Encyclopedia of Crystallographic Prototypes

AFLOW Prototype: AB3C6_cI80_206_b_d_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)

Bixbyite (Mn2O3, $D5_{3}$) Structure: AB3C6_cI80_206_b_d_e

Picture of Structure; Click for Big Picture
Prototype : (Mn,Fe)2O3
AFLOW prototype label : AB3C6_cI80_206_b_d_e
Strukturbericht designation : $D5_{3}$
Pearson symbol : cI80
Space group number : 206
Space group symbol : $\text{Ia}\bar{3}$
AFLOW prototype command : aflow --proto=AB3C6_cI80_206_b_d_e
--params=
$a$,$x_{2}$,$x_{3}$,$y_{3}$,$z_{3}$


Other compounds with this structure

  • Am2O3, As2Mg3, As2Zn3, Cd3P2, Ce2O3, Fe2O3, La2O3, Lu2O3, Tb2O3, Tm2O3, P2Zn3, many others.

  • A search for bixbyite on the American Mineralogist Crystal Structure Database (Downs, 2003) shows two structures with the Mn atoms on the (8a) sites and one with Mn on the (8b) site. We use the structure that agrees with the data for pure Mn2O3 bixbyite in (Villars, 1991) Vol. IV, 4346-7. The referenced data is for (Mn,Fe)2O3, with Mn and Fe randomly populating the (8b) and (24d) sites. The pictures and the CIF file put Fe atoms on the (8b) sites and Mn atoms on the (24d) sites in order to better delineate the difference in the crystallographic behavior of the sites, but both sites are randomly occupied. An earlier version of this page (and the article) used the label AB3C6_cI80_206_a_d_e. The label has now been corrected to AB3C6_cI80_206_b_d_e.

Body-centered Cubic primitive vectors:

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

Basis vectors:

