Encyclopedia of Crystallographic Prototypes

AFLOW Prototype: A11B4_cF120_227_acdf_e

  • M. J. Mehl, D. Hicks, C. Toher, O. Levy, R. M. Hanson, G. L. W. Hart, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 1, Comp. Mat. Sci. 136, S1-S828 (2017). (doi=10.1016/j.commatsci.2017.01.017)
  • D. Hicks, M. J. Mehl, E. Gossett, C. Toher, O. Levy, R. M. Hanson, G. L. W. Hart, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 2, Comp. Mat. Sci. 161, S1-S1011 (2019). (doi=10.1016/j.commatsci.2018.10.043)
  • D. Hicks, M.J. Mehl, M. Esters, C. Oses, O. Levy, G.L.W. Hart, C. Toher, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 3, Comp. Mat. Sci. 199, 110450 (2021). (doi=10.1016/j.commatsci.2021.110450)

$\gamma$–Ga2O3 Structure : A11B4_cF120_227_acdf_e

Picture of Structure; Click for Big Picture
Prototype : Ga2O3
AFLOW prototype label : A11B4_cF120_227_acdf_e
Strukturbericht designation : None
Pearson symbol : cF120
Space group number : 227
Space group symbol : $Fd\bar{3}m$
AFLOW prototype command : aflow --proto=A11B4_cF120_227_acdf_e
--params=
$a$,$x_{4}$,$x_{5}$



