AFLOW Prototype: A2B_hR18_148_2f_f
Prototype | : | PdCl2 |
AFLOW prototype label | : | A2B_hR18_148_2f_f |
Strukturbericht designation | : | None |
Pearson symbol | : | hR18 |
Space group number | : | 148 |
Space group symbol | : | $R\bar{3}$ |
AFLOW prototype command | : | aflow --proto=A2B_hR18_148_2f_f [--hex] --params=$a$,$c/a$,$x_{1}$,$y_{1}$,$z_{1}$,$x_{2}$,$y_{2}$,$z_{2}$,$x_{3}$,$y_{3}$,$z_{3}$ |
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} + y_{1} \, \mathbf{a}_{2} + z_{1} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{1}-z_{1}\right)a \, \mathbf{\hat{x}} + \left(-\frac{1}{2\sqrt{3}}x_{1}+\frac{1}{\sqrt{3}}y_{1}-\frac{1}{2\sqrt{3}}z_{1}\right)a \, \mathbf{\hat{y}} + \frac{1}{3}\left(x_{1}+y_{1}+z_{1}\right)c \, \mathbf{\hat{z}} & \left(6f\right) & \text{Cl I} \\ \mathbf{B}_{2} & = & z_{1} \, \mathbf{a}_{1} + x_{1} \, \mathbf{a}_{2} + y_{1} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(-y_{1}+z_{1}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{\sqrt{3}}x_{1}-\frac{1}{2\sqrt{3}}y_{1}-\frac{1}{2\sqrt{3}}z_{1}\right)a \, \mathbf{\hat{y}} + \frac{1}{3}\left(x_{1}+y_{1}+z_{1}\right)c \, \mathbf{\hat{z}} & \left(6f\right) & \text{Cl I} \\ \mathbf{B}_{3} & = & y_{1} \, \mathbf{a}_{1} + z_{1} \, \mathbf{a}_{2} + x_{1} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(-x_{1}+y_{1}\right)a \, \mathbf{\hat{x}} + \left(-\frac{1}{2\sqrt{3}}x_{1}-\frac{1}{2\sqrt{3}}y_{1}+\frac{1}{\sqrt{3}}z_{1}\right)a \, \mathbf{\hat{y}} + \frac{1}{3}\left(x_{1}+y_{1}+z_{1}\right)c \, \mathbf{\hat{z}} & \left(6f\right) & \text{Cl I} \\ \mathbf{B}_{4} & = & -x_{1} \, \mathbf{a}_{1}-y_{1} \, \mathbf{a}_{2}-z_{1} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(-x_{1}+z_{1}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2\sqrt{3}}x_{1}-\frac{1}{\sqrt{3}}y_{1}+\frac{1}{2\sqrt{3}}z_{1}\right)a \, \mathbf{\hat{y}}-\frac{1}{3}\left(x_{1}+y_{1}+z_{1}\right)c \, \mathbf{\hat{z}} & \left(6f\right) & \text{Cl I} \\ \mathbf{B}_{5} & = & -z_{1} \, \mathbf{a}_{1}-x_{1} \, \mathbf{a}_{2}-y_{1} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(y_{1}-z_{1}\right)a \, \mathbf{\hat{x}} + \left(-\frac{1}{\sqrt{3}}x_{1}+\frac{1}{2\sqrt{3}}y_{1}+\frac{1}{2\sqrt{3}}z_{1}\right)a \, \mathbf{\hat{y}}-\frac{1}{3}\left(x_{1}+y_{1}+z_{1}\right)c \, \mathbf{\hat{z}} & \left(6f\right) & \text{Cl I} \\ \mathbf{B}_{6} & = & -y_{1} \, \mathbf{a}_{1}-z_{1} \, \mathbf{a}_{2}-x_{1} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{1}-y_{1}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2\sqrt{3}}x_{1}+\frac{1}{2\sqrt{3}}y_{1}-\frac{1}{\sqrt{3}}z_{1}\right)a \, \mathbf{\hat{y}}-\frac{1}{3}\left(x_{1}+y_{1}+z_{1}\right)c \, \mathbf{\hat{z}} & \left(6f\right) & \text{Cl I} \\ \mathbf{B}_{7} & = & x_{2} \, \mathbf{a}_{1} + y_{2} \, \mathbf{a}_{2} + z_{2} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{2}-z_{2}\right)a \, \mathbf{\hat{x}} + \left(-\frac{1}{2\sqrt{3}}x_{2}+\frac{1}{\sqrt{3}}y_{2}-\frac{1}{2\sqrt{3}}z_{2}\right)a \, \mathbf{\hat{y}} + \frac{1}{3}\left(x_{2}+y_{2}+z_{2}\right)c \, \mathbf{\hat{z}} & \left(6f\right) & \text{Cl II} \\ \mathbf{B}_{8} & = & z_{2} \, \mathbf{a}_{1} + x_{2} \, \mathbf{a}_{2} + y_{2} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(-y_{2}+z_{2}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{\sqrt{3}}x_{2}-\frac{1}{2\sqrt{3}}y_{2}-\frac{1}{2\sqrt{3}}z_{2}\right)a \, \mathbf{\hat{y}} + \frac{1}{3}\left(x_{2}+y_{2}+z_{2}\right)c \, \mathbf{\hat{z}} & \left(6f\right) & \text{Cl II} \\ \mathbf{B}_{9} & = & y_{2} \, \mathbf{a}_{1} + z_{2} \, \mathbf{a}_{2} + x_{2} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(-x_{2}+y_{2}\right)a \, \mathbf{\hat{x}} + \left(-\frac{1}{2\sqrt{3}}x_{2}-\frac{1}{2\sqrt{3}}y_{2}+\frac{1}{\sqrt{3}}z_{2}\right)a \, \mathbf{\hat{y}} + \frac{1}{3}\left(x_{2}+y_{2}+z_{2}\right)c \, \mathbf{\hat{z}} & \left(6f\right) & \text{Cl II} \\ \mathbf{B}_{10} & = & -x_{2} \, \mathbf{a}_{1}-y_{2} \, \mathbf{a}_{2}-z_{2} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(-x_{2}+z_{2}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2\sqrt{3}}x_{2}-\frac{1}{\sqrt{3}}y_{2}+\frac{1}{2\sqrt{3}}z_{2}\right)a \, \mathbf{\hat{y}}-\frac{1}{3}\left(x_{2}+y_{2}+z_{2}\right)c \, \mathbf{\hat{z}} & \left(6f\right) & \text{Cl II} \\ \mathbf{B}_{11} & = & -z_{2} \, \mathbf{a}_{1}-x_{2} \, \mathbf{a}_{2}-y_{2} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(y_{2}-z_{2}\right)a \, \mathbf{\hat{x}} + \left(-\frac{1}{\sqrt{3}}x_{2}+\frac{1}{2\sqrt{3}}y_{2}+\frac{1}{2\sqrt{3}}z_{2}\right)a \, \mathbf{\hat{y}}-\frac{1}{3}\left(x_{2}+y_{2}+z_{2}\right)c \, \mathbf{\hat{z}} & \left(6f\right) & \text{Cl II} \\ \mathbf{B}_{12} & = & -y_{2} \, \mathbf{a}_{1}-z_{2} \, \mathbf{a}_{2}-x_{2} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{2}-y_{2}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2\sqrt{3}}x_{2}+\frac{1}{2\sqrt{3}}y_{2}-\frac{1}{\sqrt{3}}z_{2}\right)a \, \mathbf{\hat{y}}-\frac{1}{3}\left(x_{2}+y_{2}+z_{2}\right)c \, \mathbf{\hat{z}} & \left(6f\right) & \text{Cl II} \\ \mathbf{B}_{13} & = & x_{3} \, \mathbf{a}_{1} + y_{3} \, \mathbf{a}_{2} + z_{3} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{3}-z_{3}\right)a \, \mathbf{\hat{x}} + \left(-\frac{1}{2\sqrt{3}}x_{3}+\frac{1}{\sqrt{3}}y_{3}-\frac{1}{2\sqrt{3}}z_{3}\right)a \, \mathbf{\hat{y}} + \frac{1}{3}\left(x_{3}+y_{3}+z_{3}\right)c \, \mathbf{\hat{z}} & \left(6f\right) & \text{Pd} \\ \mathbf{B}_{14} & = & z_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + y_{3} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(-y_{3}+z_{3}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{\sqrt{3}}x_{3}-\frac{1}{2\sqrt{3}}y_{3}-\frac{1}{2\sqrt{3}}z_{3}\right)a \, \mathbf{\hat{y}} + \frac{1}{3}\left(x_{3}+y_{3}+z_{3}\right)c \, \mathbf{\hat{z}} & \left(6f\right) & \text{Pd} \\ \mathbf{B}_{15} & = & y_{3} \, \mathbf{a}_{1} + z_{3} \, \mathbf{a}_{2} + x_{3} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(-x_{3}+y_{3}\right)a \, \mathbf{\hat{x}} + \left(-\frac{1}{2\sqrt{3}}x_{3}-\frac{1}{2\sqrt{3}}y_{3}+\frac{1}{\sqrt{3}}z_{3}\right)a \, \mathbf{\hat{y}} + \frac{1}{3}\left(x_{3}+y_{3}+z_{3}\right)c \, \mathbf{\hat{z}} & \left(6f\right) & \text{Pd} \\ \mathbf{B}_{16} & = & -x_{3} \, \mathbf{a}_{1}-y_{3} \, \mathbf{a}_{2}-z_{3} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(-x_{3}+z_{3}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2\sqrt{3}}x_{3}-\frac{1}{\sqrt{3}}y_{3}+\frac{1}{2\sqrt{3}}z_{3}\right)a \, \mathbf{\hat{y}}-\frac{1}{3}\left(x_{3}+y_{3}+z_{3}\right)c \, \mathbf{\hat{z}} & \left(6f\right) & \text{Pd} \\ \mathbf{B}_{17} & = & -z_{3} \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2}-y_{3} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(y_{3}-z_{3}\right)a \, \mathbf{\hat{x}} + \left(-\frac{1}{\sqrt{3}}x_{3}+\frac{1}{2\sqrt{3}}y_{3}+\frac{1}{2\sqrt{3}}z_{3}\right)a \, \mathbf{\hat{y}}-\frac{1}{3}\left(x_{3}+y_{3}+z_{3}\right)c \, \mathbf{\hat{z}} & \left(6f\right) & \text{Pd} \\ \mathbf{B}_{18} & = & -y_{3} \, \mathbf{a}_{1}-z_{3} \, \mathbf{a}_{2}-x_{3} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{3}-y_{3}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2\sqrt{3}}x_{3}+\frac{1}{2\sqrt{3}}y_{3}-\frac{1}{\sqrt{3}}z_{3}\right)a \, \mathbf{\hat{y}}-\frac{1}{3}\left(x_{3}+y_{3}+z_{3}\right)c \, \mathbf{\hat{z}} & \left(6f\right) & \text{Pd} \\ \end{array} \]