Tetragonal PZT [Pb(Zr$_{x}$Ti$_{1-x}$)O$_{3}$] Structure: A3BC_tP5_99_ac_b_a-002
| Prototype | O$_{3}$PbZr |
| AFLOW prototype label | A3BC_tP5_99_ac_b_a-002 |
| Mineral name | `PZT' |
| ICSD | 92059 |
| Pearson symbol | tP5 |
| Space group number | 99 |
| Space group symbol | $P4mm$ |
| AFLOW prototype command |
aflow --proto=A3BC_tP5_99_ac_b_a-002
--params=$a, \allowbreak c/a, \allowbreak z_{1}, \allowbreak z_{2}, \allowbreak z_{3}, \allowbreak z_{4}$ |
- This is a tetragonal ferroelectric distortion of the cubic perovskite structure, $E2_{1}$. In Pb(Zr$_{x}$Ti$_{1-x}$)O$_{3}$ (aka PZT) it is found for $x \le 0.52$. Although the first (2b) site is nearly equally occupied by zirconium and titanium atoms, the pictures use Zr atoms. Compare this to the monoclinic PZT structure.
- To recover the cubic perovskite structure, take $c=a, z_{1}=0, z_{2}=1/2, z_{3} = 0, z_{4} = 1/2$.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $z_{1} \, \mathbf{a}_{3}$ | = | $c z_{1} \,\mathbf{\hat{z}}$ | (1a) | O I |
| $\mathbf{B_{2}}$ | = | $z_{2} \, \mathbf{a}_{3}$ | = | $c z_{2} \,\mathbf{\hat{z}}$ | (1a) | Zr I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (1b) | Pb I |
| $\mathbf{B_{4}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+z_{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+c z_{4} \,\mathbf{\hat{z}}$ | (2c) | O II |
| $\mathbf{B_{5}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (2c) | O II |
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 PbZr$_{0.52}$Ti$_{0.48}$O$_3$, Phys. Rev. B 61, 8687–8695 (2000), doi:10.1103/PhysRevB.61.8687.
Prototype Generator
aflow --proto=A3BC_tP5_99_ac_b_a --params=$a,c/a,z_{1},z_{2},z_{3},z_{4}$