AFLOW Prototype: ABC3_oP20_54_e_d_cf
Prototype | : | BiGaO3 |
AFLOW prototype label | : | ABC3_oP20_54_e_d_cf |
Strukturbericht designation | : | None |
Pearson symbol | : | oP20 |
Space group number | : | 54 |
Space group symbol | : | $Pcca$ |
AFLOW prototype command | : | aflow --proto=ABC3_oP20_54_e_d_cf --params=$a$,$b/a$,$c/a$,$y_{1}$,$z_{2}$,$z_{3}$,$x_{4}$,$y_{4}$,$z_{4}$ |
Basis vectors:
\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{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{O I} \\ \mathbf{B}_{2} & = & \frac{1}{2} \, \mathbf{a}_{1}-y_{1} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}-y_{1}b \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(4c\right) & \text{O I} \\ \mathbf{B}_{3} & = & -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{O I} \\ \mathbf{B}_{4} & = & \frac{1}{2} \, \mathbf{a}_{1} + y_{1} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + y_{1}b \, \mathbf{\hat{y}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(4c\right) & \text{O I} \\ \mathbf{B}_{5} & = & \frac{1}{4} \, \mathbf{a}_{1} + z_{2} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + z_{2}c \, \mathbf{\hat{z}} & \left(4d\right) & \text{Ga} \\ \mathbf{B}_{6} & = & \frac{3}{4} \, \mathbf{a}_{1} + \left(\frac{1}{2} - z_{2}\right) \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - z_{2}\right)c \, \mathbf{\hat{z}} & \left(4d\right) & \text{Ga} \\ \mathbf{B}_{7} & = & \frac{3}{4} \, \mathbf{a}_{1}-z_{2} \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}}-z_{2}c \, \mathbf{\hat{z}} & \left(4d\right) & \text{Ga} \\ \mathbf{B}_{8} & = & \frac{1}{4} \, \mathbf{a}_{1} + \left(\frac{1}{2} +z_{2}\right) \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +z_{2}\right)c \, \mathbf{\hat{z}} & \left(4d\right) & \text{Ga} \\ \mathbf{B}_{9} & = & \frac{1}{4} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + z_{3} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{2}b \, \mathbf{\hat{y}} + z_{3}c \, \mathbf{\hat{z}} & \left(4e\right) & \text{Bi} \\ \mathbf{B}_{10} & = & \frac{3}{4} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{3}\right) \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}} + \frac{1}{2}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} - z_{3}\right)c \, \mathbf{\hat{z}} & \left(4e\right) & \text{Bi} \\ \mathbf{B}_{11} & = & \frac{3}{4} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2}-z_{3} \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}} + \frac{1}{2}b \, \mathbf{\hat{y}}-z_{3}c \, \mathbf{\hat{z}} & \left(4e\right) & \text{Bi} \\ \mathbf{B}_{12} & = & \frac{1}{4} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{3}\right) \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{2}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{3}\right)c \, \mathbf{\hat{z}} & \left(4e\right) & \text{Bi} \\ \mathbf{B}_{13} & = & x_{4} \, \mathbf{a}_{1} + y_{4} \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}} + y_{4}b \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(8f\right) & \text{O II} \\ \mathbf{B}_{14} & = & \left(\frac{1}{2} - x_{4}\right) \, \mathbf{a}_{1}-y_{4} \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - x_{4}\right)a \, \mathbf{\hat{x}}-y_{4}b \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(8f\right) & \text{O II} \\ \mathbf{B}_{15} & = & -x_{4} \, \mathbf{a}_{1} + y_{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{4}\right) \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}} + y_{4}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} - z_{4}\right)c \, \mathbf{\hat{z}} & \left(8f\right) & \text{O II} \\ \mathbf{B}_{16} & = & \left(\frac{1}{2} +x_{4}\right) \, \mathbf{a}_{1}-y_{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{4}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{4}\right)a \, \mathbf{\hat{x}}-y_{4}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} - z_{4}\right)c \, \mathbf{\hat{z}} & \left(8f\right) & \text{O II} \\ \mathbf{B}_{17} & = & -x_{4} \, \mathbf{a}_{1}-y_{4} \, \mathbf{a}_{2}-z_{4} \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}}-y_{4}b \, \mathbf{\hat{y}}-z_{4}c \, \mathbf{\hat{z}} & \left(8f\right) & \text{O II} \\ \mathbf{B}_{18} & = & \left(\frac{1}{2} +x_{4}\right) \, \mathbf{a}_{1} + y_{4} \, \mathbf{a}_{2}-z_{4} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{4}\right)a \, \mathbf{\hat{x}} + y_{4}b \, \mathbf{\hat{y}}-z_{4}c \, \mathbf{\hat{z}} & \left(8f\right) & \text{O II} \\ \mathbf{B}_{19} & = & x_{4} \, \mathbf{a}_{1}-y_{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{4}\right) \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}}-y_{4}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{4}\right)c \, \mathbf{\hat{z}} & \left(8f\right) & \text{O II} \\ \mathbf{B}_{20} & = & \left(\frac{1}{2} - x_{4}\right) \, \mathbf{a}_{1} + y_{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{4}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - x_{4}\right)a \, \mathbf{\hat{x}} + y_{4}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{4}\right)c \, \mathbf{\hat{z}} & \left(8f\right) & \text{O II} \\ \end{array} \]