AFLOW Prototype: A6B_hR7_166_g_a
Prototype | : | CaC6 |
AFLOW prototype label | : | A6B_hR7_166_g_a |
Strukturbericht designation | : | None |
Pearson symbol | : | hR7 |
Space group number | : | 166 |
Space group symbol | : | $\text{R}\bar{3}\text{m}$ |
AFLOW prototype command | : | aflow --proto=A6B_hR7_166_g_a [--hex] --params=$a$,$c/a$,$x_{2}$ |
Basis vectors:
\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1} & =&0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & =&0 \mathbf{\hat{x}} + 0 \mathbf{\hat{y}} + 0 \mathbf{\hat{z}} & \left(1a\right) & \text{Ca} \\ \mathbf{B}_{2} & =&x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& =&\left(\frac12 x_{2} + \frac34\right) \, a \, \mathbf{\hat{x}}- \frac1{4\sqrt3} \left(1 + 6 x_{2}\right) \, a \, \mathbf{\hat{y}}+ \frac16 \, c \, \mathbf{\hat{z}}& \left(6g\right) & \text{C} \\ \mathbf{B}_{3} & =&\frac12 \, \mathbf{a}_{1}+ x_{2} \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}& =&\left(\frac12 x_{2} + \frac14\right) \, a \, \mathbf{\hat{x}}- \frac1{4\sqrt3} \left(1 - 6 x_{2}\right) \, a \, \mathbf{\hat{y}}+ \frac16 \, c \, \mathbf{\hat{z}}& \left(6g\right) & \text{C} \\ \mathbf{B}_{4} & =&- x_{2} \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}+ x_{2} \, \mathbf{a}_{3}& =&- x_{2} \, a \, \mathbf{\hat{x}}+ \frac1{2\sqrt3} \, a \, \mathbf{\hat{y}}+ \frac16 \, c \, \mathbf{\hat{z}}& \left(6g\right) & \text{C} \\ \mathbf{B}_{5} & =&- x_{2} \, \mathbf{a}_{1}+ x_{2} \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& =&\left(\frac34 - \frac12 x_{2}\right) \, a \, \mathbf{\hat{x}}- \frac1{4\sqrt3} \left(1 - 6 x_{2}\right) \, a \, \mathbf{\hat{y}}+ \frac16 \, c \, \mathbf{\hat{z}}& \left(6g\right) & \text{C} \\ \mathbf{B}_{6} & =&\frac12 \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}+ x_{2} \, \mathbf{a}_{3}& =&\left(\frac14 - \frac12 x_{2}\right) \, a \, \mathbf{\hat{x}}- \frac1{4\sqrt3} \left(1 + 6 x_{2}\right) \, a \, \mathbf{\hat{y}}+ \frac16 \, c \, \mathbf{\hat{z}}& \left(6g\right) & \text{C} \\ \mathbf{B}_{7} & =&x_{2} \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}& =&x_{2} \, a \, \mathbf{\hat{x}}+ \frac1{2\sqrt3} \, a \, \mathbf{\hat{y}}+ \frac16 \, c \, \mathbf{\hat{z}}& \left(6g\right) & \text{C} \\ \end{array} \]