AFLOW Prototype: A4B12C3_cI76_220_c_e_a
Prototype | : | Bi4O12Si3 |
AFLOW prototype label | : | A4B12C3_cI76_220_c_e_a |
Strukturbericht designation | : | $S1_{5}$ |
Pearson symbol | : | cI76 |
Space group number | : | 220 |
Space group symbol | : | $I\bar{4}3d$ |
AFLOW prototype command | : | aflow --proto=A4B12C3_cI76_220_c_e_a --params=$a$,$x_{2}$,$x_{3}$,$y_{3}$,$z_{3}$ |
Basis vectors:
\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1} & = & \frac{1}{4} \, \mathbf{a}_{1} + \frac{5}{8} \, \mathbf{a}_{2} + \frac{3}{8} \, \mathbf{a}_{3} & = & \frac{3}{8}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(12a\right) & \text{Si} \\ \mathbf{B}_{2} & = & \frac{3}{4} \, \mathbf{a}_{1} + \frac{7}{8} \, \mathbf{a}_{2} + \frac{1}{8} \, \mathbf{a}_{3} & = & \frac{1}{8}a \, \mathbf{\hat{x}} + \frac{3}{4}a \, \mathbf{\hat{z}} & \left(12a\right) & \text{Si} \\ \mathbf{B}_{3} & = & \frac{3}{8} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \frac{5}{8} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{3}{8}a \, \mathbf{\hat{y}} & \left(12a\right) & \text{Si} \\ \mathbf{B}_{4} & = & \frac{1}{8} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \frac{7}{8} \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}} + \frac{1}{8}a \, \mathbf{\hat{y}} & \left(12a\right) & \text{Si} \\ \mathbf{B}_{5} & = & \frac{5}{8} \, \mathbf{a}_{1} + \frac{3}{8} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{3}{8}a \, \mathbf{\hat{z}} & \left(12a\right) & \text{Si} \\ \mathbf{B}_{6} & = & \frac{7}{8} \, \mathbf{a}_{1} + \frac{1}{8} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{y}} + \frac{1}{8}a \, \mathbf{\hat{z}} & \left(12a\right) & \text{Si} \\ \mathbf{B}_{7} & = & 2x_{2} \, \mathbf{a}_{1} + 2x_{2} \, \mathbf{a}_{2} + 2x_{2} \, \mathbf{a}_{3} & = & x_{2}a \, \mathbf{\hat{x}} + x_{2}a \, \mathbf{\hat{y}} + x_{2}a \, \mathbf{\hat{z}} & \left(16c\right) & \text{Bi} \\ \mathbf{B}_{8} & = & \frac{1}{2} \, \mathbf{a}_{1} + \left(\frac{1}{2} - 2x_{2}\right) \, \mathbf{a}_{3} & = & -x_{2}a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-x_{2}\right)a \, \mathbf{\hat{y}} + x_{2}a \, \mathbf{\hat{z}} & \left(16c\right) & \text{Bi} \\ \mathbf{B}_{9} & = & \left(\frac{1}{2} - 2x_{2}\right) \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{2}\right)a \, \mathbf{\hat{x}} + x_{2}a \, \mathbf{\hat{y}}-x_{2}a \, \mathbf{\hat{z}} & \left(16c\right) & \text{Bi} \\ \mathbf{B}_{10} & = & \left(\frac{1}{2} - 2x_{2}\right) \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} & = & x_{2}a \, \mathbf{\hat{x}}-x_{2}a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-x_{2}\right)a \, \mathbf{\hat{z}} & \left(16c\right) & \text{Bi} \\ \mathbf{B}_{11} & = & \left(\frac{1}{2} +2x_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +2x_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +2x_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{2}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{2}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{2}\right)a \, \mathbf{\hat{z}} & \left(16c\right) & \text{Bi} \\ \mathbf{B}_{12} & = & \frac{1}{2} \, \mathbf{a}_{1}-2x_{2} \, \mathbf{a}_{3} & = & -\left(x_{2}+\frac{1}{4}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-x_{2}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{2}\right)a \, \mathbf{\hat{z}} & \left(16c\right) & \text{Bi} \\ \mathbf{B}_{13} & = & -2x_{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} & = & \left(\frac{1}{4} +x_{2}\right)a \, \mathbf{\hat{x}}-\left(x_{2}+\frac{1}{4}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-x_{2}\right)a \, \mathbf{\hat{z}} & \left(16c\right) & \text{Bi} \\ \mathbf{B}_{14} & = & -2x_{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{2}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{2}\right)a \, \mathbf{\hat{y}}-\left(x_{2}+\frac{1}{4}\right)a \, \mathbf{\hat{z}} & \left(16c\right) & \text{Bi} \\ \mathbf{B}_{15} & = & \left(y_{3}+z_{3}\right) \, \mathbf{a}_{1} + \left(x_{3}+z_{3}\right) \, \mathbf{a}_{2} + \left(x_{3}+y_{3}\right) \, \mathbf{a}_{3} & = & x_{3}a \, \mathbf{\hat{x}} + y_{3}a \, \mathbf{\hat{y}} + z_{3}a \, \mathbf{\hat{z}} & \left(48e\right) & \text{O} \\ \mathbf{B}_{16} & = & \left(\frac{1}{2} - y_{3} + z_{3}\right) \, \mathbf{a}_{1} + \left(-x_{3}+z_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{3} - y_{3}\right) \, \mathbf{a}_{3} & = & -x_{3}a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-y_{3}\right)a \, \mathbf{\hat{y}} + z_{3}a \, \mathbf{\hat{z}} & \left(48e\right) & \text{O} \\ \mathbf{B}_{17} & = & \left(y_{3}-z_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{3} - z_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{3} + y_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{3}\right)a \, \mathbf{\hat{x}} + y_{3}a \, \mathbf{\hat{y}}-z_{3}a \, \mathbf{\hat{z}} & \left(48e\right) & \text{O} \\ \mathbf{B}_{18} & = & \left(\frac{1}{2} - y_{3} - z_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{3} - z_{3}\right) \, \mathbf{a}_{2} + \left(x_{3}-y_{3}\right) \, \mathbf{a}_{3} & = & x_{3}a \, \mathbf{\hat{x}}-y_{3}a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{3}\right)a \, \mathbf{\hat{z}} & \left(48e\right) & \text{O} \\ \mathbf{B}_{19} & = & \left(x_{3}+y_{3}\right) \, \mathbf{a}_{1} + \left(y_{3}+z_{3}\right) \, \mathbf{a}_{2} + \left(x_{3}+z_{3}\right) \, \mathbf{a}_{3} & = & z_{3}a \, \mathbf{\hat{x}} + x_{3}a \, \mathbf{\hat{y}} + y_{3}a \, \mathbf{\hat{z}} & \left(48e\right) & \text{O} \\ \mathbf{B}_{20} & = & \left(\frac{1}{2} - x_{3} - y_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{3} + z_{3}\right) \, \mathbf{a}_{2} + \left(-x_{3}+z_{3}\right) \, \mathbf{a}_{3} & = & z_{3}a \, \mathbf{\hat{x}}-x_{3}a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-y_{3}\right)a \, \mathbf{\hat{z}} & \left(48e\right) & \text{O} \\ \mathbf{B}_{21} & = & \left(\frac{1}{2} - x_{3} + y_{3}\right) \, \mathbf{a}_{1} + \left(y_{3}-z_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{3} - z_{3}\right) \, \mathbf{a}_{3} & = & -z_{3}a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-x_{3}\right)a \, \mathbf{\hat{y}} + y_{3}a \, \mathbf{\hat{z}} & \left(48e\right) & \text{O} \\ \mathbf{B}_{22} & = & \left(x_{3}-y_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{3} - z_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{3} - z_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-z_{3}\right)a \, \mathbf{\hat{x}} + x_{3}a \, \mathbf{\hat{y}}-y_{3}a \, \mathbf{\hat{z}} & \left(48e\right) & \text{O} \\ \mathbf{B}_{23} & = & \left(x_{3}+z_{3}\right) \, \mathbf{a}_{1} + \left(x_{3}+y_{3}\right) \, \mathbf{a}_{2} + \left(y_{3}+z_{3}\right) \, \mathbf{a}_{3} & = & y_{3}a \, \mathbf{\hat{x}} + z_{3}a \, \mathbf{\hat{y}} + x_{3}a \, \mathbf{\hat{z}} & \left(48e\right) & \text{O} \\ \mathbf{B}_{24} & = & \left(-x_{3}+z_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{3} - y_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - y_{3} + z_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-y_{3}\right)a \, \mathbf{\hat{x}} + z_{3}a \, \mathbf{\hat{y}}-x_{3}a \, \mathbf{\hat{z}} & \left(48e\right) & \text{O} \\ \mathbf{B}_{25} & = & \left(\frac{1}{2} - x_{3} - z_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{3} + y_{3}\right) \, \mathbf{a}_{2} + \left(y_{3}-z_{3}\right) \, \mathbf{a}_{3} & = & y_{3}a \, \mathbf{\hat{x}}-z_{3}a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-x_{3}\right)a \, \mathbf{\hat{z}} & \left(48e\right) & \text{O} \\ \mathbf{B}_{26} & = & \left(\frac{1}{2} +x_{3} - z_{3}\right) \, \mathbf{a}_{1} + \left(x_{3}-y_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - y_{3} - z_{3}\right) \, \mathbf{a}_{3} & = & -y_{3}a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-z_{3}\right)a \, \mathbf{\hat{y}} + x_{3}a \, \mathbf{\hat{z}} & \left(48e\right) & \text{O} \\ \mathbf{B}_{27} & = & \left(\frac{1}{2} +x_{3} + z_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +y_{3} + z_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{3} + y_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +y_{3}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{3}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{3}\right)a \, \mathbf{\hat{z}} & \left(48e\right) & \text{O} \\ \mathbf{B}_{28} & = & \left(\frac{1}{2} - x_{3} + z_{3}\right) \, \mathbf{a}_{1} + \left(-y_{3}+z_{3}\right) \, \mathbf{a}_{2} + \left(-x_{3}-y_{3}\right) \, \mathbf{a}_{3} & = & -\left(y_{3}+\frac{1}{4}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-x_{3}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{3}\right)a \, \mathbf{\hat{z}} & \left(48e\right) & \text{O} \\ \mathbf{B}_{29} & = & \left(-x_{3}-z_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +y_{3} - z_{3}\right) \, \mathbf{a}_{2} + \left(-x_{3}+y_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +y_{3}\right)a \, \mathbf{\hat{x}}-\left(x_{3}+\frac{1}{4}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-z_{3}\right)a \, \mathbf{\hat{z}} & \left(48e\right) & \text{O} \\ \mathbf{B}_{30} & = & \left(x_{3}-z_{3}\right) \, \mathbf{a}_{1} + \left(-y_{3}-z_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{3} - y_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-y_{3}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{3}\right)a \, \mathbf{\hat{y}}-\left(z_{3}+\frac{1}{4}\right)a \, \mathbf{\hat{z}} & \left(48e\right) & \text{O} \\ \mathbf{B}_{31} & = & \left(\frac{1}{2} +y_{3} + z_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{3} + y_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{3} + z_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{3}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +z_{3}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +y_{3}\right)a \, \mathbf{\hat{z}} & \left(48e\right) & \text{O} \\ \mathbf{B}_{32} & = & \left(-y_{3}+z_{3}\right) \, \mathbf{a}_{1} + \left(-x_{3}-y_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{3} + z_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{3}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +z_{3}\right)a \, \mathbf{\hat{y}}-\left(y_{3}+\frac{1}{4}\right)a \, \mathbf{\hat{z}} & \left(48e\right) & \text{O} \\ \mathbf{B}_{33} & = & \left(\frac{1}{2} +y_{3} - z_{3}\right) \, \mathbf{a}_{1} + \left(-x_{3}+y_{3}\right) \, \mathbf{a}_{2} + \left(-x_{3}-z_{3}\right) \, \mathbf{a}_{3} & = & -\left(x_{3}+\frac{1}{4}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-z_{3}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +y_{3}\right)a \, \mathbf{\hat{z}} & \left(48e\right) & \text{O} \\ \mathbf{B}_{34} & = & \left(-y_{3}-z_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{3} - y_{3}\right) \, \mathbf{a}_{2} + \left(x_{3}-z_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{3}\right)a \, \mathbf{\hat{x}}-\left(z_{3}+\frac{1}{4}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-y_{3}\right)a \, \mathbf{\hat{z}} & \left(48e\right) & \text{O} \\ \mathbf{B}_{35} & = & \left(\frac{1}{2} +x_{3} + y_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{3} + z_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +y_{3} + z_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +z_{3}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +y_{3}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{3}\right)a \, \mathbf{\hat{z}} & \left(48e\right) & \text{O} \\ \mathbf{B}_{36} & = & \left(-x_{3}-y_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{3} + z_{3}\right) \, \mathbf{a}_{2} + \left(-y_{3}+z_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +z_{3}\right)a \, \mathbf{\hat{x}}-\left(y_{3}+\frac{1}{4}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-x_{3}\right)a \, \mathbf{\hat{z}} & \left(48e\right) & \text{O} \\ \mathbf{B}_{37} & = & \left(-x_{3}+y_{3}\right) \, \mathbf{a}_{1} + \left(-x_{3}-z_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +y_{3} - z_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-z_{3}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +y_{3}\right)a \, \mathbf{\hat{y}}-\left(x_{3}+\frac{1}{4}\right)a \, \mathbf{\hat{z}} & \left(48e\right) & \text{O} \\ \mathbf{B}_{38} & = & \left(\frac{1}{2} +x_{3} - y_{3}\right) \, \mathbf{a}_{1} + \left(x_{3}-z_{3}\right) \, \mathbf{a}_{2} + \left(-y_{3}-z_{3}\right) \, \mathbf{a}_{3} & = & -\left(z_{3}+\frac{1}{4}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-y_{3}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{3}\right)a \, \mathbf{\hat{z}} & \left(48e\right) & \text{O} \\ \end{array} \]