CaB6 (D21) Structure: A6B_cP7_221_f_a
| Prototype | : | CaB6 |
| AFLOW prototype label | : | A6B_cP7_221_f_a |
| Strukturbericht designation | : | $D2_{1}$ |
| Pearson symbol | : | cP7 |
| Space group number | : | 221 |
| Space group symbol | : | $\mbox{Pm}\bar{3}\mbox{m}$ |
| AFLOW prototype command | : | aflow --proto=A6B_cP7_221_f_a --params=$a,x_{2}$ |
Simple Cubic primitive vectors:
\[
\begin{array}{ccc}
\mathbf{a}_1 & = & a \, \mathbf{\hat{x}} \\
\mathbf{a}_2 & = & a \, \mathbf{\hat{y}} \\
\mathbf{a}_3 & = & a \, \mathbf{\hat{z}}
\end{array}
\]
Basis vectors:
\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = &0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & = &0 \mathbf{\hat{x}} + 0 \mathbf{\hat{y}} + 0 \mathbf{\hat{z}} & \left(1a\right) & \mbox{Ca} \\ \mathbf{B}_{2} & = &x_{2} \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &x_{2} \, a \, \mathbf{\hat{x}}+ \frac12 \, a \, \mathbf{\hat{y}}+ \frac12 \, a \, \mathbf{\hat{z}}& \left(6f\right) & \mbox{B} \\ \mathbf{B}_{3} & = &- x_{2} \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &- x_{2} \, a \, \mathbf{\hat{x}}+ \frac12 \, a \, \mathbf{\hat{y}}+ \frac12 \, a \, \mathbf{\hat{z}}& \left(6f\right) & \mbox{B} \\ \mathbf{B}_{4} & = &\frac12 \, \mathbf{a}_{1}+ x_{2} \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ x_{2} \, a \, \mathbf{\hat{y}}+ \frac12 \, a \, \mathbf{\hat{z}}& \left(6f\right) & \mbox{B} \\ \mathbf{B}_{5} & = &\frac12 \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}- x_{2} \, a \, \mathbf{\hat{y}}+ \frac12 \, a \, \mathbf{\hat{z}}& \left(6f\right) & \mbox{B} \\ \mathbf{B}_{6} & = &\frac12 \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}+ x_{2} \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \frac12 \, a \, \mathbf{\hat{y}}+ x_{2} \, a \, \mathbf{\hat{z}}& \left(6f\right) & \mbox{B} \\ \mathbf{B}_{7} & = &\frac12 \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \frac12 \, a \, \mathbf{\hat{y}}- x_{2} \, a \, \mathbf{\hat{z}}& \left(6f\right) & \mbox{B} \\ \end{array} \]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.