Anatase (TiO$_{2}$, $C5$) Structure: A2B_tI12_141_e_a-001
| Prototype | O$_{2}$Ti |
| AFLOW prototype label | A2B_tI12_141_e_a-001 |
| Strukturbericht designation | $C5$ |
| Mineral name | anatase |
| ICSD | 63711 |
| Pearson symbol | tI12 |
| Space group number | 141 |
| Space group symbol | $I4_1/amd$ |
| AFLOW prototype command |
aflow --proto=A2B_tI12_141_e_a-001
--params=$a, \allowbreak c/a, \allowbreak z_{2}$ |
- TiO$_{2}$ can also be found as rutile ($C4$) and brookite ($C21$).
- (Howard, 1991) gives the positions of the atoms in terms of setting 1 of space group $I4_{1}/amd$ #141. Previously, when we translated this to our standard setting 2 we entered an incorrect position for the oxygen z coordinate, giving incorrect Ti-O bond lengths and angles. This has been corrected in the current version of the CIF and the POSCAR.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
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) | Ti 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) | Ti I |
| $\mathbf{B_{3}}$ | = | $\left(z_{2} + \frac{1}{4}\right) \, \mathbf{a}_{1}+z_{2} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (8e) | O I |
| $\mathbf{B_{4}}$ | = | $z_{2} \, \mathbf{a}_{1}+\left(z_{2} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+c \left(z_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8e) | O I |
| $\mathbf{B_{5}}$ | = | $- \left(z_{2} - \frac{3}{4}\right) \, \mathbf{a}_{1}- z_{2} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{y}}- c z_{2} \,\mathbf{\hat{z}}$ | (8e) | O I |
| $\mathbf{B_{6}}$ | = | $- z_{2} \, \mathbf{a}_{1}- \left(z_{2} - \frac{3}{4}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{4}a \,\mathbf{\hat{y}}- c \left(z_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8e) | O I |
References
- C. J. Howard, T. M. Sabine, and F. Dickson, Structural and thermal parameters for rutile and anatase, Acta Crystallogr. Sect. B 47, 462–468 (1991), doi:10.1107/S010876819100335X.
Prototype Generator
aflow --proto=A2B_tI12_141_e_a --params=$a,c/a,z_{2}$