Lattice dynamics of PbTiO 3

Inelastic neutron scattering experiments were performed to investigate the phonon dispersion relations along the (1,0,0), (1,1,0) and (1,1,1) directions in cubic PbTiO3. All of the transverse optic (TO) branches soften significantly toward the zone center around Tc. The zone-center TO mode stiffens considerably at 1173 K. The energies of the (ξ, 0, 0) TO branch for PbTiO3 measured at 793 K are considerably higher than those for Pb(Zn1/3Nb2/3)O3 at 423 K in the entire zone. The (ξ, 0, 0) transverse acoustic (TA) branch is found to soften slightly at 793 K. The (ξ, ξ, ξ) TA branch exhibits two minima at the middle point (1/4,1/4,1/4) and the zone boundary (1/2,1/2,1/2). These two modes are weakly temperature dependent up to 1173 K.