Structural studies of Nd-modified lead zirconate titanate ceramics between 11 and 680 K at the morphotropic phase boundary

Raman spectroscopy between 11 and 680 K was used together with room-temperature x-ray-diffraction experiments for structural studies of ferroelectric Nd-modified lead zirconate titanate ceramics at the morphotropic phase boundary. The Nd addition was found to have a strong effect on the balance between tetragonal and trigonal phases in the structure. The tetragonal phase fraction increased and the size of trigonal domains decreased with the increasing Nd addition. The tetragonal $c/a$ ratio was found to increase at small Nd concentrations below 1% of the $A$-cation sites and then decrease again at higher concentrations. A similar behavior was found also with the Nd addition into ${\mathrm{PbTiO}}_3$ ceramics, but the $c/a$ ratio had a maximum at Nd concentrations of around 0.1%. Raman results revealed a subpeak structure of tetragonal $A_1\left(1\mathrm{}\mathrm{TO}\right)$-mode frequencies in agreement with earlier findings in ${\mathrm{PbTiO}}_3$ single crystals and ceramics. The observed subpeak frequencies of the $A_1\left(1\mathrm{}\mathrm{TO}\right)$ mode were approximately fit by energy levels of an anharmonic double-well potential both in symmetric (paraelectric) and asymmetric (ferroelectric) forms from the mean-field approach. In addition to the four subpeaks, an additional mode was also found at about $55{\mathrm{cm}}^{\mathrm{-}1}.$ Peak fit together with the second derivatives of Raman spectra were used to reveal different Raman peaks from tetragonal and trigonal phases in the intermediate-frequency region between 180 and $400{\mathrm{cm}}^{\mathrm{-}1}.$ The high-temperature Raman spectra from the samples were compared with spectra measured from ${\mathrm{Pb}}_{0.865}{\mathrm{La}}_{0.09}{(\mathrm{Z}\mathrm{r}}_{0.65}{\mathrm{Ti}}_{0.35}{)\mathrm{O}}_3$ ceramics which is a well-known relaxor material.