AFLOW Prototype: A3B2_hP5_164_ad_d
Prototype | : | Al3Ni2 |
AFLOW prototype label | : | A3B2_hP5_164_ad_d |
Strukturbericht designation | : | $D5_{13}$ |
Pearson symbol | : | hP5 |
Space group number | : | 164 |
Space group symbol | : | $\text{P}\bar{3}\text{m1}$ |
AFLOW prototype command | : | aflow --proto=A3B2_hP5_164_ad_d --params=$a$,$c/a$,$z_2$,$z_3$ |
Basis vectors:
\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B_1} & = & 0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & = & 0 \mathbf{\hat{x}} + 0 \mathbf{\hat{y}} + 0 \mathbf{\hat{z}} & \left(1a\right) & \text{Al I} \\ \mathbf{B_2} & =& \frac13 \, \mathbf{a}_{1} + \frac23 \, \mathbf{a}_{2} + z_2 \, \mathbf{a}_{3}& =& \frac12 \, a \, \mathbf{\hat{x}} + \frac1{2\sqrt{3}} \, a \, \mathbf{\hat{y}} +z_2 \, c \, \mathbf{\hat{z}}& \left(2d\right) & \text{Al II} \\ \mathbf{B_3} & =& \frac23 \, \mathbf{a}_{1} + \frac13 \, \mathbf{a}_{2} - z_2 \, \mathbf{a}_{3}& =& \frac12 \, a \, \mathbf{\hat{x}} - \frac1{2\sqrt{3}} \, a \, \mathbf{\hat{y}} -z_2 \, c \, \mathbf{\hat{z}}& \left(2d\right) & \text{Al II} \\ \mathbf{B_4} & =& \frac13 \, \mathbf{a}_{1} + \frac23 \, \mathbf{a}_{2} + z_3 \, \mathbf{a}_{3}& =& \frac12 \, a \, \mathbf{\hat{x}} + \frac1{2\sqrt{3}} \, a \, \mathbf{\hat{y}} +z_3 \, c \, \mathbf{\hat{z}}& \left(2d\right) & \text{Ni} \\ \mathbf{B_5} & =& \frac23 \, \mathbf{a}_{1} + \frac13 \, \mathbf{a}_{2} - z_3 \, \mathbf{a}_{3}& =& \frac12 \, a \, \mathbf{\hat{x}} - \frac1{2\sqrt{3}} \, a \, \mathbf{\hat{y}} -z_3 \, c \, \mathbf{\hat{z}}& \left(2d\right) & \text{Ni} \\ \end{array} \]