Encyclopedia of Crystallographic Prototypes

AFLOW Prototype: AB3C_hR10_148_c_f_c

  • M. J. Mehl, D. Hicks, C. Toher, O. Levy, R. M. Hanson, G. L. W. Hart, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 1, Comp. Mat. Sci. 136, S1-S828 (2017). (doi=10.1016/j.commatsci.2017.01.017)
  • D. Hicks, M. J. Mehl, E. Gossett, C. Toher, O. Levy, R. M. Hanson, G. L. W. Hart, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 2, Comp. Mat. Sci. 161, S1-S1011 (2019). (doi=10.1016/j.commatsci.2018.10.043)
  • D. Hicks, M.J. Mehl, M. Esters, C. Oses, O. Levy, G.L.W. Hart, C. Toher, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 3, Comp. Mat. Sci. 199, 110450 (2021). (doi=10.1016/j.commatsci.2021.110450)

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 : $\text{R}\bar{3}$
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} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{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) & \text{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) & \text{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) & \text{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) & \text{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) & \text{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) & \text{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) & \text{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) & \text{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) & \text{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) & \text{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


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