Bixbyite (Mn$_{2}$O$_{3}$, $D5_{3}$) Structure: AB3C6_cI80_206_a_d_e-001
| Prototype | Mn$_{2}$O$_{3}$ |
| AFLOW prototype label | AB3C6_cI80_206_a_d_e-001 |
| Strukturbericht designation | $D5_{3}$ |
| Mineral name | bixbyite |
| ICSD | 30237 |
| Pearson symbol | cI80 |
| Space group number | 206 |
| Space group symbol | $Ia\overline{3}$ |
| AFLOW prototype command |
aflow --proto=AB3C6_cI80_206_a_d_e-001
--params=$a, \allowbreak x_{2}, \allowbreak x_{3}, \allowbreak y_{3}, \allowbreak z_{3}$ |
Other compounds with this structure
Am$_{2}$O$_{3}$, As$_{2}$Mg$_{3}$, As$_{2}$Zn$_{3}$, Cd$_{3}$P$_{2}$, Ce$_{2}$O$_{3}$, Dy$_{2}$O$_{3}$, Er$_{2}$O$_{3}$, Eu$_{2}$O$_{3}$, Fe$_{2}$O$_{3}$, Gd$_{2}$O$_{3}$, Ho$_{2}$O$_{3}$, In$_{2}$O$_{3}$, La$_{2}$O$_{3}$, Lu$_{2}$O$_{3}$, $\alpha$-N$_{2}$Be$_{3}$, N$_{2}$Ca$_{3}$, N$_{2}$Cd$_{3}$, N$_{2}$Mg$_{3}$, N$_{2}$Zn$_{3}$, P$_{2}$Be$_{3}$, P$_{2}$Mg$_{3}$, P$_{2}$Zn$_{3}$, Pr$_{2}$O$_{3}$, Pu$_{2}$O$_{3}$, Sc$_{2}$O$_{3}$, Sm$_{2}$O$_{3}$, Tb$_{2}$O$_{3}$, TeCu$_{3}$O$_{6}$, Tl$_{2}$O$_{3}$, Tm$_{2}$O$_{3}$, U$_{2}$N$_{3}$, Y$_{2}$O$_{3}$ (yttria), Yb$_{2}$O$_{3}$
- 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 Mn$_{2}$O$_{3}$ bixbyite in (Villars, 1991) Vol. IV, 4346-7. - The referenced data is for (Mn,Fe)$_{2}$O$_{3}$, 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.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}a \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (8a) | Fe I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}$ | (8a) | Fe I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}$ | (8a) | Fe I |
| $\mathbf{B_{4}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{z}}$ | (8a) | Fe I |
| $\mathbf{B_{5}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\left(x_{2} + \frac{1}{4}\right) \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24d) | Mn I |
| $\mathbf{B_{6}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}- \left(x_{2} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24d) | Mn I |
| $\mathbf{B_{7}}$ | = | $x_{2} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\left(x_{2} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}$ | (24d) | Mn I |
| $\mathbf{B_{8}}$ | = | $- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- \left(x_{2} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (24d) | Mn I |
| $\mathbf{B_{9}}$ | = | $\left(x_{2} + \frac{1}{4}\right) \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{y}}+a x_{2} \,\mathbf{\hat{z}}$ | (24d) | Mn I |
| $\mathbf{B_{10}}$ | = | $- \left(x_{2} - \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}- a x_{2} \,\mathbf{\hat{z}}$ | (24d) | Mn I |
| $\mathbf{B_{11}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}- \left(x_{2} - \frac{3}{4}\right) \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{z}}$ | (24d) | Mn I |
| $\mathbf{B_{12}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\left(x_{2} + \frac{3}{4}\right) \, \mathbf{a}_{2}+\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24d) | Mn I |
| $\mathbf{B_{13}}$ | = | $- x_{2} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- \left(x_{2} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}$ | (24d) | Mn I |
| $\mathbf{B_{14}}$ | = | $\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\left(x_{2} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{y}}$ | (24d) | Mn I |
| $\mathbf{B_{15}}$ | = | $- \left(x_{2} - \frac{3}{4}\right) \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{y}}- a x_{2} \,\mathbf{\hat{z}}$ | (24d) | Mn I |
| $\mathbf{B_{16}}$ | = | $\left(x_{2} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{y}}+a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24d) | Mn I |
| $\mathbf{B_{17}}$ | = | $\left(y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(x_{3} + y_{3}\right) \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a y_{3} \,\mathbf{\hat{y}}+a z_{3} \,\mathbf{\hat{z}}$ | (48e) | O I |
| $\mathbf{B_{18}}$ | = | $\left(- y_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{3} - z_{3}\right) \, \mathbf{a}_{2}- \left(x_{3} + y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a z_{3} \,\mathbf{\hat{z}}$ | (48e) | O I |
| $\mathbf{B_{19}}$ | = | $\left(y_{3} - z_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} + z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(- x_{3} + y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a y_{3} \,\mathbf{\hat{y}}- a z_{3} \,\mathbf{\hat{z}}$ | (48e) | O I |
| $\mathbf{B_{20}}$ | = | $- \left(y_{3} + z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{3} - z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{3} - y_{3}\right) \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}- a y_{3} \,\mathbf{\hat{y}}- a \left(z_{3} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (48e) | O I |
| $\mathbf{B_{21}}$ | = | $\left(x_{3} + y_{3}\right) \, \mathbf{a}_{1}+\left(y_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(x_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $a z_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}+a y_{3} \,\mathbf{\hat{z}}$ | (48e) | O I |
| $\mathbf{B_{22}}$ | = | $- \left(x_{3} + y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- y_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $a z_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (48e) | O I |
