Cubic Perovskite (CaTiO3, $E2_{1}$) Structure: AB3C_cP5_221_a_c_b

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Prototype : CaTiO3
AFLOW prototype label : AB3C_cP5_221_a_c_b
Strukturbericht designation : $E2_{1}$
Pearson symbol : cP5
Space group number : 221
Space group symbol : $\mbox{Pm}\bar{3}\mbox{m}$
AFLOW prototype command : aflow --proto=AB3C_cP5_221_a_c_b
--params=
$a$


Other compounds with this structure

  • BaTiO3, PbTiO3, PbZrO3

  • Cubic perovskite is actually the high-temperature phase of the compounds listed below. The ground states are usually distorted perovskite structures. Many of these substances are ferroelectric. By removing one atom type we get various structures, all with space group Pm3m : Removing the calcium atoms leads to the $\alpha$–ReO3 (D09) structure; removing the titanium atoms leads to the Cu3Au (L12) structure; removing the oxygen atoms leads to the CsCl (B2) structure; removing the calcium or titanium and the oxygen atoms leads to the simple cubic (Ah) structure. (Ewald, 1931) originally gave this compound the Strukturbericht Designation $G4$, but this was changed by (Gottfried, 1937) to $E2_{1}$.

Simple Cubic primitive vectors:

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

Basis vectors:

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

References

  • T. Barth, Die Kristallstruktur von Perowskit und verwandten Verbindungen, Norsk. Geol. Tidssk. 8, 14–19 (1925).
  • P. P. Ewald and C. Hermann, Strukturbericht 1913-1928 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1931).
  • C. Gottfried and F. Schossberger, Strukturbericht Band III 1933-1935 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1937).

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=AB3C_cP5_221_a_c_b --params=

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