Phonon dispersion calculations using the Vaks model in antiferroelectric lead zirconate

Abstract

The calculations of low-energy phonon dispersion relations in lead zirconate (PZ) have been carried out using the Vaks model. This model takes into account only five low-energy phonon modes and their interactions. It has been shown that this model allows to achieve good agreement not only between calculated and experimental transverse acoustic phonon dispersion but also between their temperature dependences. It has been shown 5-mode system, which describes low-energy phonon dispersion in PZ, is close to unstable state. Even a little change of interaction parameter can lead to lattice instability with nonzero wave vector q crit . Wave vector q crit could have any value, including irrational one. In this case, system will undergo an incommensurate phase transition.

Mode Coupling at around M-Point in PZT

“…At the positions with there were clear minima of the DS intensity. Similar results were obtained for the PZT with 0.7% of Ti (PZT0.7) [ 33 ]. The conclusion was made, that the observed scattering features are related to the “interactions between the Pb-related modes and the octahedra tilting modes”.…”

“…Lattice dynamics of the antiferroelectric and ferroelectric materials of the PZO group were studied both experimentally [ 11 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 ] and theoretically [ 26 , 27 , 28 , 29 , 30 ]. In addition to the direct measurements of the phonon spectra using the optical spectroscopy and inelastic X-ray scattering (IXS) complementary diffuse scattering (DS) studies were done [ 14 , 31 , 32 , 33 , 34 ] The main attention was paid to the dynamic origin of the AFE phase and the details of the phonon dispersion around the -point ( ) and the R-point ( ).…”