Encyclopedia of Crystallographic Prototypes

AFLOW Prototype: A2B3_oF40_43_b_ab

  • 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)

Ag2O3 Structure : A2B3_oF40_43_b_ab

Picture of Structure; Click for Big Picture
Prototype : Ag2O3
AFLOW prototype label : A2B3_oF40_43_b_ab
Strukturbericht designation : None
Pearson symbol : oF40
Space group number : 43
Space group symbol : $Fdd2$
AFLOW prototype command : aflow --proto=A2B3_oF40_43_b_ab
--params=
$a$,$b/a$,$c/a$,$z_{1}$,$x_{2}$,$y_{2}$,$z_{2}$,$x_{3}$,$y_{3}$,$z_{3}$


  • This structure is a distortion of the $D5_{5}$ Ag2O3 structure (A3B2_cP10_224_d_b), although (Standke, 1986) does not seem to be aware of the earlier work. This is most likely closer to the correct structure for Ag2O3 than the $D5_{5}$ structure is.

Face-centered Orthorhombic primitive vectors:

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

Basis vectors:

\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1} & = & z_{1} \, \mathbf{a}_{1} + z_{1} \, \mathbf{a}_{2}-z_{1} \, \mathbf{a}_{3} & = & z_{1}c \, \mathbf{\hat{z}} & \left(8a\right) & \text{O I} \\ \mathbf{B}_{2} & = & \left(\frac{1}{4} +z_{1}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} +z_{1}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} - z_{1}\right) \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{1}\right)c \, \mathbf{\hat{z}} & \left(8a\right) & \text{O I} \\ \mathbf{B}_{3} & = & \left(-x_{2}+y_{2}+z_{2}\right) \, \mathbf{a}_{1} + \left(x_{2}-y_{2}+z_{2}\right) \, \mathbf{a}_{2} + \left(x_{2}+y_{2}-z_{2}\right) \, \mathbf{a}_{3} & = & x_{2}a \, \mathbf{\hat{x}} + y_{2}b \, \mathbf{\hat{y}} + z_{2}c \, \mathbf{\hat{z}} & \left(16b\right) & \text{Ag} \\ \mathbf{B}_{4} & = & \left(x_{2}-y_{2}+z_{2}\right) \, \mathbf{a}_{1} + \left(-x_{2}+y_{2}+z_{2}\right) \, \mathbf{a}_{2} + \left(-x_{2}-y_{2}-z_{2}\right) \, \mathbf{a}_{3} & = & -x_{2}a \, \mathbf{\hat{x}}-y_{2}b \, \mathbf{\hat{y}} + z_{2}c \, \mathbf{\hat{z}} & \left(16b\right) & \text{Ag} \\ \mathbf{B}_{5} & = & \left(\frac{1}{4} - x_{2} - y_{2} + z_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} +x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} +x_{2} - y_{2} - z_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{2}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-y_{2}\right)b \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{2}\right)c \, \mathbf{\hat{z}} & \left(16b\right) & \text{Ag} \\ \mathbf{B}_{6} & = & \left(\frac{1}{4} +x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} - x_{2} - y_{2} + z_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} - x_{2} + y_{2} - z_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{2}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +y_{2}\right)b \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{2}\right)c \, \mathbf{\hat{z}} & \left(16b\right) & \text{Ag} \\ \mathbf{B}_{7} & = & \left(-x_{3}+y_{3}+z_{3}\right) \, \mathbf{a}_{1} + \left(x_{3}-y_{3}+z_{3}\right) \, \mathbf{a}_{2} + \left(x_{3}+y_{3}-z_{3}\right) \, \mathbf{a}_{3} & = & x_{3}a \, \mathbf{\hat{x}} + y_{3}b \, \mathbf{\hat{y}} + z_{3}c \, \mathbf{\hat{z}} & \left(16b\right) & \text{O II} \\ \mathbf{B}_{8} & = & \left(x_{3}-y_{3}+z_{3}\right) \, \mathbf{a}_{1} + \left(-x_{3}+y_{3}+z_{3}\right) \, \mathbf{a}_{2} + \left(-x_{3}-y_{3}-z_{3}\right) \, \mathbf{a}_{3} & = & -x_{3}a \, \mathbf{\hat{x}}-y_{3}b \, \mathbf{\hat{y}} + z_{3}c \, \mathbf{\hat{z}} & \left(16b\right) & \text{O II} \\ \mathbf{B}_{9} & = & \left(\frac{1}{4} - x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} +x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} +x_{3} - y_{3} - z_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{3}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-y_{3}\right)b \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{3}\right)c \, \mathbf{\hat{z}} & \left(16b\right) & \text{O II} \\ \mathbf{B}_{10} & = & \left(\frac{1}{4} +x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} - x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} - x_{3} + y_{3} - z_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{3}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +y_{3}\right)b \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{3}\right)c \, \mathbf{\hat{z}} & \left(16b\right) & \text{O II} \\ \end{array} \]

References

  • B. Standke and M. Jansen, Darstellung und Kristallstruktur von Ag2O3, Z. Anorg. Allg. Chem. 535, 39–46 (1986), doi:10.1002/zaac.19865350406.

Geometry files


Prototype Generator

aflow --proto=A2B3_oF40_43_b_ab --params=

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