AFLOW Prototype: AB2_hP9_162_ad_k
Prototype | : | $\beta$–V2N |
AFLOW prototype label | : | AB2_hP9_162_ad_k |
Strukturbericht designation | : | $L'3_{2}$ |
Pearson symbol | : | hP9 |
Space group number | : | 162 |
Space group symbol | : | $\text{P}\bar{3}\text{1m}$ |
AFLOW prototype command | : | aflow --proto=AB2_hP9_162_ad_k --params=$a$,$c/a$,$x_{3}$,$z_{3}$ |
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{N I} \\ \mathbf{B}_{2} & =&\frac13 \, \mathbf{a}_{1}+ \frac23 \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& =&\frac12 \, a \, \mathbf{\hat{x}}+ \frac1{2\sqrt3} \, a \, \mathbf{\hat{y}}+ \frac12 \, c \, \mathbf{\hat{z}}& \left(2d\right) & \text{N II} \\ \mathbf{B}_{3} & =&\frac23 \, \mathbf{a}_{1}+ \frac13 \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& =&\frac12 \, a \, \mathbf{\hat{x}}- \frac1{2\sqrt3} \, a \, \mathbf{\hat{y}}+ \frac12 \, c \, \mathbf{\hat{z}}& \left(2d\right) & \text{N II} \\ \mathbf{B}_{4} & =&x_{3} \, \mathbf{a}_{1}+ z_{3} \, \mathbf{a}_{3}& =&\frac12 \, x_{3} \, a \, \mathbf{\hat{x}}- \frac{\sqrt3}2 \, x_{3} \, a \, \mathbf{\hat{y}}+ z_{3} \, c \, \mathbf{\hat{z}}& \left(6k\right) & \text{V} \\ \mathbf{B}_{5} & =&x_{3} \, \mathbf{a}_{2}+ z_{3} \, \mathbf{a}_{3}& =&\frac12 \, x_{3} \, a \, \mathbf{\hat{x}}+ \frac{\sqrt3}2 \, x_{3} \, a \, \mathbf{\hat{y}}+ z_{3} \, c \, \mathbf{\hat{z}}& \left(6k\right) & \text{V} \\ \mathbf{B}_{6} & =&- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+ z_{3} \, \mathbf{a}_{3}& =&- x_{3} \, a \, \mathbf{\hat{x}}+ z_{3} \, c \, \mathbf{\hat{z}}& \left(6k\right) & \text{V} \\ \mathbf{B}_{7} & =&- x_{3} \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}& =&- \frac12 \, x_{3} \, a \, \mathbf{\hat{x}}- \frac{\sqrt3}2 \, x_{3} \, a \, \mathbf{\hat{y}}- z_{3} \, c \, \mathbf{\hat{z}}& \left(6k\right) & \text{V} \\ \mathbf{B}_{8} & =&- x_{3} \, \mathbf{a}_{1}- z_{3} \, \mathbf{a}_{3}& =&- \frac12 \, x_{3} \, a \, \mathbf{\hat{x}}+ \frac{\sqrt3}2 \, x_{3} \, a \, \mathbf{\hat{y}}- z_{3} \, c \, \mathbf{\hat{z}}& \left(6k\right) & \text{V} \\ \mathbf{B}_{9} & =&x_{3} \, \mathbf{a}_{1}+ x_{3} \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}& =&x_{3} \, a \, \mathbf{\hat{x}}- z_{3} \, c \, \mathbf{\hat{z}}& \left(6k\right) & \text{V} \\ \end{array} \]