AFLOW Prototype: AB3_hP8_182_c_g
Prototype | : | Fe3C |
AFLOW prototype label | : | AB3_hP8_182_c_g |
Strukturbericht designation | : | None |
Pearson symbol | : | hP8 |
Space group number | : | 182 |
Space group symbol | : | $\text{P6}_{3}\text{22}$ |
AFLOW prototype command | : | aflow --proto=AB3_hP8_182_c_g --params=$a$,$c/a$,$x_{2}$ |
Basis vectors:
\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1}& = &\frac13 \, \mathbf{a}_{1}+ \frac23 \, \mathbf{a}_{2}+ \frac14 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \frac1{2\sqrt3} \, a \, \mathbf{\hat{y}}+ \frac14 \, c \, \mathbf{\hat{z}}& \left(2c\right) & \text{C} \\ \mathbf{B}_{2}& = &\frac23 \, \mathbf{a}_{1}+ \frac13 \, \mathbf{a}_{2}+ \frac34 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}- \frac1{2\sqrt3} \, a \, \mathbf{\hat{y}}+ \frac34 \, c \, \mathbf{\hat{z}}& \left(2c\right) & \text{C} \\ \mathbf{B}_{3}& = &x_{2} \, \mathbf{a}_{1}& = &\frac12 \, x_{2} \, a \, \mathbf{\hat{x}}- \frac{\sqrt3}2 \, x_{2} \, a \mathbf{\hat{y}}& \left(6g\right) & \text{Fe} \\ \mathbf{B}_{4}& = &x_{2} \, \mathbf{a}_{2}& = &\frac12 \, x_{2} \, a \, \mathbf{\hat{x}}+ \frac{\sqrt3}2 \, x_{2} \, a \mathbf{\hat{y}}& \left(6g\right) & \text{Fe} \\ \mathbf{B}_{5}& = &- x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}& = &- x_{2} \, a \, \mathbf{\hat{x}}& \left(6g\right) & \text{Fe} \\ \mathbf{B}_{6}& = &- x_{2} \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{3}& = &- \frac12 \, x_{2} \, a \, \mathbf{\hat{x}}+ \frac{\sqrt3}2 \, x_{2} \, a \mathbf{\hat{y}}+ \frac12 \, c \, \mathbf{\hat{z}}& \left(6g\right) & \text{Fe} \\ \mathbf{B}_{7}& = &- x_{2} \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &- \frac12 \, x_{2} \, a \, \mathbf{\hat{x}}- \frac{\sqrt3}2 \, x_{2} \, a \mathbf{\hat{y}}+ \frac12 \, c \, \mathbf{\hat{z}}& \left(6g\right) & \text{Fe} \\ \mathbf{B}_{8}& = &x_{2} \, \mathbf{a}_{1}+ x_{2} \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &+ x_{2} \, a \, \mathbf{\hat{x}}+ \frac12 \, c \, \mathbf{\hat{z}}& \left(6g\right) & \text{Fe} \\ \end{array} \]