An analysis of the phonon dispersion curves of lead hafnate in the cubic phase using lattice-dynamical models

We have analyzed the phonon dispersion curves in the paraelectric phase of a lead hafnate crystal (PbHfO₃) by means of two different lattice-dynamical models. Both the rigid-ion model and the shell one provided an acceptable description of the available experimental data. The atomic displacement patterns were qualitatively different for the two models. In the rigid-ion model the motion in the characteristic low-energy flattened transverse acoustic branch contained both lead and hafnium displacements, while for the shell model it corresponded mainly to lead displacements with the small contribution of oxygen displacements. The shell model allows simultaneous description of the phonon dispersion curves and the correct value of the dielectric constant.