AFLOW Prototype: A4BC12D2_oC76_63_eg_c_f3gh_g
Prototype | : | Al4FeO12Si2 |
AFLOW prototype label | : | A4BC12D2_oC76_63_eg_c_f3gh_g |
Strukturbericht designation | : | $S0_{4}$ |
Pearson symbol | : | oC76 |
Space group number | : | 63 |
Space group symbol | : | $Cmcm$ |
AFLOW prototype command | : | aflow --proto=A4BC12D2_oC76_63_eg_c_f3gh_g --params=$a$,$b/a$,$c/a$,$y_{1}$,$x_{2}$,$y_{3}$,$z_{3}$,$x_{4}$,$y_{4}$,$x_{5}$,$y_{5}$,$x_{6}$,$y_{6}$,$x_{7}$,$y_{7}$,$x_{8}$,$y_{8}$,$x_{9}$,$y_{9}$,$z_{9}$ |
Basis vectors:
\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1} & = & -y_{1} \, \mathbf{a}_{1} + y_{1} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & y_{1}b \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(4c\right) & \text{Fe} \\ \mathbf{B}_{2} & = & y_{1} \, \mathbf{a}_{1}-y_{1} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & -y_{1}b \, \mathbf{\hat{y}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(4c\right) & \text{Fe} \\ \mathbf{B}_{3} & = & x_{2} \, \mathbf{a}_{1} + x_{2} \, \mathbf{a}_{2} & = & x_{2}a \, \mathbf{\hat{x}} & \left(8e\right) & \text{Al I} \\ \mathbf{B}_{4} & = & -x_{2} \, \mathbf{a}_{1}-x_{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & -x_{2}a \, \mathbf{\hat{x}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(8e\right) & \text{Al I} \\ \mathbf{B}_{5} & = & -x_{2} \, \mathbf{a}_{1}-x_{2} \, \mathbf{a}_{2} & = & -x_{2}a \, \mathbf{\hat{x}} & \left(8e\right) & \text{Al I} \\ \mathbf{B}_{6} & = & x_{2} \, \mathbf{a}_{1} + x_{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & x_{2}a \, \mathbf{\hat{x}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(8e\right) & \text{Al I} \\ \mathbf{B}_{7} & = & -y_{3} \, \mathbf{a}_{1} + y_{3} \, \mathbf{a}_{2} + z_{3} \, \mathbf{a}_{3} & = & y_{3}b \, \mathbf{\hat{y}} + z_{3}c \, \mathbf{\hat{z}} & \left(8f\right) & \text{O I} \\ \mathbf{B}_{8} & = & y_{3} \, \mathbf{a}_{1}-y_{3} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{3}\right) \, \mathbf{a}_{3} & = & -y_{3}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{3}\right)c \, \mathbf{\hat{z}} & \left(8f\right) & \text{O I} \\ \mathbf{B}_{9} & = & -y_{3} \, \mathbf{a}_{1} + y_{3} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{3}\right) \, \mathbf{a}_{3} & = & y_{3}b \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{3}\right)c \, \mathbf{\hat{z}} & \left(8f\right) & \text{O I} \\ \mathbf{B}_{10} & = & y_{3} \, \mathbf{a}_{1}-y_{3} \, \mathbf{a}_{2}-z_{3} \, \mathbf{a}_{3} & = & -y_{3}b \, \mathbf{\hat{y}}-z_{3}c \, \mathbf{\hat{z}} & \left(8f\right) & \text{O I} \\ \mathbf{B}_{11} & = & \left(x_{4}-y_{4}\right) \, \mathbf{a}_{1} + \left(x_{4}+y_{4}\right) \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}} + y_{4}b \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(8g\right) & \text{Al II} \\ \mathbf{B}_{12} & = & \left(-x_{4}+y_{4}\right) \, \mathbf{a}_{1} + \left(-x_{4}-y_{4}\right) \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}}-y_{4}b \, \mathbf{\hat{y}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(8g\right) & \text{Al II} \\ \mathbf{B}_{13} & = & \left(-x_{4}-y_{4}\right) \, \mathbf{a}_{1} + \left(-x_{4}+y_{4}\right) \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}} + y_{4}b \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(8g\right) & \text{Al II} \\ \mathbf{B}_{14} & = & \left(x_{4}+y_{4}\right) \, \mathbf{a}_{1} + \left(x_{4}-y_{4}\right) \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}}-y_{4}b \, \mathbf{\hat{y}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(8g\right) & \text{Al II} \\ \mathbf{B}_{15} & = & \left(x_{5}-y_{5}\right) \, \mathbf{a}_{1} + \left(x_{5}+y_{5}\right) \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & x_{5}a \, \mathbf{\hat{x}} + y_{5}b \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(8g\right) & \text{O II} \\ \mathbf{B}_{16} & = & \left(-x_{5}+y_{5}\right) \, \mathbf{a}_{1} + \left(-x_{5}-y_{5}\right) \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{x}}-y_{5}b \, \mathbf{\hat{y}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(8g\right) & \text{O II} \\ \mathbf{B}_{17} & = & \left(-x_{5}-y_{5}\right) \, \mathbf{a}_{1} + \left(-x_{5}+y_{5}\right) \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{x}} + y_{5}b \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(8g\right) & \text{O II} \\ \mathbf{B}_{18} & = & \left(x_{5}+y_{5}\right) \, \mathbf{a}_{1} + \left(x_{5}-y_{5}\right) \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & x_{5}a \, \mathbf{\hat{x}}-y_{5}b \, \mathbf{\hat{y}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(8g\right) & \text{O II} \\ \mathbf{B}_{19} & = & \left(x_{6}-y_{6}\right) \, \mathbf{a}_{1} + \left(x_{6}+y_{6}\right) \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & x_{6}a \, \mathbf{\hat{x}} + y_{6}b \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(8g\right) & \text{O III} \\ \mathbf{B}_{20} & = & \left(-x_{6}+y_{6}\right) \, \mathbf{a}_{1} + \left(-x_{6}-y_{6}\right) \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & -x_{6}a \, \mathbf{\hat{x}}-y_{6}b \, \mathbf{\hat{y}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(8g\right) & \text{O III} \\ \mathbf{B}_{21} & = & \left(-x_{6}-y_{6}\right) \, \mathbf{a}_{1} + \left(-x_{6}+y_{6}\right) \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & -x_{6}a \, \mathbf{\hat{x}} + y_{6}b \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(8g\right) & \text{O III} \\ \mathbf{B}_{22} & = & \left(x_{6}+y_{6}\right) \, \mathbf{a}_{1} + \left(x_{6}-y_{6}\right) \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & x_{6}a \, \mathbf{\hat{x}}-y_{6}b \, \mathbf{\hat{y}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(8g\right) & \text{O III} \\ \mathbf{B}_{23} & = & \left(x_{7}-y_{7}\right) \, \mathbf{a}_{1} + \left(x_{7}+y_{7}\right) \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & x_{7}a \, \mathbf{\hat{x}} + y_{7}b \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(8g\right) & \text{O IV} \\ \mathbf{B}_{24} & = & \left(-x_{7}+y_{7}\right) \, \mathbf{a}_{1} + \left(-x_{7}-y_{7}\right) \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & -x_{7}a \, \mathbf{\hat{x}}-y_{7}b \, \mathbf{\hat{y}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(8g\right) & \text{O IV} \\ \mathbf{B}_{25} & = & \left(-x_{7}-y_{7}\right) \, \mathbf{a}_{1} + \left(-x_{7}+y_{7}\right) \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & -x_{7}a \, \mathbf{\hat{x}} + y_{7}b \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(8g\right) & \text{O IV} \\ \mathbf{B}_{26} & = & \left(x_{7}+y_{7}\right) \, \mathbf{a}_{1} + \left(x_{7}-y_{7}\right) \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & x_{7}a \, \mathbf{\hat{x}}-y_{7}b \, \mathbf{\hat{y}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(8g\right) & \text{O IV} \\ \mathbf{B}_{27} & = & \left(x_{8}-y_{8}\right) \, \mathbf{a}_{1} + \left(x_{8}+y_{8}\right) \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & x_{8}a \, \mathbf{\hat{x}} + y_{8}b \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(8g\right) & \text{Si} \\ \mathbf{B}_{28} & = & \left(-x_{8}+y_{8}\right) \, \mathbf{a}_{1} + \left(-x_{8}-y_{8}\right) \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & -x_{8}a \, \mathbf{\hat{x}}-y_{8}b \, \mathbf{\hat{y}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(8g\right) & \text{Si} \\ \mathbf{B}_{29} & = & \left(-x_{8}-y_{8}\right) \, \mathbf{a}_{1} + \left(-x_{8}+y_{8}\right) \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & -x_{8}a \, \mathbf{\hat{x}} + y_{8}b \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(8g\right) & \text{Si} \\ \mathbf{B}_{30} & = & \left(x_{8}+y_{8}\right) \, \mathbf{a}_{1} + \left(x_{8}-y_{8}\right) \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & x_{8}a \, \mathbf{\hat{x}}-y_{8}b \, \mathbf{\hat{y}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(8g\right) & \text{Si} \\ \mathbf{B}_{31} & = & \left(x_{9}-y_{9}\right) \, \mathbf{a}_{1} + \left(x_{9}+y_{9}\right) \, \mathbf{a}_{2} + z_{9} \, \mathbf{a}_{3} & = & x_{9}a \, \mathbf{\hat{x}} + y_{9}b \, \mathbf{\hat{y}} + z_{9}c \, \mathbf{\hat{z}} & \left(16h\right) & \text{O V} \\ \mathbf{B}_{32} & = & \left(-x_{9}+y_{9}\right) \, \mathbf{a}_{1} + \left(-x_{9}-y_{9}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{9}\right) \, \mathbf{a}_{3} & = & -x_{9}a \, \mathbf{\hat{x}}-y_{9}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{9}\right)c \, \mathbf{\hat{z}} & \left(16h\right) & \text{O V} \\ \mathbf{B}_{33} & = & \left(-x_{9}-y_{9}\right) \, \mathbf{a}_{1} + \left(-x_{9}+y_{9}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{9}\right) \, \mathbf{a}_{3} & = & -x_{9}a \, \mathbf{\hat{x}} + y_{9}b \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{9}\right)c \, \mathbf{\hat{z}} & \left(16h\right) & \text{O V} \\ \mathbf{B}_{34} & = & \left(x_{9}+y_{9}\right) \, \mathbf{a}_{1} + \left(x_{9}-y_{9}\right) \, \mathbf{a}_{2}-z_{9} \, \mathbf{a}_{3} & = & x_{9}a \, \mathbf{\hat{x}}-y_{9}b \, \mathbf{\hat{y}}-z_{9}c \, \mathbf{\hat{z}} & \left(16h\right) & \text{O V} \\ \mathbf{B}_{35} & = & \left(-x_{9}+y_{9}\right) \, \mathbf{a}_{1} + \left(-x_{9}-y_{9}\right) \, \mathbf{a}_{2}-z_{9} \, \mathbf{a}_{3} & = & -x_{9}a \, \mathbf{\hat{x}}-y_{9}b \, \mathbf{\hat{y}}-z_{9}c \, \mathbf{\hat{z}} & \left(16h\right) & \text{O V} \\ \mathbf{B}_{36} & = & \left(x_{9}-y_{9}\right) \, \mathbf{a}_{1} + \left(x_{9}+y_{9}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{9}\right) \, \mathbf{a}_{3} & = & x_{9}a \, \mathbf{\hat{x}} + y_{9}b \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{9}\right)c \, \mathbf{\hat{z}} & \left(16h\right) & \text{O V} \\ \mathbf{B}_{37} & = & \left(x_{9}+y_{9}\right) \, \mathbf{a}_{1} + \left(x_{9}-y_{9}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{9}\right) \, \mathbf{a}_{3} & = & x_{9}a \, \mathbf{\hat{x}}-y_{9}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{9}\right)c \, \mathbf{\hat{z}} & \left(16h\right) & \text{O V} \\ \mathbf{B}_{38} & = & \left(-x_{9}-y_{9}\right) \, \mathbf{a}_{1} + \left(-x_{9}+y_{9}\right) \, \mathbf{a}_{2} + z_{9} \, \mathbf{a}_{3} & = & -x_{9}a \, \mathbf{\hat{x}} + y_{9}b \, \mathbf{\hat{y}} + z_{9}c \, \mathbf{\hat{z}} & \left(16h\right) & \text{O V} \\ \end{array} \]