2}}$ | = | $x_{2} \, \mathbf{a}_{1}$ | = | $a x_{2} \,\mathbf{\hat{x}}$ | (6e) | B I |
| $\mathbf{B_{3}}$ | = | $- x_{2} \, \mathbf{a}_{1}$ | = | $- a x_{2} \,\mathbf{\hat{x}}$ | (6e) | B I |
| $\mathbf{B_{4}}$ | = | $x_{2} \, \mathbf{a}_{2}$ | = | $a x_{2} \,\mathbf{\hat{y}}$ | (6e) | B I |
| $\mathbf{B_{5}}$ | = | $- x_{2} \, \mathbf{a}_{2}$ | = | $- a x_{2} \,\mathbf{\hat{y}}$ | (6e) | B I |
| $\mathbf{B_{6}}$ | = | $x_{2} \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{z}}$ | (6e) | B I |
| $\mathbf{B_{7}}$ | = | $- x_{2} \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{z}}$ | (6e) | B I |
References
- Z. Yahia, S. Turrell, G. Turrell, and J. P. Mercurio, Infrared and Raman spectra of hexaborides: force-field calculations, and isotopic effects, J. Mol. Struct. 224, 303–312 (1990), doi:10.1016/0022-2860(90)87025-S.
- L. Pauling and S. Weinbaum, The Structure of Calcium Boride, CaB$_{6}$, Z. Krystallogr. 87, 181–182 (1934), doi:10.1524/zkri.1934.87.1.181.
Prototype Generator
aflow --proto=A6B_cP7_221_e_b --params=$a,x_{2}$