Phonon dispersion calculations using the Vaks model in antiferroelectric lead zirconate

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.