Face-centered Cubic primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & \frac12 \, a \, \mathbf{\hat{y}} + \frac12 \, a \, \mathbf{\hat{z}} \\ \mathbf{a}_2 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, a \, \mathbf{\hat{z}} \\ \mathbf{a}_3 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, a \, \mathbf{\hat{y}} \\ \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1} & = & \frac{1}{8} \, \mathbf{a}_{1} + \frac{1}{8} \, \mathbf{a}_{2} + \frac{1}{8} \, \mathbf{a}_{3} & = & \frac{1}{8}a \, \mathbf{\hat{x}} + \frac{1}{8}a \, \mathbf{\hat{y}} + \frac{1}{8}a \, \mathbf{\hat{z}} & \left(8a\right) & \text{Ga I} \\ \mathbf{B}_{2} & = & \frac{7}{8} \, \mathbf{a}_{1} + \frac{7}{8} \, \mathbf{a}_{2} + \frac{7}{8} \, \mathbf{a}_{3} & = & \frac{7}{8}a \, \mathbf{\hat{x}} + \frac{7}{8}a \, \mathbf{\hat{y}} + \frac{7}{8}a \, \mathbf{\hat{z}} & \left(8a\right) & \text{Ga I} \\ \mathbf{B}_{3} & = & 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(16c\right) & \text{Ga II} \\ \mathbf{B}_{4} & = & \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} & \left(16c\right) & \text{Ga II} \\ \mathbf{B}_{5} & = & \frac{1}{2} \, \mathbf{a}_{2} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(16c\right) & \text{Ga II} \\ \mathbf{B}_{6} & = & \frac{1}{2} \, \mathbf{a}_{1} & = & \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(16c\right) & \text{Ga II} \\ \mathbf{B}_{7} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(16d\right) & \text{Ga III} \\ \mathbf{B}_{8} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(16d\right) & \text{Ga III} \\ \mathbf{B}_{9} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(16d\right) & \text{Ga III} \\ \mathbf{B}_{10} & = & \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(16d\right) & \text{Ga III} \\ \mathbf{B}_{11} & = & x_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} + x_{4} \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}} + x_{4}a \, \mathbf{\hat{y}} + x_{4}a \, \mathbf{\hat{z}} & \left(32e\right) & \text{O} \\ \mathbf{B}_{12} & = & x_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} - 3x_{4}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{4}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-x_{4}\right)a \, \mathbf{\hat{y}} + x_{4}a \, \mathbf{\hat{z}} & \left(32e\right) & \text{O} \\ \mathbf{B}_{13} & = & x_{4} \, \mathbf{a}_{1} + \left(\frac{1}{2} - 3x_{4}\right) \, \mathbf{a}_{2} + x_{4} \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{4}\right)a \, \mathbf{\hat{x}} + x_{4}a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-x_{4}\right)a \, \mathbf{\hat{z}} & \left(32e\right) & \text{O} \\ \mathbf{B}_{14} & = & \left(\frac{1}{2} - 3x_{4}\right) \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} + x_{4} \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-x_{4}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-x_{4}\right)a \, \mathbf{\hat{z}} & \left(32e\right) & \text{O} \\ \mathbf{B}_{15} & = & -x_{4} \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} +3x_{4}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{4}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{4}\right)a \, \mathbf{\hat{y}}-x_{4}a \, \mathbf{\hat{z}} & \left(32e\right) & \text{O} \\ \mathbf{B}_{16} & = & -x_{4} \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2}-x_{4} \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}}-x_{4}a \, \mathbf{\hat{y}}-x_{4}a \, \mathbf{\hat{z}} & \left(32e\right) & \text{O} \\ \mathbf{B}_{17} & = & -x_{4} \, \mathbf{a}_{1} + \left(\frac{1}{2} +3x_{4}\right) \, \mathbf{a}_{2}-x_{4} \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{4}\right)a \, \mathbf{\hat{x}}-x_{4}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{4}\right)a \, \mathbf{\hat{z}} & \left(32e\right) & \text{O} \\ \mathbf{B}_{18} & = & \left(\frac{1}{2} +3x_{4}\right) \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2}-x_{4} \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{4}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{4}\right)a \, \mathbf{\hat{z}} & \left(32e\right) & \text{O} \\ \mathbf{B}_{19} & = & \left(\frac{1}{4} - x_{5}\right) \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2} + x_{5} \, \mathbf{a}_{3} & = & x_{5}a \, \mathbf{\hat{x}} + \frac{1}{8}a \, \mathbf{\hat{y}} + \frac{1}{8}a \, \mathbf{\hat{z}} & \left(48f\right) & \text{Ga IV} \\ \mathbf{B}_{20} & = & x_{5} \, \mathbf{a}_{1} + \left(\frac{1}{4} - x_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} - x_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{5}\right)a \, \mathbf{\hat{x}} + \frac{1}{8}a \, \mathbf{\hat{y}} + \frac{1}{8}a \, \mathbf{\hat{z}} & \left(48f\right) & \text{Ga IV} \\ \mathbf{B}_{21} & = & x_{5} \, \mathbf{a}_{1} + \left(\frac{1}{4} - x_{5}\right) \, \mathbf{a}_{2} + x_{5} \, \mathbf{a}_{3} & = & \frac{1}{8}a \, \mathbf{\hat{x}} + x_{5}a \, \mathbf{\hat{y}} + \frac{1}{8}a \, \mathbf{\hat{z}} & \left(48f\right) & \text{Ga IV} \\ \mathbf{B}_{22} & = & \left(\frac{1}{4} - x_{5}\right) \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2} + \left(\frac{1}{4} - x_{5}\right) \, \mathbf{a}_{3} & = & \frac{1}{8}a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-x_{5}\right)a \, \mathbf{\hat{y}} + \frac{1}{8}a \, \mathbf{\hat{z}} & \left(48f\right) & \text{Ga IV} \\ \mathbf{B}_{23} & = & x_{5} \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2} + \left(\frac{1}{4} - x_{5}\right) \, \mathbf{a}_{3} & = & \frac{1}{8}a \, \mathbf{\hat{x}} + \frac{1}{8}a \, \mathbf{\hat{y}} + x_{5}a \, \mathbf{\hat{z}} & \left(48f\right) & \text{Ga IV} \\ \mathbf{B}_{24} & = & \left(\frac{1}{4} - x_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} - x_{5}\right) \, \mathbf{a}_{2} + x_{5} \, \mathbf{a}_{3} & = & \frac{1}{8}a \, \mathbf{\hat{x}} + \frac{1}{8}a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-x_{5}\right)a \, \mathbf{\hat{z}} & \left(48f\right) & \text{Ga IV} \\ \mathbf{B}_{25} & = & \left(\frac{3}{4} +x_{5}\right) \, \mathbf{a}_{1}-x_{5} \, \mathbf{a}_{2} + \left(\frac{3}{4} +x_{5}\right) \, \mathbf{a}_{3} & = & \frac{3}{8}a \, \mathbf{\hat{x}} + \left(\frac{3}{4} +x_{5}\right)a \, \mathbf{\hat{y}} + \frac{3}{8}a \, \mathbf{\hat{z}} & \left(48f\right) & \text{Ga IV} \\ \mathbf{B}_{26} & = & -x_{5} \, \mathbf{a}_{1} + \left(\frac{3}{4} +x_{5}\right) \, \mathbf{a}_{2}-x_{5} \, \mathbf{a}_{3} & = & \frac{3}{8}a \, \mathbf{\hat{x}}-x_{5}a \, \mathbf{\hat{y}} + \frac{3}{8}a \, \mathbf{\hat{z}} & \left(48f\right) & \text{Ga IV} \\ \mathbf{B}_{27} & = & -x_{5} \, \mathbf{a}_{1} + \left(\frac{3}{4} +x_{5}\right) \, \mathbf{a}_{2} + \left(\frac{3}{4} +x_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{3}{4} +x_{5}\right)a \, \mathbf{\hat{x}} + \frac{3}{8}a \, \mathbf{\hat{y}} + \frac{3}{8}a \, \mathbf{\hat{z}} & \left(48f\right) & \text{Ga IV} \\ \mathbf{B}_{28} & = & \left(\frac{3}{4} +x_{5}\right) \, \mathbf{a}_{1}-x_{5} \, \mathbf{a}_{2}-x_{5} \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{x}} + \frac{3}{8}a \, \mathbf{\hat{y}} + \frac{3}{8}a \, \mathbf{\hat{z}} & \left(48f\right) & \text{Ga IV} \\ \mathbf{B}_{29} & = & -x_{5} \, \mathbf{a}_{1}-x_{5} \, \mathbf{a}_{2} + \left(\frac{3}{4} +x_{5}\right) \, \mathbf{a}_{3} & = & \frac{3}{8}a \, \mathbf{\hat{x}} + \frac{3}{8}a \, \mathbf{\hat{y}}-x_{5}a \, \mathbf{\hat{z}} & \left(48f\right) & \text{Ga IV} \\ \mathbf{B}_{30} & = & \left(\frac{3}{4} +x_{5}\right) \, \mathbf{a}_{1} + \left(\frac{3}{4} +x_{5}\right) \, \mathbf{a}_{2}-x_{5} \, \mathbf{a}_{3} & = & \frac{3}{8}a \, \mathbf{\hat{x}} + \frac{3}{8}a \, \mathbf{\hat{y}} + \left(\frac{3}{4} +x_{5}\right)a \, \mathbf{\hat{z}} & \left(48f\right) & \text{Ga IV} \\ \end{array} \]

References

  • H. Y. Playford, A. C. Hannon, E. R. Barney, and R. I. Walton, Structures of Uncharacterised Polymorphs of Gallium Oxide from Total Neutron Diffraction, Chem.: Eur. J. 19, 2803–2813 (2013), doi:10.1002/chem.201203359.

Geometry files


Prototype Generator

aflow --proto=A11B4_cF120_227_acdf_e --params=

Species:

Running:

Output: