Monoclinic PZT [Pb(ZrxTi1–x)O3] Structure: A3BC_mC10_8_ab_a_a

Picture of Structure; Click for Big Picture
Prototype : Pb(Zr0.52Ti0.48)O3
AFLOW prototype label : A3BC_mC10_8_ab_a_a
Strukturbericht designation : None
Pearson symbol : mC10
Space group number : 8
Space group symbol : $\mbox{Cm}$
AFLOW prototype command : aflow --proto=A3BC_mC10_8_ab_a_a
--params=
$a$,$b/a$,$c/a$,$\beta$,$x_{1}$,$z_{1}$,$x_{2}$,$z_{2}$,$x_{3}$,$z_{3}$,$x_{4}$,$y_{4}$,$z_{4}$


  • This is a monoclinic ferroelectric distortion of the perovskite structure. In Pb(ZrxTi1–x)O3 (aka PZT) it is found only when $x=0.52$. Although the second (2a) site is nearly equally occupied by Zr and Ti atoms, the pictures use Zr atoms. Compare this to the tetragonal PZT structure.

Base-centered Monoclinic primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & \frac12 \, a \, \mathbf{\hat{x}} - \frac12 \, b \, \mathbf{\hat{y}} \\ \mathbf{a}_2 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, b \, \mathbf{\hat{y}} \\ \mathbf{a}_3 & = & c \cos\beta \, \mathbf{\hat{x}} + c \sin\beta \, \mathbf{\hat{z}} \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & =& x_{1} \, \mathbf{a}_{1} + x_{1} \, \mathbf{a}_{2} + z_{1} \, \mathbf{a}_{3}& =& \left(x_{1} \, a + z_{1} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ z_{1} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(2a\right) & \mbox{O I} \\ \mathbf{B}_{2} & =& x_{2} \, \mathbf{a}_{1} + x_{2} \, \mathbf{a}_{2} + z_{2} \, \mathbf{a}_{3}& =& \left(x_{2} \, a + z_{2} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ z_{2} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(2a\right) & \mbox{Pb} \\ \mathbf{B}_{3} & =& x_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + z_{3} \, \mathbf{a}_{3}& =& \left(x_{3} \, a + z_{3} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ z_{3} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(2a\right) & \mbox{Zr} \\ \mathbf{B}_{4} & =& \left(x_{4} - y_{4}\right) \, \mathbf{a}_{1} + \left(x_{4} + y_{4}\right) \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3}& =& \left(x_{4} \, a + z_{4} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ y_{4} \, b \, \mathbf{\hat{y}}+ z_{4} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4b\right) & \mbox{O II} \\ \mathbf{B}_{5} & =& \left(x_{4} + y_{4}\right) \, \mathbf{a}_{1} + \left(x_{4} - y_{4}\right) \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3}& =& \left(x_{4} \, a + z_{4} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}- y_{4} \, b \, \mathbf{\hat{y}}+ z_{4} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4b\right) & \mbox{O II} \\ \end{array} \]

References

  • B. Noheda, J. A. Gonzalo, L. E. Cross, R. Guo, S.–E. Park, D. E. Cox, and G. Shirane, Tetragonal–to–monoclinic phase transition in a ferroelectric perovskite: The structure of PbZr0.52Ti0.48O3, Phys. Rev. B 61, 8687–8695 (2000), doi:10.1103/PhysRevB.61.8687.

Geometry files


Prototype Generator

aflow --proto=A3BC_mC10_8_ab_a_a --params=

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Running:

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