| $\mathbf{B_{23}}$ | = | $\left(- x_{3} + y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{3} - z_{3}\right) \, \mathbf{a}_{2}- \left(x_{3} + z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a z_{3} \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a y_{3} \,\mathbf{\hat{z}}$ | (48e) | O I |
| $\mathbf{B_{24}}$ | = | $\left(x_{3} - y_{3}\right) \, \mathbf{a}_{1}- \left(y_{3} + z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{3} - z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}- a y_{3} \,\mathbf{\hat{z}}$ | (48e) | O I |
| $\mathbf{B_{25}}$ | = | $\left(x_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} + y_{3}\right) \, \mathbf{a}_{2}+\left(y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{x}}+a z_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (48e) | O I |
| $\mathbf{B_{26}}$ | = | $- \left(x_{3} - z_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} + y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(- y_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a z_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (48e) | O I |
| $\mathbf{B_{27}}$ | = | $- \left(x_{3} + z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- x_{3} + y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{x}}- a z_{3} \,\mathbf{\hat{y}}- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (48e) | O I |
| $\mathbf{B_{28}}$ | = | $\left(x_{3} - z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{3} - y_{3}\right) \, \mathbf{a}_{2}- \left(y_{3} + z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{x}}- a \left(z_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (48e) | O I |
| $\mathbf{B_{29}}$ | = | $- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} + z_{3}\right) \, \mathbf{a}_{2}- \left(x_{3} + y_{3}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a y_{3} \,\mathbf{\hat{y}}- a z_{3} \,\mathbf{\hat{z}}$ | (48e) | O I |
| $\mathbf{B_{30}}$ | = | $\left(y_{3} - z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{3} - z_{3}\right) \, \mathbf{a}_{2}+\left(x_{3} + y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a z_{3} \,\mathbf{\hat{z}}$ | (48e) | O I |
| $\mathbf{B_{31}}$ | = | $- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{3} - y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a y_{3} \,\mathbf{\hat{y}}+a z_{3} \,\mathbf{\hat{z}}$ | (48e) | O I |
| $\mathbf{B_{32}}$ | = | $\left(y_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- x_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{3} - y_{3}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+a y_{3} \,\mathbf{\hat{y}}+a \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (48e) | O I |
| $\mathbf{B_{33}}$ | = | $- \left(x_{3} + y_{3}\right) \, \mathbf{a}_{1}- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{2}- \left(x_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a z_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}- a y_{3} \,\mathbf{\hat{z}}$ | (48e) | O I |
| $\mathbf{B_{34}}$ | = | $\left(x_{3} + y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{3} - z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a z_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}+a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (48e) | O I |
| $\mathbf{B_{35}}$ | = | $\left(x_{3} - y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{2}+\left(x_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a z_{3} \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a y_{3} \,\mathbf{\hat{z}}$ | (48e) | O I |
| $\mathbf{B_{36}}$ | = | $- \left(x_{3} - y_{3}\right) \, \mathbf{a}_{1}+\left(y_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(- x_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}+a y_{3} \,\mathbf{\hat{z}}$ | (48e) | O I |
| $\mathbf{B_{37}}$ | = | $- \left(x_{3} + z_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} + y_{3}\right) \, \mathbf{a}_{2}- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{x}}- a z_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (48e) | O I |
| $\mathbf{B_{38}}$ | = | $\left(x_{3} - z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} + y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{3} - z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a z_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (48e) | O I |
| $\mathbf{B_{39}}$ | = | $\left(x_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{3} - y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{x}}+a z_{3} \,\mathbf{\hat{y}}+a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (48e) | O I |
| $\mathbf{B_{40}}$ | = | $\left(- x_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{3} - y_{3}\right) \, \mathbf{a}_{2}+\left(y_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{x}}+a \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (48e) | O I |
References
- H. Dachs, Die Kristallstruktur des Bixbyits (Fe,Mn)$_2$O$_3$, Z. Krystallogr. 107, S, 370–395 (1956), doi:10.1524/zkri.1956.107.5-6.370.
- 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).
Prototype Generator
aflow --proto=AB3C6_cI80_206_a_d_e --params=$a,x_{2},x_{3},y_{3},z_{3}$