AFLOW Prototype: A3B_hR4_160_b_a
Prototype | : | H3S |
AFLOW prototype label | : | A3B_hR4_160_b_a |
Strukturbericht designation | : | None |
Pearson symbol | : | hR4 |
Space group number | : | 160 |
Space group symbol | : | $R3m$ |
AFLOW prototype command | : | aflow --proto=A3B_hR4_160_b_a [--hex] --params=$a$,$c/a$,$x_{1}$,$x_{2}$,$z_{2}$ |
Basis vectors:
\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1} & = & x_{1} \, \mathbf{a}_{1} + x_{1} \, \mathbf{a}_{2} + x_{1} \, \mathbf{a}_{3} & = & x_{1}c \, \mathbf{\hat{z}} & \left(1a\right) & \text{S} \\ \mathbf{B}_{2} & = & x_{2} \, \mathbf{a}_{1} + x_{2} \, \mathbf{a}_{2} + z_{2} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{2}-z_{2}\right)a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}\left(x_{2}-z_{2}\right)a \, \mathbf{\hat{y}} + \left(\frac{2}{3}x_{2}+\frac{1}{3}z_{2}\right)c \, \mathbf{\hat{z}} & \left(3b\right) & \text{H} \\ \mathbf{B}_{3} & = & z_{2} \, \mathbf{a}_{1} + x_{2} \, \mathbf{a}_{2} + x_{2} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(-x_{2}+z_{2}\right)a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}\left(x_{2}-z_{2}\right)a \, \mathbf{\hat{y}} + \left(\frac{2}{3}x_{2}+\frac{1}{3}z_{2}\right)c \, \mathbf{\hat{z}} & \left(3b\right) & \text{H} \\ \mathbf{B}_{4} & = & x_{2} \, \mathbf{a}_{1} + z_{2} \, \mathbf{a}_{2} + x_{2} \, \mathbf{a}_{3} & = & \frac{1}{\sqrt{3}}\left(-x_{2}+z_{2}\right)a \, \mathbf{\hat{y}} + \left(\frac{2}{3}x_{2}+\frac{1}{3}z_{2}\right)c \, \mathbf{\hat{z}} & \left(3b\right) & \text{H} \\ \end{array} \]