Tetragonal PZT [Pb(ZrxTi1–x)O3] Structure: A3BC_tP5_99_bc_a_b

Picture of Structure; Click for Big Picture
Prototype : Pb(Zr0.52Ti0.48)O3
AFLOW prototype label : A3BC_tP5_99_bc_a_b
Strukturbericht designation : None
Pearson symbol : tP5
Space group number : 99
Space group symbol : $\mbox{P4mm}$
AFLOW prototype command : aflow --proto=A3BC_tP5_99_bc_a_b
--params=
$a$,$c/a$,$z_{1}$,$z_{2}$,$z_{3}$,$z_{4}$


  • This is a tetragonal ferroelectric distortion of the perovskite structure. In PbZrxTi1–xO3 (aka PZT) it is found for $x<0.52$. Although the first (2b) site is nearly equally occupied by Zr and Ti atoms, the pictures use Zr atoms. Compare this to the monoclinic PZT structure. To recover the cubic perovskite structure, take $c=a$, $z_{1}=0$, $z_{2}=1/2$, $z_{3}=0$, $z_{4}=1/2$.

Simple Tetragonal primitive vectors:

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

Basis vectors:

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

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_tP5_99_bc_a_b --params=

Species:

Running:

Output: