AFLOW Prototype: A10B3_oF52_42_2abce_ab
Prototype | : | W3O10 |
AFLOW prototype label | : | A10B3_oF52_42_2abce_ab |
Strukturbericht designation | : | None |
Pearson symbol | : | oF52 |
Space group number | : | 42 |
Space group symbol | : | $Fmm2$ |
AFLOW prototype command | : | aflow --proto=A10B3_oF52_42_2abce_ab --params=$a$,$b/a$,$c/a$,$z_{1}$,$z_{2}$,$z_{3}$,$z_{4}$,$z_{5}$,$y_{6}$,$z_{6}$,$x_{7}$,$y_{7}$,$z_{7}$ |
Basis vectors:
\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1} & = & z_{1} \, \mathbf{a}_{1} + z_{1} \, \mathbf{a}_{2}-z_{1} \, \mathbf{a}_{3} & = & z_{1}c \, \mathbf{\hat{z}} & \left(4a\right) & \text{O I} \\ \mathbf{B}_{2} & = & z_{2} \, \mathbf{a}_{1} + z_{2} \, \mathbf{a}_{2}-z_{2} \, \mathbf{a}_{3} & = & z_{2}c \, \mathbf{\hat{z}} & \left(4a\right) & \text{O II} \\ \mathbf{B}_{3} & = & z_{3} \, \mathbf{a}_{1} + z_{3} \, \mathbf{a}_{2}-z_{3} \, \mathbf{a}_{3} & = & z_{3}c \, \mathbf{\hat{z}} & \left(4a\right) & \text{W I} \\ \mathbf{B}_{4} & = & z_{4} \, \mathbf{a}_{1} + z_{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{4}\right) \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(8b\right) & \text{O III} \\ \mathbf{B}_{5} & = & \left(\frac{1}{2} +z_{4}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +z_{4}\right) \, \mathbf{a}_{2}-z_{4} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{4}\right)c \, \mathbf{\hat{z}} & \left(8b\right) & \text{O III} \\ \mathbf{B}_{6} & = & z_{5} \, \mathbf{a}_{1} + z_{5} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{5}\right) \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}} + z_{5}c \, \mathbf{\hat{z}} & \left(8b\right) & \text{W II} \\ \mathbf{B}_{7} & = & \left(\frac{1}{2} +z_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +z_{5}\right) \, \mathbf{a}_{2}-z_{5} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{5}\right)c \, \mathbf{\hat{z}} & \left(8b\right) & \text{W II} \\ \mathbf{B}_{8} & = & \left(y_{6}+z_{6}\right) \, \mathbf{a}_{1} + \left(-y_{6}+z_{6}\right) \, \mathbf{a}_{2} + \left(y_{6}-z_{6}\right) \, \mathbf{a}_{3} & = & y_{6}b \, \mathbf{\hat{y}} + z_{6}c \, \mathbf{\hat{z}} & \left(8c\right) & \text{O IV} \\ \mathbf{B}_{9} & = & \left(-y_{6}+z_{6}\right) \, \mathbf{a}_{1} + \left(y_{6}+z_{6}\right) \, \mathbf{a}_{2} + \left(-y_{6}-z_{6}\right) \, \mathbf{a}_{3} & = & -y_{6}b \, \mathbf{\hat{y}} + z_{6}c \, \mathbf{\hat{z}} & \left(8c\right) & \text{O IV} \\ \mathbf{B}_{10} & = & \left(-x_{7}+y_{7}+z_{7}\right) \, \mathbf{a}_{1} + \left(x_{7}-y_{7}+z_{7}\right) \, \mathbf{a}_{2} + \left(x_{7}+y_{7}-z_{7}\right) \, \mathbf{a}_{3} & = & x_{7}a \, \mathbf{\hat{x}} + y_{7}b \, \mathbf{\hat{y}} + z_{7}c \, \mathbf{\hat{z}} & \left(16e\right) & \text{O V} \\ \mathbf{B}_{11} & = & \left(x_{7}-y_{7}+z_{7}\right) \, \mathbf{a}_{1} + \left(-x_{7}+y_{7}+z_{7}\right) \, \mathbf{a}_{2} + \left(-x_{7}-y_{7}-z_{7}\right) \, \mathbf{a}_{3} & = & -x_{7}a \, \mathbf{\hat{x}}-y_{7}b \, \mathbf{\hat{y}} + z_{7}c \, \mathbf{\hat{z}} & \left(16e\right) & \text{O V} \\ \mathbf{B}_{12} & = & \left(-x_{7}-y_{7}+z_{7}\right) \, \mathbf{a}_{1} + \left(x_{7}+y_{7}+z_{7}\right) \, \mathbf{a}_{2} + \left(x_{7}-y_{7}-z_{7}\right) \, \mathbf{a}_{3} & = & x_{7}a \, \mathbf{\hat{x}}-y_{7}b \, \mathbf{\hat{y}} + z_{7}c \, \mathbf{\hat{z}} & \left(16e\right) & \text{O V} \\ \mathbf{B}_{13} & = & \left(x_{7}+y_{7}+z_{7}\right) \, \mathbf{a}_{1} + \left(-x_{7}-y_{7}+z_{7}\right) \, \mathbf{a}_{2} + \left(-x_{7}+y_{7}-z_{7}\right) \, \mathbf{a}_{3} & = & -x_{7}a \, \mathbf{\hat{x}} + y_{7}b \, \mathbf{\hat{y}} + z_{7}c \, \mathbf{\hat{z}} & \left(16e\right) & \text{O V} \\ \end{array} \]