Haussmannite (Mn$_{3}$O$_{4}$) Structure: A3B4_tI28_141_ad_h-001
| Prototype | Mn$_{3}$O$_{4}$ |
| AFLOW prototype label | A3B4_tI28_141_ad_h-001 |
| Mineral name | haussmannite |
| ICSD | 68174 |
| Pearson symbol | tI28 |
| Space group number | 141 |
| Space group symbol | $I4_1/amd$ |
| AFLOW prototype command |
aflow --proto=A3B4_tI28_141_ad_h-001
--params=$a, \allowbreak c/a, \allowbreak y_{3}, \allowbreak z_{3}$ |
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{7}{8} \, \mathbf{a}_{1}+\frac{1}{8} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{y}}+\frac{1}{8}c \,\mathbf{\hat{z}}$ | (4a) | Mn I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{8} \, \mathbf{a}_{1}+\frac{7}{8} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{4}a \,\mathbf{\hat{y}}+\frac{3}{8}c \,\mathbf{\hat{z}}$ | (4a) | Mn I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}c \,\mathbf{\hat{z}}$ | (8d) | Mn II |
| $\mathbf{B_{4}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}$ | (8d) | Mn II |
| $\mathbf{B_{5}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}$ | = | $- \frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (8d) | Mn II |
| $\mathbf{B_{6}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (8d) | Mn II |
| $\mathbf{B_{7}}$ | = | $\left(y_{3} + z_{3}\right) \, \mathbf{a}_{1}+z_{3} \, \mathbf{a}_{2}+y_{3} \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (16h) | O I |
| $\mathbf{B_{8}}$ | = | $\left(- y_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{3} \, \mathbf{a}_{2}- \left(y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (16h) | O I |
| $\mathbf{B_{9}}$ | = | $z_{3} \, \mathbf{a}_{1}+\left(- y_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}- y_{3} \, \mathbf{a}_{3}$ | = | $- a \left(y_{3} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- \frac{1}{4}a \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16h) | O I |
| $\mathbf{B_{10}}$ | = | $z_{3} \, \mathbf{a}_{1}+\left(y_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+c \left(z_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16h) | O I |
| $\mathbf{B_{11}}$ | = | $\left(y_{3} - z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{3} \, \mathbf{a}_{2}+\left(y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{3} \,\mathbf{\hat{z}}$ | (16h) | O I |
| $\mathbf{B_{12}}$ | = | $- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{1}- z_{3} \, \mathbf{a}_{2}- y_{3} \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{y}}- c z_{3} \,\mathbf{\hat{z}}$ | (16h) | O I |
| $\mathbf{B_{13}}$ | = | $- z_{3} \, \mathbf{a}_{1}+\left(y_{3} - z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+y_{3} \, \mathbf{a}_{3}$ | = | $a \left(y_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- \frac{1}{4}a \,\mathbf{\hat{y}}- c \left(z_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16h) | O I |
| $\mathbf{B_{14}}$ | = | $- z_{3} \, \mathbf{a}_{1}- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{2}- \left(y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{3} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}- c \left(z_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16h) | O I |
References
- D. Jarosch, Crystal structure refinement and reflectance measurements of hausmannite, Mn$_3$O$_4$, Mineralogy and Petrology 37, 15–23 (1987), doi:10.1007/BF01163155.
Found in
- P. Villars and L. Calvert, Pearson's Handbook of Crystallographic Data for Intermetallic Phases (ASM International, Materials Park, OH, 1991), 2nd edn.
Prototype Generator
aflow --proto=A3B4_tI28_141_ad_h --params=$a,c/a,y_{3},z_{3}$