AFLOW Prototype: AB4C8_hR13_160_a_ab_2a2b
Prototype | : | GaMo4S8 |
AFLOW prototype label | : | AB4C8_hR13_160_a_ab_2a2b |
Strukturbericht designation | : | None |
Pearson symbol | : | hR13 |
Space group number | : | 160 |
Space group symbol | : | $R3m$ |
AFLOW prototype command | : | aflow --proto=AB4C8_hR13_160_a_ab_2a2b --params=$a$,$c/a$,$x_{1}$,$x_{2}$,$x_{3}$,$x_{4}$,$x_{5}$,$z_{5}$,$x_{6}$,$z_{6}$,$x_{7}$,$z_{7}$ |
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{Ga} \\ \mathbf{B}_{2} & = & x_{2} \, \mathbf{a}_{1} + x_{2} \, \mathbf{a}_{2} + x_{2} \, \mathbf{a}_{3} & = & x_{2}c \, \mathbf{\hat{z}} & \left(1a\right) & \text{Mo I} \\ \mathbf{B}_{3} & = & x_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + x_{3} \, \mathbf{a}_{3} & = & x_{3}c \, \mathbf{\hat{z}} & \left(1a\right) & \text{Si I} \\ \mathbf{B}_{4} & = & x_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} + x_{4} \, \mathbf{a}_{3} & = & x_{4}c \, \mathbf{\hat{z}} & \left(1a\right) & \text{Si II} \\ \mathbf{B}_{5} & = & x_{5} \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{5}-z_{5}\right)a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}\left(x_{5}-z_{5}\right)a \, \mathbf{\hat{y}} + \left(\frac{2}{3}x_{5}+\frac{1}{3}z_{5}\right)c \, \mathbf{\hat{z}} & \left(3b\right) & \text{Mo II} \\ \mathbf{B}_{6} & = & z_{5} \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2} + x_{5} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(-x_{5}+z_{5}\right)a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}\left(x_{5}-z_{5}\right)a \, \mathbf{\hat{y}} + \left(\frac{2}{3}x_{5}+\frac{1}{3}z_{5}\right)c \, \mathbf{\hat{z}} & \left(3b\right) & \text{Mo II} \\ \mathbf{B}_{7} & = & x_{5} \, \mathbf{a}_{1} + z_{5} \, \mathbf{a}_{2} + x_{5} \, \mathbf{a}_{3} & = & \frac{1}{\sqrt{3}}\left(-x_{5}+z_{5}\right)a \, \mathbf{\hat{y}} + \left(\frac{2}{3}x_{5}+\frac{1}{3}z_{5}\right)c \, \mathbf{\hat{z}} & \left(3b\right) & \text{Mo II} \\ \mathbf{B}_{8} & = & x_{6} \, \mathbf{a}_{1} + x_{6} \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{6}-z_{6}\right)a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}\left(x_{6}-z_{6}\right)a \, \mathbf{\hat{y}} + \left(\frac{2}{3}x_{6}+\frac{1}{3}z_{6}\right)c \, \mathbf{\hat{z}} & \left(3b\right) & \text{Si III} \\ \mathbf{B}_{9} & = & z_{6} \, \mathbf{a}_{1} + x_{6} \, \mathbf{a}_{2} + x_{6} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(-x_{6}+z_{6}\right)a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}\left(x_{6}-z_{6}\right)a \, \mathbf{\hat{y}} + \left(\frac{2}{3}x_{6}+\frac{1}{3}z_{6}\right)c \, \mathbf{\hat{z}} & \left(3b\right) & \text{Si III} \\ \mathbf{B}_{10} & = & x_{6} \, \mathbf{a}_{1} + z_{6} \, \mathbf{a}_{2} + x_{6} \, \mathbf{a}_{3} & = & \frac{1}{\sqrt{3}}\left(-x_{6}+z_{6}\right)a \, \mathbf{\hat{y}} + \left(\frac{2}{3}x_{6}+\frac{1}{3}z_{6}\right)c \, \mathbf{\hat{z}} & \left(3b\right) & \text{Si III} \\ \mathbf{B}_{11} & = & x_{7} \, \mathbf{a}_{1} + x_{7} \, \mathbf{a}_{2} + z_{7} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{7}-z_{7}\right)a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}\left(x_{7}-z_{7}\right)a \, \mathbf{\hat{y}} + \left(\frac{2}{3}x_{7}+\frac{1}{3}z_{7}\right)c \, \mathbf{\hat{z}} & \left(3b\right) & \text{Si IV} \\ \mathbf{B}_{12} & = & z_{7} \, \mathbf{a}_{1} + x_{7} \, \mathbf{a}_{2} + x_{7} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(-x_{7}+z_{7}\right)a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}\left(x_{7}-z_{7}\right)a \, \mathbf{\hat{y}} + \left(\frac{2}{3}x_{7}+\frac{1}{3}z_{7}\right)c \, \mathbf{\hat{z}} & \left(3b\right) & \text{Si IV} \\ \mathbf{B}_{13} & = & x_{7} \, \mathbf{a}_{1} + z_{7} \, \mathbf{a}_{2} + x_{7} \, \mathbf{a}_{3} & = & \frac{1}{\sqrt{3}}\left(-x_{7}+z_{7}\right)a \, \mathbf{\hat{y}} + \left(\frac{2}{3}x_{7}+\frac{1}{3}z_{7}\right)c \, \mathbf{\hat{z}} & \left(3b\right) & \text{Si IV} \\ \end{array} \]