Ilmenite (FeTiO3, $E2_{2}$) Structure: AB3C_hR10_148_c_f_c

Picture of Structure; Click for Big Picture
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).

Geometry files


Prototype Generator

aflow --proto=AB3C_hR10_148_c_f_c --params=

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