AFLOW Prototype: 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 | : | $\text{Pm}\bar{3}\text{m}$ |
AFLOW prototype command | : | aflow --proto=A6B_cP7_221_f_a --params=$a$,$x_{2}$ |
Basis vectors:
\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1} & = &0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & = &0 \mathbf{\hat{x}} + 0 \mathbf{\hat{y}} + 0 \mathbf{\hat{z}} & \left(1a\right) & \text{Ca} \\ \mathbf{B}_{2} & = &x_{2} \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &x_{2} \, a \, \mathbf{\hat{x}}+ \frac12 \, a \, \mathbf{\hat{y}}+ \frac12 \, a \, \mathbf{\hat{z}}& \left(6f\right) & \text{B} \\ \mathbf{B}_{3} & = &- x_{2} \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &- x_{2} \, a \, \mathbf{\hat{x}}+ \frac12 \, a \, \mathbf{\hat{y}}+ \frac12 \, a \, \mathbf{\hat{z}}& \left(6f\right) & \text{B} \\ \mathbf{B}_{4} & = &\frac12 \, \mathbf{a}_{1}+ x_{2} \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ x_{2} \, a \, \mathbf{\hat{y}}+ \frac12 \, a \, \mathbf{\hat{z}}& \left(6f\right) & \text{B} \\ \mathbf{B}_{5} & = &\frac12 \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}- x_{2} \, a \, \mathbf{\hat{y}}+ \frac12 \, a \, \mathbf{\hat{z}}& \left(6f\right) & \text{B} \\ \mathbf{B}_{6} & = &\frac12 \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}+ x_{2} \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \frac12 \, a \, \mathbf{\hat{y}}+ x_{2} \, a \, \mathbf{\hat{z}}& \left(6f\right) & \text{B} \\ \mathbf{B}_{7} & = &\frac12 \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \frac12 \, a \, \mathbf{\hat{y}}- x_{2} \, a \, \mathbf{\hat{z}}& \left(6f\right) & \text{B} \\ \end{array} \]