Tetragonal-to-monoclinic phase transition in a ferroelectric perovskite: The structure of ${\mathrm{PbZr}}_{0.52}{\mathrm{Ti}}_{0.48}{\mathrm{O}}_3$

The perovskitelike ferroelectric system ${\mathrm{PbZr}}_{1-x}{\mathrm{Ti}}_x{\mathrm{O}}_3$ (PZT) has a nearly vertical morphotropic phase boundary (MPB) around $x=0.45\mathrm{}–\mathrm{0.50.}$ Recent synchrotron x-ray powder diffraction measurements by Noheda et al. [Appl. Phys. Lett. 74, 2059 (1999)] have revealed a monoclinic phase between the previously established tetragonal and rhombohedral regions. In the present work we describe a Rietveld analysis of the detailed structure of the tetragonal and monoclinic PZT phases on a sample with $x=0.48\mathrm{}$ for which the lattice parameters are, respectively, $a_t=4.044\mathrm{}$ Å, $c_t=4.138\mathrm{}$ Å, at 325 K, and $a_m=5.721\mathrm{}$ Å, $b_m=5.708\mathrm{}$ Å, $c_m=4.138\mathrm{}$ Å, $\beta =90.496\mathrm{}°,$ at 20 K. In the tetragonal phase the shifts of the atoms along the polar [001] direction are similar to those in ${\mathrm{PbTiO}}_3$ but the refinement indicates that there are, in addition, local disordered shifts of the Pb atoms of $\sim 0.2$ Å perpendicular to the polar axis. The monoclinic structure can be viewed as a condensation along one of the $〈110〉$ directions of the local displacements present in the tetragonal phase. It equally well corresponds to a freezing-out of the local displacements along one of the $〈100〉$ directions recently reported by Corker et al. [J. Phys.: Condens. Matter 10, 6251 (1998)] for rhombohedral PZT. The monoclinic structure therefore provides a microscopic picture of the MPB region in which one of the “locally” monoclinic phases in the “average” rhombohedral or tetragonal structures freezes out, and thus represents a bridge between these two phases.