AFLOW Prototype: AB4C_hP6_191_a_h_b
Prototype | : | AlB4Mg |
AFLOW prototype label | : | AB4C_hP6_191_a_h_b |
Strukturbericht designation | : | None |
Pearson symbol | : | hP6 |
Space group number | : | 191 |
Space group symbol | : | $\text{P6/mmm}$ |
AFLOW prototype command | : | aflow --proto=AB4C_hP6_191_a_h_b --params=$a$,$c/a$,$z_{3}$ |
Basis vectors:
\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1} & = & 0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & = & 0 \mathbf{\hat{x}} + 0 \mathbf{\hat{y}} + 0 \mathbf{\hat{z}} & \left(1a\right) & \text{Al} \\ \mathbf{B}_{2} & = & \frac12 \, \mathbf{a}_{3} & = & \frac12 \, c \, \mathbf{\hat{z}} & \left(1b\right) & \text{Mg} \\ \mathbf{B}_{3} & =&\frac13 \mathbf{a}_{1}+ \frac23 \mathbf{a}_{2}+ z_{3} \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \frac1{2\sqrt{3}} \, a \, \mathbf{\hat{y}}+ z_{3} \, c \, \mathbf{\hat{z}}& \left(4h\right) & \text{B} \\ \mathbf{B}_{4} & =&\frac23 \mathbf{a}_{1}+ \frac13 \mathbf{a}_{2}+ z_{3} \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}- \frac1{2\sqrt{3}} \, a \, \mathbf{\hat{y}}+ z_{3} \, c \, \mathbf{\hat{z}}& \left(4h\right) & \text{B} \\ \mathbf{B}_{5} & =&\frac23 \mathbf{a}_{1}+ \frac13 \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}- \frac1{2\sqrt{3}} \, a \, \mathbf{\hat{y}}- z_{3} \, c \, \mathbf{\hat{z}}& \left(4h\right) & \text{B} \\ \mathbf{B}_{6} & =&\frac13 \mathbf{a}_{1}+ \frac23 \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \frac1{2\sqrt{3}} \, a \, \mathbf{\hat{y}}- z_{3} \, c \, \mathbf{\hat{z}}& \left(4h\right) & \text{B} \\ \end{array} \]