Rutile (TiO$_{2}$, $C4$) Structure: A2B_tP6_136_f_a-001
| Prototype | O$_{2}$Ti |
| AFLOW prototype label | A2B_tP6_136_f_a-001 |
| Strukturbericht designation | $C4$ |
| Mineral name | rutile |
| ICSD | 80843 |
| Pearson symbol | tP6 |
| Space group number | 136 |
| Space group symbol | $P4_2/mnm$ |
| AFLOW prototype command |
aflow --proto=A2B_tP6_136_f_a-001
--params=$a, \allowbreak c/a, \allowbreak x_{2}$ |
Other compounds with this structure
CoF$_{2}$, CrO$_{2}$, GeO$_{2}$, IrO$_{2}$, MgF$_{2}$, MnF$_{2}$, MoO$_{2}$, NbO$_{2}$, NiF$_{2}$, OsO$_{2}$, PbO$_{2}$, RuO$_{2}$, SiO$_{2}$ (stishovite), SnO$_{2}$ (cassiterite), TaO$_{2}$, TeO$_{2}$, VO$_{2}$ (HT), WO$_{2}$, ZnF$_{2}$
- TiO$_{2}$ can also be found as anatase ($C5$) and brookite ($C21$).
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (2a) | Ti I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (2a) | Ti I |
| $\mathbf{B_{3}}$ | = | $x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}$ | = | $a x_{2} \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}$ | (4f) | O I |
| $\mathbf{B_{4}}$ | = | $- x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}$ | = | $- a x_{2} \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}$ | (4f) | O I |
| $\mathbf{B_{5}}$ | = | $- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4f) | O I |
| $\mathbf{B_{6}}$ | = | $\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4f) | O I |
References
- R. J. Swope, J. R. Smyth, and A. C. Larson, H in rutile-type compounds: I. Single-crystal neutron and X-ray diffraction study of H in rutile, Am. Mineral. 80, 448–453 (1995).
Found in
- J. Donohue, The Structures of the Elements (Robert E. Krieger Publishing Company, New York, 1974).
Prototype Generator
aflow --proto=A2B_tP6_136_f_a --params=$a,c/a,x_{2}$