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 : $\mbox{Ia}\bar{3}$
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} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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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