AFLOW Prototype: A3B_hP24_151_3c_2a
Prototype | : | CrCl3 |
AFLOW prototype label | : | A3B_hP24_151_3c_2a |
Strukturbericht designation | : | $D0_{4}$ |
Pearson symbol | : | hP24 |
Space group number | : | 151 |
Space group symbol | : | $\text{P3}_{1}\text{12}$ |
AFLOW prototype command | : | aflow --proto=A3B_hP24_151_3c_2a --params=$a$,$c/a$,$x_{1}$,$x_{2}$,$x_{3}$,$y_{3}$,$z_{3}$,$x_{4}$,$y_{4}$,$z_{4}$,$x_{5}$,$y_{5}$,$z_{5}$ |
Basis vectors:
\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1} & = &x_{1} \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{2}+ \frac13 \, \mathbf{a}_{3}& =&- \sqrt{3} \, x_{1} \, a \, \mathbf{\hat{y}}+ \frac13 \, c \, \mathbf{\hat{z}}& \left(3a\right) & \text{Cr I} \\ \mathbf{B}_{2} & = &x_{1} \, \mathbf{a}_{1}+ 2 x_{1} \, \mathbf{a}_{2}+ \frac23 \, \mathbf{a}_{3}& =&\frac32 \, x_{1} \, a \, \mathbf{\hat{x}}+ \frac{\sqrt{3}}{2} \, x_{1} \, a \, \mathbf{\hat{y}}+ \frac23 \, c \, \mathbf{\hat{z}}& \left(3a\right) & \text{Cr I} \\ \mathbf{B}_{3} & = &- 2 x_{1} \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{2}& =&- \frac32 \, x_{1} \, a \, \mathbf{\hat{x}}+ \frac{\sqrt{3}}{2} \, x_{1} \, a \, \mathbf{\hat{y}}& \left(3a\right) & \text{Cr I} \\ \mathbf{B}_{4} & = &x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}+ \frac13 \, \mathbf{a}_{3}& =&- \sqrt{3} \, x_{2} \, a \, \mathbf{\hat{y}}+ \frac13 \, c \, \mathbf{\hat{z}}& \left(3a\right) & \text{Cr II} \\ \mathbf{B}_{5} & = &x_{2} \, \mathbf{a}_{1}+ 2 x_{2} \, \mathbf{a}_{2}+ \frac23 \, \mathbf{a}_{3}& =&\frac32 \, x_{2} \, a \, \mathbf{\hat{x}}+ \frac{\sqrt{3}}{2} \, x_{2} \, a \, \mathbf{\hat{y}}+ \frac23 \, c \, \mathbf{\hat{z}}& \left(3a\right) & \text{Cr II} \\ \mathbf{B}_{6} & = &- 2 x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}& =&- \frac32 \, x_{2} \, a \, \mathbf{\hat{x}}+ \frac{\sqrt{3}}{2} \, x_{2} \, a \, \mathbf{\hat{y}}& \left(3a\right) & \text{Cr II} \\ \mathbf{B}_{7} & = &x_{3} \, \mathbf{a}_{1}+ y_{3} \, \mathbf{a}_{2}+ z_{3} \, \mathbf{a}_{3}& =&\frac12 \, \left(x_{3} + y_{3}\right) \, a \, \mathbf{\hat{x}}+ \frac{\sqrt{3}}{2} \, \left(y_{3} - x_{3}\right) \, a \, \mathbf{\hat{y}}+ z_{3} \, c \, \mathbf{\hat{z}}& \left(6c\right) & \text{Cl I} \\ \mathbf{B}_{8} & = &- y_{3} \, \mathbf{a}_{1}+ \left(x_{3} - y_{3}\right) \, \mathbf{a}_{2}+ \left(\frac13 + z_{3}\right) \, \mathbf{a}_{3}& =&\frac12 \, \left(x_{3} - 2 y_{3}\right) \, a \, \mathbf{\hat{x}}+ \frac{\sqrt{3}}{2} \, x_{3} \, a \, \mathbf{\hat{y}}+ \left(\frac13 + z_{3}\right) \, c \, \mathbf{\hat{z}}& \left(6c\right) & \text{Cl I} \\ \mathbf{B}_{9} & = &\left(y_{3} - x_{3}\right) \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+ \left(\frac23 + z_{3}\right) \, \mathbf{a}_{3}& =&\frac12 \, \left(y_{3} - 2 x_{3}\right) \, a \, \mathbf{\hat{x}}- \frac{\sqrt{3}}{2} \, y_{3} \, a \, \mathbf{\hat{y}}+ \left(\frac23 + z_{3}\right) \, c \, \mathbf{\hat{z}}& \left(6c\right) & \text{Cl I} \\ \mathbf{B}_{10} & = &- y_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+ \left(\frac23 - z_{3}\right) \, \mathbf{a}_{3}& =&- \frac12 \, \left(x_{3} + y_{3}\right) \, a \, \mathbf{\hat{x}}+ \frac{\sqrt{3}}{2} \, \left(y_{3} - x_{3}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac23 - z_{3}\right) \, c \, \mathbf{\hat{z}}& \left(6c\right) & \text{Cl I} \\ \mathbf{B}_{11} & = &\left(y_{3} - x_{3}\right) \, \mathbf{a}_{1}+ y_{3} \, \mathbf{a}_{2}+ \left(\frac13 - z_{3}\right) \, \mathbf{a}_{3}& =&\frac12 \, \left(2 y_{3} - x_{3}\right) \, a \, \mathbf{\hat{x}}+ \frac{\sqrt{3}}{2} \, x_{3} \, a \, \mathbf{\hat{y}}+ \left(\frac13 - z_{3}\right) \, c \, \mathbf{\hat{z}}& \left(6c\right) & \text{Cl I} \\ \mathbf{B}_{12} & = &x_{3} \, \mathbf{a}_{1}+ \left(x_{3} - y_{3}\right) \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}& =&\frac12 \, \left(2 x_{3} - y_{3}\right) \, a \, \mathbf{\hat{x}}- \frac{\sqrt{3}}{2} \, y_{3} \, a \, \mathbf{\hat{y}}- z_{3} \, c \, \mathbf{\hat{z}}& \left(6c\right) & \text{Cl I} \\ \mathbf{B}_{13} & = &x_{4} \, \mathbf{a}_{1}+ y_{4} \, \mathbf{a}_{2}+ z_{4} \, \mathbf{a}_{3}& =&\frac12 \, \left(x_{4} + y_{4}\right) \, a \, \mathbf{\hat{x}}+ \frac{\sqrt{3}}{2} \, \left(y_{4} - x_{4}\right) \, a \, \mathbf{\hat{y}}+ z_{4} \, c \, \mathbf{\hat{z}}& \left(6c\right) & \text{Cl II} \\ \mathbf{B}_{14} & = &- y_{4} \, \mathbf{a}_{1}+ \left(x_{4} - y_{4}\right) \, \mathbf{a}_{2}+ \left(\frac13 + z_{4}\right) \, \mathbf{a}_{3}& =&\frac12 \, \left(x_{4} - 2 y_{4}\right) \, a \, \mathbf{\hat{x}}+ \frac{\sqrt{3}}{2} \, x_{4} \, a \, \mathbf{\hat{y}}+ \left(\frac13 + z_{4}\right) \, c \, \mathbf{\hat{z}}& \left(6c\right) & \text{Cl II} \\ \mathbf{B}_{15} & = &\left(y_{4} - x_{4}\right) \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+ \left(\frac23 + z_{4}\right) \, \mathbf{a}_{3}& =&\frac12 \, \left(y_{4} - 2 x_{4}\right) \, a \, \mathbf{\hat{x}}- \frac{\sqrt{3}}{2} \, y_{4} \, a \, \mathbf{\hat{y}}+ \left(\frac23 + z_{4}\right) \, c \, \mathbf{\hat{z}}& \left(6c\right) & \text{Cl II} \\ \mathbf{B}_{16} & = &- y_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+ \left(\frac23 - z_{4}\right) \, \mathbf{a}_{3}& =&- \frac12 \, \left(x_{4} + y_{4}\right) \, a \, \mathbf{\hat{x}}+ \frac{\sqrt{3}}{2} \, \left(y_{4} - x_{4}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac23 - z_{4}\right) \, c \, \mathbf{\hat{z}}& \left(6c\right) & \text{Cl II} \\ \mathbf{B}_{17} & = &\left(y_{4} - x_{4}\right) \, \mathbf{a}_{1}+ y_{4} \, \mathbf{a}_{2}+ \left(\frac13 - z_{4}\right) \, \mathbf{a}_{3}& =&\frac12 \, \left(2 y_{4} - x_{4}\right) \, a \, \mathbf{\hat{x}}+ \frac{\sqrt{3}}{2} \, x_{4} \, a \, \mathbf{\hat{y}}+ \left(\frac13 - z_{4}\right) \, c \, \mathbf{\hat{z}}& \left(6c\right) & \text{Cl II} \\ \mathbf{B}_{18} & = &x_{4} \, \mathbf{a}_{1}+ \left(x_{4} - y_{4}\right) \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}& =&\frac12 \, \left(2 x_{4} - y_{4}\right) \, a \, \mathbf{\hat{x}}- \frac{\sqrt{3}}{2} \, y_{4} \, a \, \mathbf{\hat{y}}- z_{4} \, c \, \mathbf{\hat{z}}& \left(6c\right) & \text{Cl II} \\ \mathbf{B}_{19} & = &x_{5} \, \mathbf{a}_{1}+ y_{5} \, \mathbf{a}_{2}+ z_{5} \, \mathbf{a}_{3}& =&\frac12 \, \left(x_{5} + y_{5}\right) \, a \, \mathbf{\hat{x}}+ \frac{\sqrt{3}}{2} \, \left(y_{5} - x_{5}\right) \, a \, \mathbf{\hat{y}}+ z_{5} \, c \, \mathbf{\hat{z}}& \left(6c\right) & \text{Cl III} \\ \mathbf{B}_{20} & = &- y_{5} \, \mathbf{a}_{1}+ \left(x_{5} - y_{5}\right) \, \mathbf{a}_{2}+ \left(\frac13 + z_{5}\right) \, \mathbf{a}_{3}& =&\frac12 \, \left(x_{5} - 2 y_{5}\right) \, a \, \mathbf{\hat{x}}+ \frac{\sqrt{3}}{2} \, x_{5} \, a \, \mathbf{\hat{y}}+ \left(\frac13 + z_{5}\right) \, c \, \mathbf{\hat{z}}& \left(6c\right) & \text{Cl III} \\ \mathbf{B}_{21} & = &\left(y_{5} - x_{5}\right) \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}+ \left(\frac23 + z_{5}\right) \, \mathbf{a}_{3}& =&\frac12 \, \left(y_{5} - 2 x_{5}\right) \, a \, \mathbf{\hat{x}}- \frac{\sqrt{3}}{2} \, y_{5} \, a \, \mathbf{\hat{y}}+ \left(\frac23 + z_{5}\right) \, c \, \mathbf{\hat{z}}& \left(6c\right) & \text{Cl III} \\ \mathbf{B}_{22} & = &- y_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}+ \left(\frac23 - z_{5}\right) \, \mathbf{a}_{3}& =&- \frac12 \, \left(x_{5} + y_{5}\right) \, a \, \mathbf{\hat{x}}+ \frac{\sqrt{3}}{2} \, \left(y_{5} - x_{5}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac23 - z_{5}\right) \, c \, \mathbf{\hat{z}}& \left(6c\right) & \text{Cl III} \\ \mathbf{B}_{23} & = &\left(y_{5} - x_{5}\right) \, \mathbf{a}_{1}+ y_{5} \, \mathbf{a}_{2}+ \left(\frac13 - z_{5}\right) \, \mathbf{a}_{3}& =&\frac12 \, \left(2 y_{5} - x_{5}\right) \, a \, \mathbf{\hat{x}}+ \frac{\sqrt{3}}{2} \, x_{5} \, a \, \mathbf{\hat{y}}+ \left(\frac13 - z_{5}\right) \, c \, \mathbf{\hat{z}}& \left(6c\right) & \text{Cl III} \\ \mathbf{B}_{24} & = &x_{5} \, \mathbf{a}_{1}+ \left(x_{5} - y_{5}\right) \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}& =&\frac12 \, \left(2 x_{5} - y_{5}\right) \, a \, \mathbf{\hat{x}}- \frac{\sqrt{3}}{2} \, y_{5} \, a \, \mathbf{\hat{y}}- z_{5} \, c \, \mathbf{\hat{z}}& \left(6c\right) & \text{Cl III} \\ \end{array} \]