\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1} & = &\frac12 \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &\frac14 \, \, a \, \mathbf{\hat{x}}+ \frac14 \, \, a \, \mathbf{\hat{y}}+ \frac14 \, \, a \, \mathbf{\hat{z}}& \left(8b\right) & \text{Fe} \\ \mathbf{B}_{2} & = &\frac12 \, \mathbf{a}_{1}& = &\frac34 \, \, a \, \mathbf{\hat{x}}+ \frac14 \, \, a \, \mathbf{\hat{y}}+ \frac14 \, \, a \, \mathbf{\hat{z}}& \left(8b\right) & \text{Fe} \\ \mathbf{B}_{3} & = &\frac12 \, \mathbf{a}_{2}& = &\frac14 \, \, a \, \mathbf{\hat{x}}+ \frac34 \, \, a \, \mathbf{\hat{y}}+ \frac14 \, \, a \, \mathbf{\hat{z}}& \left(8b\right) & \text{Fe} \\ \mathbf{B}_{4} & = &\frac12 \, \mathbf{a}_{3}& = &\frac14 \, \, a \, \mathbf{\hat{x}}+ \frac14 \, \, a \, \mathbf{\hat{y}}+ \frac34 \, \, a \, \mathbf{\hat{z}}& \left(8b\right) & \text{Fe} \\ \mathbf{B}_{5} & = &\frac14 \, \mathbf{a}_{1}+ \left(\frac14 + x_{2}\right) \, \mathbf{a}_{2}+ x_{2} \, \mathbf{a}_{3}& = &x_{2} \, \, a \, \mathbf{\hat{x}}+ \frac14 \, \, a \, \mathbf{\hat{z}}& \left(24d\right) & \text{Mn} \\ \mathbf{B}_{6} & = &\frac34 \, \mathbf{a}_{1}+ \left(\frac14 - x_{2}\right) \, \mathbf{a}_{2}+ \left(\frac12 - x_{2}\right) \, \mathbf{a}_{3}& = &- x_{2} \, \, a \, \mathbf{\hat{x}}+ \frac12 \, \, a \, \mathbf{\hat{y}}+ \frac14 \, \, a \, \mathbf{\hat{z}}& \left(24d\right) & \text{Mn} \\ \mathbf{B}_{7} & = &x_{2} \, \mathbf{a}_{1}+ \frac14 \, \mathbf{a}_{2}+ \left(\frac14 + x_{2}\right) \, \mathbf{a}_{3}& = &\frac14 \, \, a \, \mathbf{\hat{x}}+ x_{2} \, \, a \, \mathbf{\hat{y}}& \left(24d\right) & \text{Mn} \\ \mathbf{B}_{8} & = &\left(\frac12 - x_{2}\right) \, \mathbf{a}_{1}+ \frac34 \, \mathbf{a}_{2}+ \left(\frac14 - x_{2}\right) \, \mathbf{a}_{3}& = &\frac14 \, \, a \, \mathbf{\hat{x}}- x_{2} \, \, a \, \mathbf{\hat{y}}+ \frac12 \, \, a \, \mathbf{\hat{z}}& \left(24d\right) & \text{Mn} \\ \mathbf{B}_{9} & = &\left(\frac14 + x_{2}\right) \, \mathbf{a}_{1}+ x_{2} \, \mathbf{a}_{2}+ \frac14 \, \mathbf{a}_{3}& = &\frac14 \, \, a \, \mathbf{\hat{y}}+ x_{2} \, \, a \, \mathbf{\hat{z}}& \left(24d\right) & \text{Mn} \\ \mathbf{B}_{10} & = &\left(\frac14 - x_{2}\right) \, \mathbf{a}_{1}+ \left(\frac12 - x_{2}\right) \, \mathbf{a}_{2}+ \frac34 \, \mathbf{a}_{3}& = &\frac12 \, \, a \, \mathbf{\hat{x}}\frac14 \, \, a \, \mathbf{\hat{y}}- x_{2} \, \, a \, \mathbf{\hat{z}}& \left(24d\right) & \text{Mn} \\ \mathbf{B}_{11} & = &\frac34 \, \mathbf{a}_{1}+ \left(\frac34 - x_{2}\right) \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}& = &- x_{2} \, \, a \, \mathbf{\hat{x}}+ \frac34 \, \, a \, \mathbf{\hat{z}}& \left(24d\right) & \text{Mn} \\ \mathbf{B}_{12} & = &\frac14 \, \mathbf{a}_{1}+ \left(\frac34 + x_{2}\right) \, \mathbf{a}_{2}+ \left(\frac12 + x_{2}\right) \, \mathbf{a}_{3}& = &\left(\frac12 + x_{2}\right) \, \, a \, \mathbf{\hat{x}}+ \frac14 \, \, a \, \mathbf{\hat{z}}& \left(24d\right) & \text{Mn} \\ \mathbf{B}_{13} & = &- x_{2} \, \mathbf{a}_{1}+ \frac34 \, \mathbf{a}_{2}+ \left(\frac34 - x_{2}\right) \, \mathbf{a}_{3}& = &\frac34 \, \, a \, \mathbf{\hat{x}}- x_{2} \, \, a \, \mathbf{\hat{y}}& \left(24d\right) & \text{Mn} \\ \mathbf{B}_{14} & = &\left(\frac12 + x_{2}\right) \, \mathbf{a}_{1}+ \frac14 \, \mathbf{a}_{2}+ \left(\frac34 + x_{2}\right) \, \mathbf{a}_{3}& = &\frac14 \, \, a \, \mathbf{\hat{x}}+ \left(\frac12 + x_{2}\right) \, \, a \, \mathbf{\hat{y}}& \left(24d\right) & \text{Mn} \\ \mathbf{B}_{15} & = &\left(\frac34 - x_{2}\right) \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}+ \frac34 \, \mathbf{a}_{3}& = &\frac34 \, \, a \, \mathbf{\hat{y}}- x_{2} \, \, a \, \mathbf{\hat{z}}& \left(24d\right) & \text{Mn} \\ \mathbf{B}_{16} & = &\left(\frac34 + x_{2}\right) \, \mathbf{a}_{1}+ \left(\frac12 + x_{2}\right) \, \mathbf{a}_{2}+ \frac14 \, \mathbf{a}_{3}& = &\frac14 \, \, a \, \mathbf{\hat{y}}+ \left(\frac12 + x_{2}\right) \, \, a \, \mathbf{\hat{z}}& \left(24d\right) & \text{Mn} \\ \mathbf{B}_{17} & = &\left(y_{3} + z_{3}\right) \, \mathbf{a}_{1}+ \left(x_{3} + z_{3}\right) \, \mathbf{a}_{2}+ \left(x_{3} + y_{3}\right) \, \mathbf{a}_{3}& = &x_{3} \, \, a \, \mathbf{\hat{x}}+ y_{3} \, \, a \, \mathbf{\hat{y}}+ z_{3} \, \, a \, \mathbf{\hat{z}}& \left(48e\right) & \text{O} \\ \mathbf{B}_{18} & = &\left(\frac12 - y_{3} + z_{3}\right) \, \mathbf{a}_{1}+ \left(z_{3} - x_{3}\right) \, \mathbf{a}_{2}+ \left(\frac12 - x_{3} - y_{3}\right) \, \mathbf{a}_{3}& = &- x_{3} \, \, a \, \mathbf{\hat{x}}+ \left(\frac12 - y_{3}\right) \, \, a \, \mathbf{\hat{y}}+ z_{3} \, \, a \, \mathbf{\hat{z}}& \left(48e\right) & \text{O} \\ \mathbf{B}_{19} & = &\left(y_{3} - z_{3}\right) \, \mathbf{a}_{1}+ \left(\frac12 - x_{3} - z_{3}\right) \, \mathbf{a}_{2}+ \left(\frac12 - x_{3} + y_{3}\right) \, \mathbf{a}_{3}& = &\left(\frac12 - x_{3}\right) \, \, a \, \mathbf{\hat{x}}+ y_{3} \, \, a \, \mathbf{\hat{y}}- z_{3} \, \, a \, \mathbf{\hat{z}}& \left(48e\right) & \text{O} \\ \mathbf{B}_{20} & = &\left(\frac12 - y_{3} - z_{3}\right) \, \mathbf{a}_{1}+ \left(\frac12 + x_{3} - z_{3}\right) \, \mathbf{a}_{2}+ \left(x_{3} - y_{3}\right) \, \mathbf{a}_{3}& = &x_{3} \, \, a \, \mathbf{\hat{x}}- y_{3} \, \, a \, \mathbf{\hat{y}}+ \left(\frac12 - z_{3}\right) \, \, a \, \mathbf{\hat{z}}& \left(48e\right) & \text{O} \\ \mathbf{B}_{21} & = &\left(x_{3} + y_{3}\right) \, \mathbf{a}_{1}+ \left(y_{3} + z_{3}\right) \, \mathbf{a}_{2}+ \left(z_{3} + x_{3}\right) \, \mathbf{a}_{3}& = &z_{3} \, \, a \, \mathbf{\hat{x}}+ x_{3} \, \, a \, \mathbf{\hat{y}}+ y_{3} \, \, a \, \mathbf{\hat{z}}& \left(48e\right) & \text{O} \\ \mathbf{B}_{22} & = &\left(\frac12 - x_{3} + y_{3}\right) \, \mathbf{a}_{1}+ \left(y_{3} - z_{3}\right) \, \mathbf{a}_{2}+ \left(\frac12 - z_{3} - x_{3}\right) \, \mathbf{a}_{3}& = &- z_{3} \, \, a \, \mathbf{\hat{x}}+ \left(\frac12 - x_{3}\right) \, \, a \, \mathbf{\hat{y}}+ y_{3} \, \, a \, \mathbf{\hat{z}}& \left(48e\right) & \text{O} \\ \mathbf{B}_{23} & = &\left(x_{3} - y_{3}\right) \, \mathbf{a}_{1}+ \left(\frac12 - z_{3} - y_{3}\right) \, \mathbf{a}_{2}+ \left(\frac12 - z_{3} + x_{3}\right) \, \mathbf{a}_{3}& = &\left(\frac12 - z_{3}\right) \, \, a \, \mathbf{\hat{x}}+ x_{3} \, \, a \, \mathbf{\hat{y}}- y_{3} \, \, a \, \mathbf{\hat{z}}& \left(48e\right) & \text{O} \\ \mathbf{B}_{24} & = &\left(\frac12 - x_{3} - y_{3}\right) \, \mathbf{a}_{1}+ \left(\frac12 + z_{3} - y_{3}\right) \, \mathbf{a}_{2}+ \left(z_{3} - x_{3}\right) \, \mathbf{a}_{3}& = &z_{3} \, \, a \, \mathbf{\hat{x}}- x_{3} \, \, a \, \mathbf{\hat{y}}+ \left(\frac12 - y_{3}\right) \, \, a \, \mathbf{\hat{z}}& \left(48e\right) & \text{O} \\ \mathbf{B}_{25} & = &\left(z_{3} + x_{3}\right) \, \mathbf{a}_{1}+ \left(x_{3} + y_{3}\right) \, \mathbf{a}_{2}+ \left(y_{3} + z_{3}\right) \, \mathbf{a}_{3}& = &y_{3} \, \, a \, \mathbf{\hat{x}}+ z_{3} \, \, a \, \mathbf{\hat{y}}+ x_{3} \, \, a \, \mathbf{\hat{z}}& \left(48e\right) & \text{O} \\ \mathbf{B}_{26} & = &\left(\frac12 - z_{3} + x_{3}\right) \, \mathbf{a}_{1}+ \left(x_{3} - y_{3}\right) \, \mathbf{a}_{2}+ \left(\frac12 - y_{3} - z_{3}\right) \, \mathbf{a}_{3}& = &- y_{3} \, \, a \, \mathbf{\hat{x}}+ \left(\frac12 - z_{3}\right) \, \, a \, \mathbf{\hat{y}}+ x_{3} \, \, a \, \mathbf{\hat{z}}& \left(48e\right) & \text{O} \\ \mathbf{B}_{27} & = &\left(z_{3} - x_{3}\right) \, \mathbf{a}_{1}+ \left(\frac12 - y_{3} - x_{3}\right) \, \mathbf{a}_{2}+ \left(\frac12 - y_{3} + z_{3}\right) \, \mathbf{a}_{3}& = &\left(\frac12 - y_{3}\right) \, \, a \, \mathbf{\hat{x}}+ z_{3} \, \, a \, \mathbf{\hat{y}}- x_{3} \, \, a \, \mathbf{\hat{z}}& \left(48e\right) & \text{O} \\ \mathbf{B}_{28} & = &\left(\frac12 - z_{3} - x_{3}\right) \, \mathbf{a}_{1}+ \left(\frac12 + y_{3} - x_{3}\right) \, \mathbf{a}_{2}+ \left(y_{3} - z_{3}\right) \, \mathbf{a}_{3}& = &y_{3} \, \, a \, \mathbf{\hat{x}}- z_{3} \, \, a \, \mathbf{\hat{y}}+ \left(\frac12 - x_{3}\right) \, \, a \, \mathbf{\hat{z}}& \left(48e\right) & \text{O} \\ \mathbf{B}_{29} & = &- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} + z_{3}\right) \, \mathbf{a}_{2}- \left(x_{3} + y_{3}\right) \, \mathbf{a}_{3}& = &- x_{3} \, \, a \, \mathbf{\hat{x}}- y_{3} \, \, a \, \mathbf{\hat{y}}- z_{3} \, \, a \, \mathbf{\hat{z}}& \left(48e\right) & \text{O} \\ \mathbf{B}_{30} & = &\left(\frac12 + y_{3} - z_{3}\right) \, \mathbf{a}_{1}+ \left(x_{3} - z_{3}\right) \, \mathbf{a}_{2}+ \left(\frac12 + x_{3} + y_{3}\right) \, \mathbf{a}_{3}& = &x_{3} \, \, a \, \mathbf{\hat{x}}+ \left(\frac12 + y_{3}\right) \, \, a \, \mathbf{\hat{y}}- z_{3} \, \, a \, \mathbf{\hat{z}}& \left(48e\right) & \text{O} \\ \mathbf{B}_{31} & = &\left(z_{3} - y_{3}\right) \, \mathbf{a}_{1}+ \left(\frac12 + x_{3} + z_{3}\right) \, \mathbf{a}_{2}+ \left(\frac12 + x_{3} - y_{3}\right) \, \mathbf{a}_{3}& = &\left(\frac12 + x_{3}\right) \, \, a \, \mathbf{\hat{x}}- y_{3} \, \, a \, \mathbf{\hat{y}}+ z_{3} \, \, a \, \mathbf{\hat{z}}& \left(48e\right) & \text{O} \\ \mathbf{B}_{32} & = &\left(\frac12 + y_{3} + z_{3}\right) \, \mathbf{a}_{1}+ \left(\frac12 - x_{3} + z_{3}\right) \, \mathbf{a}_{2}+ \left(y_{3} - x_{3}\right) \, \mathbf{a}_{3}& = &- x_{3} \, \, a \, \mathbf{\hat{x}}+ y_{3} \, \, a \, \mathbf{\hat{y}}+ \left(\frac12 + z_{3}\right) \, \, a \, \mathbf{\hat{z}}& \left(48e\right) & \text{O} \\ \mathbf{B}_{33} & = &- \left(x_{3} + y_{3}\right) \, \mathbf{a}_{1}- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{2}- \left(z_{3} + x_{3}\right) \, \mathbf{a}_{3}& = &- z_{3} \, \, a \, \mathbf{\hat{x}}- x_{3} \, \, a \, \mathbf{\hat{y}}- y_{3} \, \, a \, \mathbf{\hat{z}}& \left(48e\right) & \text{O} \\ \mathbf{B}_{34} & = &\left(\frac12 + x_{3} - y_{3}\right) \, \mathbf{a}_{1}+ \left(z_{3} - y_{3}\right) \, \mathbf{a}_{2}+ \left(\frac12 + x_{3} + z_{3}\right) \, \mathbf{a}_{3}& = &z_{3} \, \, a \, \mathbf{\hat{x}}+ \left(\frac12 + x_{3}\right) \, \, a \, \mathbf{\hat{y}}- y_{3} \, \, a \, \mathbf{\hat{z}}& \left(48e\right) & \text{O} \\ \mathbf{B}_{35} & = &\left(y_{3} - x_{3}\right) \, \mathbf{a}_{1}+ \left(\frac12 + y_{3} + z_{3}\right) \, \mathbf{a}_{2}+ \left(\frac12 + z_{3} - x_{3}\right) \, \mathbf{a}_{3}& = &\left(\frac12 + z_{3}\right) \, \, a \, \mathbf{\hat{x}}- x_{3} \, \, a \, \mathbf{\hat{y}}+ y_{3} \, \, a \, \mathbf{\hat{z}}& \left(48e\right) & \text{O} \\ \mathbf{B}_{36} & = &\left(\frac12 + x_{3} + y_{3}\right) \, \mathbf{a}_{1}+ \left(\frac12 - z_{3} + y_{3}\right) \, \mathbf{a}_{2}+ \left(x_{3} - z_{3}\right) \, \mathbf{a}_{3}& = &- z_{3} \, \, a \, \mathbf{\hat{x}}+ x_{3} \, \, a \, \mathbf{\hat{y}}+ \left(\frac12 + y_{3}\right) \, \, a \, \mathbf{\hat{z}}& \left(48e\right) & \text{O} \\ \mathbf{B}_{37} & = &- \left(x_{3} + z_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} + y_{3}\right) \, \mathbf{a}_{2}- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{3}& = &- y_{3} \, \, a \, \mathbf{\hat{x}}- z_{3} \, \, a \, \mathbf{\hat{y}}- x_{3} \, \, a \, \mathbf{\hat{z}}& \left(48e\right) & \text{O} \\ \mathbf{B}_{38} & = &\left(\frac12 + z_{3} - x_{3}\right) \, \mathbf{a}_{1}+ \left(y_{3} - x_{3}\right) \, \mathbf{a}_{2}+ \left(\frac12 + y_{3} + z_{3}\right) \, \mathbf{a}_{3}& = &y_{3} \, \, a \, \mathbf{\hat{x}}+ \left(\frac12 + z_{3}\right) \, \, a \, \mathbf{\hat{y}}- x_{3} \, \, a \, \mathbf{\hat{z}}& \left(48e\right) & \text{O} \\ \mathbf{B}_{39} & = &\left(x_{3} - z_{3}\right) \, \mathbf{a}_{1}+ \left(\frac12 + y_{3} + x_{3}\right) \, \mathbf{a}_{2}+ \left(\frac12 + y_{3} - z_{3}\right) \, \mathbf{a}_{3}& = &\left(\frac12 + y_{3}\right) \, \, a \, \mathbf{\hat{x}}- z_{3} \, \, a \, \mathbf{\hat{y}}+ x_{3} \, \, a \, \mathbf{\hat{z}}& \left(48e\right) & \text{O} \\ \mathbf{B}_{40} & = &\left(\frac12 + x_{3} + z_{3}\right) \, \mathbf{a}_{1}+ \left(\frac12 + x_{3} - y_{3}\right) \, \mathbf{a}_{2}+ \left(z_{3} - y_{3}\right) \, \mathbf{a}_{3}& = &- y_{3} \, \, a \, \mathbf{\hat{x}}+ z_{3} \, \, a \, \mathbf{\hat{y}}+ \left(\frac12 + x_{3}\right) \, \, a \, \mathbf{\hat{z}}& \left(48e\right) & \text{O} \\ \end{array} \]

References

  • H. Dachs, Die Kristallstruktur des Bixbyits (Fe,Mn)2O3, Zeitschrift für Kristallographie – Crystalline Materials 107, 370–395 (1956), doi:10.1524/zkri.1956.107.16.370.
  • P. Villars and L. Calvert, Pearson's Handbook of Crystallographic Data for Intermetallic Phases (ASM International, Materials Park, OH, 1991), 2nd edn.

Found in

  • R. T. Downs and M. Hall–Wallace, The American Mineralogist Crystal Structure Database, Am. Mineral. 88, 247–250 (2003).

Geometry files


Prototype Generator

aflow --proto=AB3C6_cI80_206_b_d_e --params=

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