Spinel (Al$_{2}$MgO$_{4}$, $H1_{1}$) Structure: A2BC4_cF56_227_c_b_e-001
| Prototype | Al$_{2}$MgO$_{4}$ |
| AFLOW prototype label | A2BC4_cF56_227_c_b_e-001 |
| Strukturbericht designation | $H1_{1}$ |
| Mineral name | spinel |
| ICSD | 26485 |
| Pearson symbol | cF56 |
| Space group number | 227 |
| Space group symbol | $Fd\overline{3}m$ |
| AFLOW prototype command |
aflow --proto=A2BC4_cF56_227_c_b_e-001
--params=$a, \allowbreak x_{3}$ |
Other compounds with this structure
Al$_{2}$CdS$_{4}$, Al$_{2}$CrS$_{4}$, Al$_{2}$ZnSe$_{4}$, Cd$_{2}$VS$_{4}$, Co$_{2}$NiS$_{4}$, Co$_{3}$Se$_{4}$, Cr$_{2}$CdTe$_{4}$, Cr$_{2}$CoS$_{4}$, Cr$_{2}$CuS$_{4}$, Cr$_{2}$CuSe$_{4}$, Cr$_{2}$CoO$_{4}$, Cr$_{2}$FeO$_{4}$, Cr$_{2}$FeS$_{4}$, Cr$_{2}$HgS$_{4}$, Cr$_{2}$MnS$_{4}$, Cr$_{2}$SeZn$_{4}$, Cr$_{2}$ZrCd$_{4}$, Cr$_{2}$ZrSe$_{4}$, Ga$_{2}$CoS$_{4}$, Fe$_{2}$NiO$_{4}$, In$_{2}$CaS$_{4}$, In$_{2}$CdSe$_{4}$, In$_{2}$CrS$_{4}$, In$_{2}$FeS$_{4}$, In$_{2}$HgS$_{4}$, In$_{2}$MgS$_{4}$, In$_{2}$MnS$_{4}$, In$_{2}$NiS$_{4}$, In$_{2}$ZrCd$_{4}$, Lu$_{2}$FeS$_{4}$, Lu$_{2}$MgS$_{4}$, Lu$_{2}$MnS$_{4}$, Mg$_{2}$GeO$_{4}$, Mn$_{2}$ZnTe$_{4}$, Ni$_{2}$FeS$_{4}$, Sc$_{2}$FeS$_{4}$, Sc$_{2}$MnS$_{4}$, Ti$_{2}$CuS$_{4}$, V$_{2}$CuS$_{4}$, V$_{2}$ZnO$_{4}$, Yb$_{2}$FeS$_{4}$, Yb$_{2}$MnS$_{4}$, Co$_{3}$O$_{4}$, Co$_{3}$S$_{4}$, Fe$_{3}$O$_{4}$, Fe$_{3}$S$_{4}$ (greigite), Ni$_{3}$S$_{4}$
- An inverse spinel has four Al atoms on the (8a) sites and (Al,Mg) alloyed on the (16d) sites.
- The binary $D7_{2}$ and ternary $H1_{1}$ spinel structures are for all intents and purposes identical. We could use $D7_{2}$ for the binary spinels and $H1_{1}$ for the ternaries, but historically this has not been the case. We dual-list this structure only to keep the historical record intact.
- (Hahn, 1955) has an extensive list of ternary spinels and inverse spinels.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{3}{8} \, \mathbf{a}_{1}+\frac{3}{8} \, \mathbf{a}_{2}+\frac{3}{8} \, \mathbf{a}_{3}$ | = | $\frac{3}{8}a \,\mathbf{\hat{x}}+\frac{3}{8}a \,\mathbf{\hat{y}}+\frac{3}{8}a \,\mathbf{\hat{z}}$ | (8b) | Mg I |
| $\mathbf{B_{2}}$ | = | $\frac{5}{8} \, \mathbf{a}_{1}+\frac{5}{8} \, \mathbf{a}_{2}+\frac{5}{8} \, \mathbf{a}_{3}$ | = | $\frac{5}{8}a \,\mathbf{\hat{x}}+\frac{5}{8}a \,\mathbf{\hat{y}}+\frac{5}{8}a \,\mathbf{\hat{z}}$ | (8b) | Mg I |
| $\mathbf{B_{3}}$ | = | $0$ | = | $0$ | (16c) | Al I |
| $\mathbf{B_{4}}$ | = | $\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}$ | (16c) | Al I |
| $\mathbf{B_{5}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (16c) | Al I |
| $\mathbf{B_{6}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}$ | = | $\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (16c) | Al I |
| $\mathbf{B_{7}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (32e) | O I |
| $\mathbf{B_{8}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}- \left(3 x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (32e) | O I |
| $\mathbf{B_{9}}$ | = | $x_{3} \, \mathbf{a}_{1}- \left(3 x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32e) | O I |
| $\mathbf{B_{10}}$ | = | $- \left(3 x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32e) | O I |
| $\mathbf{B_{11}}$ | = | $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+\left(3 x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (32e) | O I |
| $\mathbf{B_{12}}$ | = | $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (32e) | O I |
| $\mathbf{B_{13}}$ | = | $- x_{3} \, \mathbf{a}_{1}+\left(3 x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}+a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32e) | O I |
| $\mathbf{B_{14}}$ | = | $\left(3 x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32e) | O I |
References
- P. Fischer, Neutronenbeugungsuntersuchung der Strukturen von MgAl$_{2}$O$_{4}$-und ZnAl$_{2}$O$_{4}$-Spinellen, in Abhängigkeit von der Vorgeschichte, Z. Krystallogr. 124, 275–302 (1967), doi:10.1524/zkri.1967.124.16.275.
- H. Hahn, G. Frank, W. Klingler, A. D. Störger, and G. Störger, Chalkogenide. VI. Über Ternäre Chalkogenide des Aluminiums, Galliums und Indiums mit Zink, Cadmium und Quecksilber, Z. Anorganische und Allgemeine Chemie 279, 241–270 (1955), doi:10.1002/zaac.19552790502.
Found in
- R. J. Hill, J. R. Craig, and G. V. Gibbs, Systematics of the Spinel Structure Type, Phys. Chem. Miner. 4, 317–339 (1979).
Prototype Generator
aflow --proto=A2BC4_cF56_227_c_b_e --params=$a,x_{3}$