$\beta$–Ga2O3 Structure : A2B3_mC20_12_2i_3i

Picture of Structure; Click for Big Picture
Prototype : Ga2O3
AFLOW prototype label : A2B3_mC20_12_2i_3i
Strukturbericht designation : None
Pearson symbol : mC20
Space group number : 12
Space group symbol : $C2/m$
AFLOW prototype command : aflow --proto=A2B3_mC20_12_2i_3i
--params=
$a$,$b/a$,$c/a$,$\beta$,$x_{1}$,$z_{1}$,$x_{2}$,$z_{2}$,$x_{3}$,$z_{3}$,$x_{4}$,$z_{4}$,$x_{5}$,$z_{5}$



Base-centered Monoclinic primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & \frac12 \, a \, \mathbf{\hat{x}} - \frac12 \, b \, \mathbf{\hat{y}} \\ \mathbf{a}_2 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, b \, \mathbf{\hat{y}} \\ \mathbf{a}_3 & = & c \cos\beta \, \mathbf{\hat{x}} + c \sin\beta \, \mathbf{\hat{z}} \\ \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & x_{1} \, \mathbf{a}_{1} + x_{1} \, \mathbf{a}_{2} + z_{1} \, \mathbf{a}_{3} & = & \left(x_{1}a+z_{1}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{1}c\sin\beta \, \mathbf{\hat{z}} & \left(4i\right) & \mbox{Ga I} \\ \mathbf{B}_{2} & = & -x_{1} \, \mathbf{a}_{1}-x_{1} \, \mathbf{a}_{2}-z_{1} \, \mathbf{a}_{3} & = & \left(-x_{1}a-z_{1}c\cos\beta\right) \, \mathbf{\hat{x}}-z_{1}c\sin\beta \, \mathbf{\hat{z}} & \left(4i\right) & \mbox{Ga I} \\ \mathbf{B}_{3} & = & x_{2} \, \mathbf{a}_{1} + x_{2} \, \mathbf{a}_{2} + z_{2} \, \mathbf{a}_{3} & = & \left(x_{2}a+z_{2}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{2}c\sin\beta \, \mathbf{\hat{z}} & \left(4i\right) & \mbox{Ga II} \\ \mathbf{B}_{4} & = & -x_{2} \, \mathbf{a}_{1}-x_{2} \, \mathbf{a}_{2}-z_{2} \, \mathbf{a}_{3} & = & \left(-x_{2}a-z_{2}c\cos\beta\right) \, \mathbf{\hat{x}}-z_{2}c\sin\beta \, \mathbf{\hat{z}} & \left(4i\right) & \mbox{Ga II} \\ \mathbf{B}_{5} & = & x_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + z_{3} \, \mathbf{a}_{3} & = & \left(x_{3}a+z_{3}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{3}c\sin\beta \, \mathbf{\hat{z}} & \left(4i\right) & \mbox{O I} \\ \mathbf{B}_{6} & = & -x_{3} \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2}-z_{3} \, \mathbf{a}_{3} & = & \left(-x_{3}a-z_{3}c\cos\beta\right) \, \mathbf{\hat{x}}-z_{3}c\sin\beta \, \mathbf{\hat{z}} & \left(4i\right) & \mbox{O I} \\ \mathbf{B}_{7} & = & x_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3} & = & \left(x_{4}a+z_{4}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{4}c\sin\beta \, \mathbf{\hat{z}} & \left(4i\right) & \mbox{O II} \\ \mathbf{B}_{8} & = & -x_{4} \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2}-z_{4} \, \mathbf{a}_{3} & = & \left(-x_{4}a-z_{4}c\cos\beta\right) \, \mathbf{\hat{x}}-z_{4}c\sin\beta \, \mathbf{\hat{z}} & \left(4i\right) & \mbox{O II} \\ \mathbf{B}_{9} & = & x_{5} \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3} & = & \left(x_{5}a+z_{5}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{5}c\sin\beta \, \mathbf{\hat{z}} & \left(4i\right) & \mbox{O III} \\ \mathbf{B}_{10} & = & -x_{5} \, \mathbf{a}_{1}-x_{5} \, \mathbf{a}_{2}-z_{5} \, \mathbf{a}_{3} & = & \left(-x_{5}a-z_{5}c\cos\beta\right) \, \mathbf{\hat{x}}-z_{5}c\sin\beta \, \mathbf{\hat{z}} & \left(4i\right) & \mbox{O III} \\ \end{array} \]

References

  • J. Åhman, G. Svensson, and J. Albertsson, A Reinvestigation of $\beta$–Gallium Oxide, Acta Crystallogr. C 52, 1336–1338 (1996), doi:10.1107/S0108270195016404.

Geometry files


Prototype Generator

aflow --proto=A2B3_mC20_12_2i_3i --params=

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