AFLOW Prototype: AB4C_oC24_63_a_fg_c
Prototype | : | MgOS |
AFLOW prototype label | : | AB4C_oC24_63_a_fg_c |
Strukturbericht designation | : | None |
Pearson symbol | : | oC24 |
Space group number | : | 63 |
Space group symbol | : | $Cmcm$ |
AFLOW prototype command | : | aflow --proto=AB4C_oC24_63_a_fg_c --params=$a$,$b/a$,$c/a$,$y_{2}$,$y_{3}$,$z_{3}$,$x_{4}$,$y_{4}$ |
Basis vectors:
\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1} & = & 0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & = & 0 \, \mathbf{\hat{x}} + 0 \, \mathbf{\hat{y}} + 0 \, \mathbf{\hat{z}} & \left(4a\right) & \text{Mg} \\ \mathbf{B}_{2} & = & \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}c \, \mathbf{\hat{z}} & \left(4a\right) & \text{Mg} \\ \mathbf{B}_{3} & = & -y_{2} \, \mathbf{a}_{1} + y_{2} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & y_{2}b \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(4c\right) & \text{S} \\ \mathbf{B}_{4} & = & y_{2} \, \mathbf{a}_{1}-y_{2} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & -y_{2}b \, \mathbf{\hat{y}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(4c\right) & \text{S} \\ \mathbf{B}_{5} & = & -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}_{6} & = & 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}_{7} & = & -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}_{8} & = & 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}_{9} & = & \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{O II} \\ \mathbf{B}_{10} & = & \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{O II} \\ \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{O 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{O II} \\ \end{array} \]