Anatase (TiO2, C5) Structure: A2B_tI12_141_e_a
| Prototype | : | TiO2 |
| AFLOW prototype label | : | A2B_tI12_141_e_a |
| Strukturbericht designation | : | $C5$ |
| Pearson symbol | : | tI12 |
| Space group number | : | 141 |
| Space group symbol | : | $\mbox{I4}_{1}\mbox{/amd}$ |
| AFLOW prototype command | : | aflow --proto=A2B_tI12_141_e_a --params=$a,c/a,z_{2}$ |
- (Howard, 1991) gives the positions of the atoms in terms of setting 1 of space group \#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
Body-centered Tetragonal primitive vectors:
\[
\begin{array}{ccc}
\mathbf{a}_1 & = & - \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, a \, \mathbf{\hat{y}} + \frac12 \, c \, \mathbf{\hat{z}}\\
\mathbf{a}_2 & = & ~ \frac12 \, a \, \mathbf{\hat{x}} - \frac12 \, a \, \mathbf{\hat{y}} + \frac12 \, c \, \mathbf{\hat{z}}\\
\mathbf{a}_3 & = & ~ \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, a \, \mathbf{\hat{y}} - \frac12 \, c \, \mathbf{\hat{z}}\\
\end{array}
\]
Basis vectors:
\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & =&\frac78 \, \mathbf{a}_{1}+ \frac18 \, \mathbf{a}_{2}+ \frac34 \, \mathbf{a}_{3}& =&\frac34 \, a \, \mathbf{\hat{y}}+ \frac18 \, c \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{Ti} \\ \mathbf{B}_{2} & =&\frac18 \, \mathbf{a}_{1}+ \frac78 \, \mathbf{a}_{2}+ \frac14 \, \mathbf{a}_{3}& =&\frac12 \, a \, \mathbf{\hat{x}}+ \frac34 \, a \, \mathbf{\hat{y}}+ \frac38 \, c \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{Ti} \\ \mathbf{B}_{3} & =&\left(\frac14 + z_{2}\right) \, \mathbf{a}_{1}+ z_{2} \, \mathbf{a}_{2}+ \frac14 \, \mathbf{a}_{3}& =&\frac14 \, a \, \mathbf{\hat{y}}+ z_{2} \, c \, \mathbf{\hat{z}}& \left(8e\right) & \mbox{O} \\ \mathbf{B}_{4} & =&z_{2} \, \mathbf{a}_{1}+ \left(\frac14 + z_{2}\right) \, \mathbf{a}_{2}+ \frac34 \, \mathbf{a}_{3}& =&\frac12 \, a \, \mathbf{\hat{x}}+ \frac14 \, a \, \mathbf{\hat{y}}+ \left(\frac34 + z_{2}\right) \, c \, \mathbf{\hat{z}}& \left(8e\right) & \mbox{O} \\ \mathbf{B}_{5} & =&\left(\frac34 - z_{2}\right) \, \mathbf{a}_{1}- z_{2} \, \mathbf{a}_{2}+ \frac34 \, \mathbf{a}_{3}& =&\frac34 \, a \, \mathbf{\hat{y}}- z_{2} \, c \, \mathbf{\hat{z}}& \left(8e\right) & \mbox{O} \\ \mathbf{B}_{6} & =&- z_{2} \, \mathbf{a}_{1}+ \left(\frac34 - z_{2}\right) \, \mathbf{a}_{2}+ \frac14 \, \mathbf{a}_{3}& =&\frac12 \, a \, \mathbf{\hat{x}}+ \frac34 \, a \, \mathbf{\hat{y}}+ \left(\frac14 - z_{2}\right) \, c \, \mathbf{\hat{z}}& \left(8e\right) & \mbox{O} \\ \end{array} \]References
- C. J. Howard, T. M. Sabine, and F. Dickson, Structural and thermal parameters for rutile and anatase, Acta Crystallogr. Sect. B Struct. Sci. 47, 462–468 (1991), doi:10.1107/S010876819100335X.