BiGaO3 Structure: ABC3_oP20_54_e_d_cf

Picture of Structure; Click for Big Picture
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=
$a$,$b/a$,$c/a$,$y_{1}$,$z_{2}$,$z_{3}$,$x_{4}$,$y_{4}$,$z_{4}$


Simple Orthorhombic primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & a \, \mathbf{\hat{x}} \\ \mathbf{a}_2 & = & b \, \mathbf{\hat{y}} \\ \mathbf{a}_3 & = & c \, \mathbf{\hat{z}} \\ \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{O II} \\ \end{array} \]

References

  • H. Yusa, A. A. Belik, E. Takayama–Muromachi, N. Hirao, and Y. Ohishi, High–pressure phase transitions in BiMO3 (M = Al, Ga, and In): it In situ x–ray diffraction and Raman scattering experiments, Phys. Rev. B 80, 214103 (2009), doi:10.1103/PhysRevB.80.214103.

Found in

  • P. Villars and K. Cenzual, Pearson's Crystal Data – Crystal Structure Database for Inorganic Compounds, ASM International (2013).

Geometry files


Prototype Generator

aflow --proto=ABC3_oP20_54_e_d_cf --params=

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