AFLOW Prototype: A2B_hP9_147_g_ad
Prototype | : | $\zeta$–AgZn |
AFLOW prototype label | : | A2B_hP9_147_g_ad |
Strukturbericht designation | : | $B_{b}$ |
Pearson symbol | : | hP9 |
Space group number | : | 147 |
Space group symbol | : | $\text{P}\bar{3}$ |
AFLOW prototype command | : | aflow --proto=A2B_hP9_147_g_ad --params=$a$,$c/a$,$z_2$,$x_3$,$y_3$,$z_3$ |
M. If the system is stoichiometric then M = (Ag4.5,Zn1.5).
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{Zn} \\ \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{Zn} \\ \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{Zn} \\ \mathbf{B_4} & =& x_3 \, \mathbf{a}_{1} + y_3 \, \mathbf{a}_{2} + z_3 \, \mathbf{a}_{3}& =& \frac12 \, \left(x_3 + y_3\right) \, a \, \mathbf{\hat{x}}+ \frac{\sqrt3}2 \, \left(y_3 - x_3\right) \, a \, \mathbf{\hat{y}}+ z_3 \, c \, \mathbf{\hat{z}}& \left(6g\right) & \text{M} \\ \mathbf{B_5} & =& -y_3 \, \mathbf{a}_{1} + \left(x_3 - y_3\right) \, \mathbf{a}_{2} + z_3 \, \mathbf{a}_{3}& =& \frac12 \, \left(x_3 -2 y_3\right) \, a \, \mathbf{\hat{x}}+ \frac{\sqrt3}2 \, x_3 \, a \, \mathbf{\hat{y}}+ z_3 \, c \, \mathbf{\hat{z}}& \left(6g\right) & \text{M} \\ \mathbf{B_6} & =& \left(y_3 - x_3\right) \, \mathbf{a}_{1} - x_3 \, \mathbf{a}_{2} + z_3 \, \mathbf{a}_{3}& =& \frac12 \, \left(y_3 -2 x_3\right) \, a \, \mathbf{\hat{x}}- \frac{\sqrt3}2 \, y_3 \, a \, \mathbf{\hat{y}}+ z_3 \, c \, \mathbf{\hat{z}}& \left(6g\right) & \text{M} \\ \mathbf{B_7} & =& - x_3 \, \mathbf{a}_{1} - y_3 \, \mathbf{a}_{2} - z_3 \, \mathbf{a}_{3}& =& - \frac12 \, \left(x_3 + y_3\right) \, a \, \mathbf{\hat{x}}+ \frac{\sqrt3}2 \, \left(x_3 - y_3\right) \, a \, \mathbf{\hat{y}}- z_3 \, c \, \mathbf{\hat{z}}& \left(6g\right) & \text{M} \\ \mathbf{B_8} & =& y_3 \, \mathbf{a}_{1} + \left(y_3 - x_3\right) \, \mathbf{a}_{2} - z_3 \, \mathbf{a}_{3}& =& \frac12 \, \left(2 y_3 - x_3\right) \, a \, \mathbf{\hat{x}}- \frac{\sqrt3}2 \, x_3 \, a \, \mathbf{\hat{y}}- z_3 \, c \, \mathbf{\hat{z}}& \left(6g\right) & \text{M} \\ \mathbf{B_9} & =& \left(x_3 - y_3\right) \, \mathbf{a}_{1} + x_3 \, \mathbf{a}_{2} - z_3 \, \mathbf{a}_{3}& =& \frac12 \, \left(2x_3 - y_3\right) \, a \, \mathbf{\hat{x}}+ \frac{\sqrt3}2 \, y_3 \, a \, \mathbf{\hat{y}}- z_3 \, c \, \mathbf{\hat{z}}& \left(6g\right) & \text{M} \\ \end{array} \]