AFLOW Prototype: A2B_hP18_180_fi_bd
Prototype | : | Mg2Ni |
AFLOW prototype label | : | A2B_hP18_180_fi_bd |
Strukturbericht designation | : | $C_{a}$ |
Pearson symbol | : | hP18 |
Space group number | : | 180 |
Space group symbol | : | $\text{P6}_{2}\text{22}$ |
AFLOW prototype command | : | aflow --proto=A2B_hP18_180_fi_bd --params=$a$,$c/a$,$z_{3}$,$x_{4}$ |
Basis vectors:
\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1}& = &\frac12 \, \mathbf{a}_{3}& = &\frac12 \, c \, \mathbf{\hat{z}}& \left(3b\right) & \text{Ni I} \\ \mathbf{B}_{2}& = &\frac16 \, \mathbf{a}_{3}& = &\frac16 \, c \, \mathbf{\hat{z}}& \left(3b\right) & \text{Ni I} \\ \mathbf{B}_{3}& = &\frac56 \, \mathbf{a}_{3}& = &\frac56 \, c \, \mathbf{\hat{z}}& \left(3b\right) & \text{Ni I} \\ \mathbf{B}_{4}& = &\frac12 \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{3}& = &\frac14 \, a \, \mathbf{\hat{x}}- \frac{\sqrt3}4 \, a \, \mathbf{\hat{y}}+ \frac12 \, c \, \mathbf{\hat{z}}& \left(3d\right) & \text{Ni II} \\ \mathbf{B}_{5}& = &\frac12 \, \mathbf{a}_{2}+ \frac16 \, \mathbf{a}_{3}& = &\frac14 \, a \, \mathbf{\hat{x}}+ \frac{\sqrt3}4 \, a \, \mathbf{\hat{y}}+ \frac16 \, c \, \mathbf{\hat{z}}& \left(3d\right) & \text{Ni II} \\ \mathbf{B}_{6}& = &\frac12 \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}+ \frac56 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \frac56 \, c \, \mathbf{\hat{z}}& \left(3d\right) & \text{Ni II} \\ \mathbf{B}_{7}& = &\frac12 \, \mathbf{a}_{1}+ z_{3} \, \mathbf{a}_{3}& = &\frac14 \, a \, \mathbf{\hat{x}}- \frac{\sqrt3}4 \, a \, \mathbf{\hat{y}}+ z_{3} \, c \, \mathbf{\hat{z}}& \left(6f\right) & \text{Mg I} \\ \mathbf{B}_{8}& = &\frac12 \, \mathbf{a}_{2}+ \left(\frac23 + z_{3}\right) \, \mathbf{a}_{3}& = &\frac14 \, a \, \mathbf{\hat{x}}+ \frac{\sqrt3}4 \, a \, \mathbf{\hat{y}}+ \left(\frac23 + z_{3}\right) \, c \, \mathbf{\hat{z}}& \left(6f\right) & \text{Mg I} \\ \mathbf{B}_{9}& = &\frac12 \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}+ \left(\frac13 + z_{3}\right) \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \left(\frac13 + z_{3}\right) \, c \, \mathbf{\hat{z}}& \left(6f\right) & \text{Mg I} \\ \mathbf{B}_{10}& = &\frac12 \, \mathbf{a}_{1}- z_{3} \, \mathbf{a}_{3}& = &\frac14 \, a \, \mathbf{\hat{x}}- \frac{\sqrt3}4 \, a \, \mathbf{\hat{y}}- z_{3} \, c \, \mathbf{\hat{z}}& \left(6f\right) & \text{Mg I} \\ \mathbf{B}_{11}& = &\frac12 \, \mathbf{a}_{2}+ \left(\frac23 - z_{3}\right) \, \mathbf{a}_{3}& = &\frac14 \, a \, \mathbf{\hat{x}}+ \frac{\sqrt3}4 \, a \, \mathbf{\hat{y}}+ \left(\frac23 - z_{3}\right) \, c \, \mathbf{\hat{z}}& \left(6f\right) & \text{Mg I} \\ \mathbf{B}_{12}& = &\frac12 \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}+ \left(\frac13 - z_{3}\right) \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \left(\frac13 - z_{3}\right) \, c \, \mathbf{\hat{z}}& \left(6f\right) & \text{Mg I} \\ \mathbf{B}_{13}& = &x_{4} \, \mathbf{a}_{1}+ 2 x_{4} \, \mathbf{a}_{2}& = &\frac32 \, x_{4} \, a \, \mathbf{\hat{x}}+ \frac{\sqrt3}2 \, x_{4} \, a \, \mathbf{\hat{y}}& \left(6i\right) & \text{Mg II} \\ \mathbf{B}_{14}& = &- 2 x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+ \frac23 \, \mathbf{a}_{3}& = &- \frac32 \, x_{4} \, a \, \mathbf{\hat{x}}+ \frac{\sqrt3}2 \, x_{4} \, a \, \mathbf{\hat{y}}+ \frac23 \, c \, \mathbf{\hat{z}}& \left(6i\right) & \text{Mg II} \\ \mathbf{B}_{15}& = &x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+ \frac13 \, \mathbf{a}_{3}& = &- \sqrt3 \, x_{4} \, a \, \mathbf{\hat{y}}+ \frac13 \, c \, \mathbf{\hat{z}}& \left(6i\right) & \text{Mg II} \\ \mathbf{B}_{16}& = &- x_{4} \, \mathbf{a}_{1}- 2 x_{4} \, \mathbf{a}_{2}& = &- \frac32 \, x_{4} \, a \, \mathbf{\hat{x}}- \frac{\sqrt3}2 \, x_{4} \, a \, \mathbf{\hat{y}}& \left(6i\right) & \text{Mg II} \\ \mathbf{B}_{17}& = &2 x_{4} \, \mathbf{a}_{1}+ x_{4} \, \mathbf{a}_{2}+ \frac23 \, \mathbf{a}_{3}& = &\frac32 \, x_{4} \, a \, \mathbf{\hat{x}}- \frac{\sqrt3}2 \, x_{4} \, a \, \mathbf{\hat{y}}+ \frac23 \, c \, \mathbf{\hat{z}}& \left(6i\right) & \text{Mg II} \\ \mathbf{B}_{18}& = &- x_{4} \, \mathbf{a}_{1}+ x_{4} \, \mathbf{a}_{2}+ \frac13 \, \mathbf{a}_{3}& = &\sqrt3 \, x_{4} \, a \, \mathbf{\hat{y}}+ \frac13 \, c \, \mathbf{\hat{z}}& \left(6i\right) & \text{Mg II} \\ \end{array} \]