Anatase (TiO2, $C5$) Structure: A2B_tI12_141_e_a

Picture of Structure; Click for Big Picture
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.

Geometry files


Prototype Generator

aflow --proto=A2B_tI12_141_e_a --params=

Species:

Running:

Output: