CaTiO3 Pnma Perovskite Structure: AB3C_oP20_62_c_cd_a

Picture of Structure; Click for Big Picture
Prototype : CaTiO3
AFLOW prototype label : AB3C_oP20_62_c_cd_a
Strukturbericht designation : None
Pearson symbol : oP20
Space group number : 62
Space group symbol : $\mbox{Pnma}$
AFLOW prototype command : aflow --proto=AB3C_oP20_62_c_cd_a
--params=
$a$,$b/a$,$c/a$,$x_{2}$,$z_{2}$,$x_{3}$,$z_{3}$,$x_{4}$,$y_{4}$,$z_{4}$


Other compounds with this structure

  • BiVO4, CeSiO4, CeVO4, DyPO4, ErPO4, ErVO4, HfSO4, HoPO4, HoVO4, LuPO4, LuVO4, NdVO4, PrVO4, ScPO4, ScVO4, TbPO4, TbVO4, ThSiO4, TmPO4, TmVO4, YPO4, YVO4, YbAsO4, YbPO4, YbVO4, LaMnO3, YAlO3, $R$FeO3 ($R$ = La, Pr, Nd, Sm, Eu, Y)

  • This is the true ground state of the prototype perovskite, CaTiO3. The standard cubic structure, E21, is a high-temperature phase.

Simple Orthorhombic primitive vectors:

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

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(4a\right) & \mbox{Ti} \\ \mathbf{B}_{2} & =&\frac12 \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{3}& =&\frac12 \, a \, \mathbf{\hat{x}}+ \frac12 \, c \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{Ti} \\ \mathbf{B}_{3} & =&\frac12 \, \mathbf{a}_{2}& =&\frac12 \, b \, \mathbf{\hat{y}}& \left(4a\right) & \mbox{Ti} \\ \mathbf{B}_{4} & =&\frac12 \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& =&\frac12 \, a \, \mathbf{\hat{x}}+ \frac12 \, b \, \mathbf{\hat{y}}+ \frac12 \, c \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{Ti} \\ \mathbf{B}_{5} & =&x_{2} \, \mathbf{a}_{1}+ \frac14 \, \mathbf{a}_{2}+ z_{2} \, \mathbf{a}_{3}& =&x_{2} \, a \, \mathbf{\hat{x}}+ \frac14 \, b \, \mathbf{\hat{y}}+ z_{2} \, c \, \mathbf{\hat{z}}& \left(4c\right) & \mbox{Ca} \\ \mathbf{B}_{6} & =&\left(\frac12 - x_{2}\right) \, \mathbf{a}_{1}+ \frac34 \, \mathbf{a}_{2}+ \left(\frac12 + z_{2}\right) \, \mathbf{a}_{3}& =&\left(\frac12 - x_{2}\right) \, a \, \mathbf{\hat{x}}+ \frac34 \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{2}\right) \, c \, \mathbf{\hat{z}}& \left(4c\right) & \mbox{Ca} \\ \mathbf{B}_{7} & =&- x_{2} \, \mathbf{a}_{1}+ \frac34 \, \mathbf{a}_{2}- z_{2} \, \mathbf{a}_{3}& =&- x_{2} \, a \, \mathbf{\hat{x}}+ \frac34 \, b \, \mathbf{\hat{y}}- z_{2} \, c \, \mathbf{\hat{z}}& \left(4c\right) & \mbox{Ca} \\ \mathbf{B}_{8} & =&\left(\frac12 + x_{2}\right) \, \mathbf{a}_{1}+ \frac14 \, \mathbf{a}_{2}+ \left(\frac12 - z_{2}\right) \, \mathbf{a}_{3}& =&\left(\frac12 + x_{2}\right) \, a \, \mathbf{\hat{x}}+ \frac14 \, b \, \mathbf{\hat{y}}+ \left(\frac12 - z_{2}\right) \, c \, \mathbf{\hat{z}}& \left(4c\right) & \mbox{Ca} \\ \mathbf{B}_{9} & =&x_{3} \, \mathbf{a}_{1}+ \frac14 \, \mathbf{a}_{2}+ z_{3} \, \mathbf{a}_{3}& =&x_{3} \, a \, \mathbf{\hat{x}}+ \frac14 \, b \, \mathbf{\hat{y}}+ z_{3} \, c \, \mathbf{\hat{z}}& \left(4c\right) & \mbox{O I} \\ \mathbf{B}_{10} & =&\left(\frac12 - x_{3}\right) \, \mathbf{a}_{1}+ \frac34 \, \mathbf{a}_{2}+ \left(\frac12 + z_{3}\right) \, \mathbf{a}_{3}& =&\left(\frac12 - x_{3}\right) \, a \, \mathbf{\hat{x}}+ \frac34 \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{3}\right) \, c \, \mathbf{\hat{z}}& \left(4c\right) & \mbox{O I} \\ \mathbf{B}_{11} & =&- x_{3} \, \mathbf{a}_{1}+ \frac34 \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}& =&- x_{3} \, a \, \mathbf{\hat{x}}+ \frac34 \, b \, \mathbf{\hat{y}}- z_{3} \, c \, \mathbf{\hat{z}}& \left(4c\right) & \mbox{O I} \\ \mathbf{B}_{12} & =&\left(\frac12 + x_{3}\right) \, \mathbf{a}_{1}+ \frac14 \, \mathbf{a}_{2}+ \left(\frac12 - z_{3}\right) \, \mathbf{a}_{3}& =&\left(\frac12 + x_{3}\right) \, a \, \mathbf{\hat{x}}+ \frac14 \, b \, \mathbf{\hat{y}}+ \left(\frac12 - z_{3}\right) \, c \, \mathbf{\hat{z}}& \left(4c\right) & \mbox{O I} \\ \mathbf{B}_{13} & =&x_{4} \, \mathbf{a}_{1}+ y_{4} \, \mathbf{a}_{2}+ z_{4} \, \mathbf{a}_{3}& =&x_{4} \, a \, \mathbf{\hat{x}}+ y_{4} \, b \, \mathbf{\hat{y}}+ z_{4} \, c \, \mathbf{\hat{z}}& \left(8d\right) & \mbox{O II} \\ \mathbf{B}_{14} & =&\left(\frac12 - x_{4}\right) \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}+ \left(\frac12 + z_{4}\right) \, \mathbf{a}_{3}& =&\left(\frac12 - x_{4}\right) \, a \, \mathbf{\hat{x}}- y_{4} \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{4}\right) \, c \, \mathbf{\hat{z}}& \left(8d\right) & \mbox{O II} \\ \mathbf{B}_{15} & =&- x_{4} \, \mathbf{a}_{1}+ \left(\frac12 + y_{4}\right) \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}& =&- x_{4} \, a \, \mathbf{\hat{x}}+ \left(\frac12 + y_{4}\right) \, b \, \mathbf{\hat{y}}- z_{4} \, c \, \mathbf{\hat{z}}& \left(8d\right) & \mbox{O II} \\ \mathbf{B}_{16} & =&\left(\frac12 + x_{4}\right) \, \mathbf{a}_{1}+ \left(\frac12 - y_{4}\right) \, \mathbf{a}_{2}+ \left(\frac12 - z_{4}\right) \, \mathbf{a}_{3}& =&\left(\frac12 + x_{4}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 - y_{4}\right) \, b \, \mathbf{\hat{y}}+ \left(\frac12 - z_{4}\right) \, c \, \mathbf{\hat{z}}& \left(8d\right) & \mbox{O II} \\ \mathbf{B}_{17} & =&- x_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}& =&- x_{4} \, a \, \mathbf{\hat{x}}- y_{4} \, b \, \mathbf{\hat{y}}- z_{4} \, c \, \mathbf{\hat{z}}& \left(8d\right) & \mbox{O II} \\ \mathbf{B}_{18} & =&\left(\frac12 + x_{4}\right) \, \mathbf{a}_{1}+ y_{4} \, \mathbf{a}_{2}+ \left(\frac12 - z_{4}\right) \, \mathbf{a}_{3}& =&\left(\frac12 + x_{4}\right) \, a \, \mathbf{\hat{x}}+ y_{4} \, b \, \mathbf{\hat{y}}+ \left(\frac12 - z_{4}\right) \, c \, \mathbf{\hat{z}}& \left(8d\right) & \mbox{O II} \\ \mathbf{B}_{19} & =&x_{4} \, \mathbf{a}_{1}+ \left(\frac12 - y_{4}\right) \, \mathbf{a}_{2}+ z_{4} \, \mathbf{a}_{3}& =&x_{4} \, a \, \mathbf{\hat{x}}+ \left(\frac12 - y_{4}\right) \, b \, \mathbf{\hat{y}}+ z_{4} \, c \, \mathbf{\hat{z}}& \left(8d\right) & \mbox{O II} \\ \mathbf{B}_{20} & =&\left(\frac12 - x_{4}\right) \, \mathbf{a}_{1}+ \left(\frac12 + y_{4}\right) \, \mathbf{a}_{2}+ \left(\frac12 + z_{4}\right) \, \mathbf{a}_{3}& =&\left(\frac12 - x_{4}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 + y_{4}\right) \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{4}\right) \, c \, \mathbf{\hat{z}}& \left(8d\right) & \mbox{O II} \\ \end{array} \]

References

  • T. Yamanaka, N. Hirai, and Y. Komatsu, Structure change of Ca1–xSrxTiO3 perovskite with composition and pressure, Am. Mineral. 87, 1183–1189 (2002).

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_oP20_62_c_cd_a --params=

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