Rutile (TiO2, $C4$) Structure: A2B_tP6_136_f_a

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Prototype : TiO2
AFLOW prototype label : A2B_tP6_136_f_a
Strukturbericht designation : $C4$
Pearson symbol : tP6
Space group number : 136
Space group symbol : $\mbox{P4}_{2}\mbox{/mnm}$
AFLOW prototype command : aflow --proto=A2B_tP6_136_f_a
--params=
$a$,$c/a$,$x_{2}$


Other compounds with this structure

  • CoF2, MgF2, MnF2, NiF2, ZnF2, GeO2, IrO2, MoO2, PbO2, SiO2 (stishovite), SnO2 (cassiterite), TaO2, WO2

Simple Tetragonal primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & a \, \mathbf{\hat{x}} \\ \mathbf{a}_2 & = & a \, \mathbf{\hat{y}} \\ \mathbf{a}_3 & = & c \, \mathbf{\hat{z}}\\ \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & =&0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & =&0 \mathbf{\hat{x}} + 0 \mathbf{\hat{y}} + 0 \mathbf{\hat{z}} & \left(2a\right) & \mbox{Ti} \\ \mathbf{B}_{2} & =&\frac12 \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& =&\frac12 \, a \, \mathbf{\hat{x}}+ \frac12 \, a \, \mathbf{\hat{y}}+ \frac12 \, c \, \mathbf{\hat{z}}& \left(2a\right) & \mbox{Ti} \\ \mathbf{B}_{3} & =&x_{2} \, \mathbf{a}_{1}+ x_{2} \, \mathbf{a}_{2}& =&x_{2} \, a \, \mathbf{\hat{x}}+ x_{2} \, a \, \mathbf{\hat{y}}& \left(4f\right) & \mbox{O} \\ \mathbf{B}_{4} & =&- x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}& =&- x_{2} \, a \, \mathbf{\hat{x}}- x_{2} \, a \, \mathbf{\hat{y}}& \left(4f\right) & \mbox{O} \\ \mathbf{B}_{5} & =&\left(\frac12 - x_{2}\right) \, \mathbf{a}_{1}+ \left(\frac12 + x_{2}\right) \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& =&\left(\frac12 - x_{2}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 + x_{2}\right) \, a \, \mathbf{\hat{y}}+ \frac12 \, c \, \mathbf{\hat{z}}& \left(4f\right) & \mbox{O} \\ \mathbf{B}_{6} & =&\left(\frac12 + x_{2}\right) \, \mathbf{a}_{1}+ \left(\frac12 - x_{2}\right) \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& =&\left(\frac12 + x_{2}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 - x_{2}\right) \, a \, \mathbf{\hat{y}}+ \frac12 \, c \, \mathbf{\hat{z}}& \left(4f\right) & \mbox{O} \\ \end{array} \]

References

  • R. Jeffrey 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

  • R. T. Downs and M. Hall–Wallace, The American Mineralogist Crystal Structure Database, Am. Mineral. 88, 247–250 (2003).

Geometry files


Prototype Generator

aflow --proto=A2B_tP6_136_f_a --params=

Species:

Running:

Output: