Ilmenite (FeTiO3, $E2_{2}$) Structure: AB3C_hR10_148_c_f_c
| Prototype | : | FeTiO3 |
| AFLOW prototype label | : | AB3C_hR10_148_c_f_c |
| Strukturbericht designation | : | $E2_{2}$ |
| Pearson symbol | : | hR10 |
| Space group number | : | 148 |
| Space group symbol | : | $\mbox{R}\bar{3}$ |
| AFLOW prototype command | : | aflow --proto=AB3C_hR10_148_c_f_c [--hex] --params=$a,c/a,x_{1},x_{2},x_{3},y_{3},z_{3}$ |
- The oxygen atoms form a nearly close-packed system, hence the classifications of this structure. Hexagonal settings of this structure can be obtained with the option ––hex. (Ewald, 1931) original gave this the Strukturbericht designation $G4$.
Rhombohedral primitive vectors:
\[
\begin{array}{ccc}
\mathbf{a}_1 & = & ~ \frac12 \, a \, \mathbf{\hat{x}} - \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}} + \frac13
\, c \, \mathbf{\hat{z}} \\
\mathbf{a}_2 & = & \frac{1}{\sqrt{3}} \, a \, \mathbf{\hat{y}} + \frac13 \, c \, \mathbf{\hat{z}} \\
\mathbf{a}_3 & = & - \frac12 \, a \, \mathbf{\hat{x}} - \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}} + \frac13
\, c \, \mathbf{\hat{z}} \\
\end{array}
\]
Basis vectors:
\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = &x_{1} \, \mathbf{a}_{1}+ x_{1} \, \mathbf{a}_{2}+ x_{1} \, \mathbf{a}_{3}& =&x_{1} \, c \, \mathbf{\hat{z}}& \left(2c\right) & \mbox{Fe} \\ \mathbf{B}_{2} & = &- x_{1} \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{2}- x_{1} \, \mathbf{a}_{3}& =&- x_{1} \, c \, \mathbf{\hat{z}}& \left(2c\right) & \mbox{Fe} \\ \mathbf{B}_{3} & = &x_{2} \, \mathbf{a}_{1}+ x_{2} \, \mathbf{a}_{2}+ x_{2} \, \mathbf{a}_{3}& =&x_{2} \, c \, \mathbf{\hat{z}}& \left(2c\right) & \mbox{Ti} \\ \mathbf{B}_{4} & = &- x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}& =&- x_{2} \, c \, \mathbf{\hat{z}}& \left(2c\right) & \mbox{Ti} \\ \mathbf{B}_{5} & =&x_{3} \, \mathbf{a}_{1}+ y_{3} \, \mathbf{a}_{2}+ z_{3} \, \mathbf{a}_{3}& =&\frac12 \, \left(x_{3} - z_{3}\right) \, a \, \mathbf{\hat{x}}+ \frac{1}{2\sqrt{3}} \, \left(2 y_{3} - z_{3} - x_{3}\right) \, a \, \mathbf{\hat{y}}+ \frac13 \, \left(x_{3} + y_{3} + z_{3}\right) \, c \, \mathbf{\hat{z}}& \left(6f\right) & \mbox{O} \\ \mathbf{B}_{6} & =&z_{3} \, \mathbf{a}_{1}+ x_{3} \, \mathbf{a}_{2}+ y_{3} \, \mathbf{a}_{3}& =&\frac12 \, \left(z_{3} - y_{3}\right) \, a \, \mathbf{\hat{x}}+ \frac{1}{2\sqrt{3}} \, \left(2 x_{3} - y_{3} - z_{3}\right) \, a \, \mathbf{\hat{y}}+ \frac13 \, \left(x_{3} + y_{3} + z_{3}\right) \, c \, \mathbf{\hat{z}}& \left(6f\right) & \mbox{O} \\ \mathbf{B}_{7} & =&y_{3} \, \mathbf{a}_{1}+ z_{3} \, \mathbf{a}_{2}+ x_{3} \, \mathbf{a}_{3}& =&\frac12 \, \left(y_{3} - x_{3}\right) \, a \, \mathbf{\hat{x}}+ \frac{1}{2\sqrt{3}} \, \left(2 z_{3} - x_{3} - y_{3}\right) \, a \, \mathbf{\hat{y}}+ \frac13 \, \left(x_{3} + y_{3} + z_{3}\right) \, c \, \mathbf{\hat{z}}& \left(6f\right) & \mbox{O} \\ \mathbf{B}_{8} & =&- x_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}& =&\frac12 \, \left(z_{3} - x_{3}\right) \, a \, \mathbf{\hat{x}}+ \frac{1}{2\sqrt{3}} \, \left(z_{3} + x_{3} - 2 y_{3}\right) \, a \, \mathbf{\hat{y}}- \frac13 \, \left(x_{3} + y_{3} + z_{3}\right) \, c \, \mathbf{\hat{z}}& \left(6f\right) & \mbox{O} \\ \mathbf{B}_{9} & =&- z_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- y_{3} \, \mathbf{a}_{3}& =&\frac12 \, \left(y_{3} - z_{3}\right) \, a \, \mathbf{\hat{x}}+ \frac{1}{2\sqrt{3}} \, \left(y_{3} + z_{3} - 2 x_{3}\right) \, a \, \mathbf{\hat{y}}- \frac13 \, \left(x_{3} + y_{3} + z_{3}\right) \, c \, \mathbf{\hat{z}}& \left(6f\right) & \mbox{O} \\ \mathbf{B}_{10} & =&- y_{3} \, \mathbf{a}_{1}- z_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}& =&\frac12 \, \left(x_{3} - y_{3}\right) \, a \, \mathbf{\hat{x}}+ \frac{1}{2\sqrt{3}} \, \left(x_{3} + y_{3} - 2 z_{3}\right) \, a \, \mathbf{\hat{y}}- \frac13 \, \left(x_{3} + y_{3} + z_{3}\right) \, c \, \mathbf{\hat{z}}& \left(6f\right) & \mbox{O} \\ \end{array} \]References
- B. A. Wechsler and C. T. Prewitt, Crystal Structure of Ilmenite (FeTiO3) at high temperature and high pressure, Am. Mineral. 69, 176–185 (1984).
- P. P. Ewald and C. Hermann, Strukturbericht 1913-1928 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1931).