AFLOW Prototype: A2BCD6_hR10_148_c_a_b_f
Prototype | : | C2CaMgO6 |
AFLOW prototype label | : | A2BCD6_hR10_148_c_a_b_f |
Strukturbericht designation | : | $G1_{1}$ |
Pearson symbol | : | hR10 |
Space group number | : | 148 |
Space group symbol | : | $R\bar{3}$ |
AFLOW prototype command | : | aflow --proto=A2BCD6_hR10_148_c_a_b_f --params=$a$,$c/a$,$x_{3}$,$x_{4}$,$y_{4}$,$z_{4}$ |
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} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}c \, \mathbf{\hat{z}} & \left(1b\right) & \text{Mg} \\ \mathbf{B}_{3} & = & x_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + x_{3} \, \mathbf{a}_{3} & = & x_{3}c \, \mathbf{\hat{z}} & \left(2c\right) & \text{C} \\ \mathbf{B}_{4} & = & -x_{3} \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2}-x_{3} \, \mathbf{a}_{3} & = & -x_{3}c \, \mathbf{\hat{z}} & \left(2c\right) & \text{C} \\ \mathbf{B}_{5} & = & x_{4} \, \mathbf{a}_{1} + y_{4} \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{4}-z_{4}\right)a \, \mathbf{\hat{x}} + \left(-\frac{1}{2\sqrt{3}}x_{4}+\frac{1}{\sqrt{3}}y_{4}-\frac{1}{2\sqrt{3}}z_{4}\right)a \, \mathbf{\hat{y}} + \frac{1}{3}\left(x_{4}+y_{4}+z_{4}\right)c \, \mathbf{\hat{z}} & \left(6f\right) & \text{O} \\ \mathbf{B}_{6} & = & z_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} + y_{4} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(-y_{4}+z_{4}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{\sqrt{3}}x_{4}-\frac{1}{2\sqrt{3}}y_{4}-\frac{1}{2\sqrt{3}}z_{4}\right)a \, \mathbf{\hat{y}} + \frac{1}{3}\left(x_{4}+y_{4}+z_{4}\right)c \, \mathbf{\hat{z}} & \left(6f\right) & \text{O} \\ \mathbf{B}_{7} & = & y_{4} \, \mathbf{a}_{1} + z_{4} \, \mathbf{a}_{2} + x_{4} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(-x_{4}+y_{4}\right)a \, \mathbf{\hat{x}} + \left(-\frac{1}{2\sqrt{3}}x_{4}-\frac{1}{2\sqrt{3}}y_{4}+\frac{1}{\sqrt{3}}z_{4}\right)a \, \mathbf{\hat{y}} + \frac{1}{3}\left(x_{4}+y_{4}+z_{4}\right)c \, \mathbf{\hat{z}} & \left(6f\right) & \text{O} \\ \mathbf{B}_{8} & = & -x_{4} \, \mathbf{a}_{1}-y_{4} \, \mathbf{a}_{2}-z_{4} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(-x_{4}+z_{4}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2\sqrt{3}}x_{4}-\frac{1}{\sqrt{3}}y_{4}+\frac{1}{2\sqrt{3}}z_{4}\right)a \, \mathbf{\hat{y}}-\frac{1}{3}\left(x_{4}+y_{4}+z_{4}\right)c \, \mathbf{\hat{z}} & \left(6f\right) & \text{O} \\ \mathbf{B}_{9} & = & -z_{4} \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2}-y_{4} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(y_{4}-z_{4}\right)a \, \mathbf{\hat{x}} + \left(-\frac{1}{\sqrt{3}}x_{4}+\frac{1}{2\sqrt{3}}y_{4}+\frac{1}{2\sqrt{3}}z_{4}\right)a \, \mathbf{\hat{y}}-\frac{1}{3}\left(x_{4}+y_{4}+z_{4}\right)c \, \mathbf{\hat{z}} & \left(6f\right) & \text{O} \\ \mathbf{B}_{10} & = & -y_{4} \, \mathbf{a}_{1}-z_{4} \, \mathbf{a}_{2}-x_{4} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{4}-y_{4}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2\sqrt{3}}x_{4}+\frac{1}{2\sqrt{3}}y_{4}-\frac{1}{\sqrt{3}}z_{4}\right)a \, \mathbf{\hat{y}}-\frac{1}{3}\left(x_{4}+y_{4}+z_{4}\right)c \, \mathbf{\hat{z}} & \left(6f\right) & \text{O} \\ \end{array} \]