DYNAMICAL STUDY OF PHONONS IN FERROELECTRIC LEAD TITANATE

Abstract
Lattice dynamical formalism using rigid ion model with long range coulomb forces and short range axially symmetric forces has been applied to the crystal of lead titanate in tetragonal phase. All zone center phonons and a few zone boundary phonons were used in determining the force constant parameters both at room temperature and close to T_c by nonlinear least squares analysis. The results indicate that the Ti-O short range forces are at least one order of magnitude larger than the Pb-O forces. Moreover oxygens retain an effective charge of 73% of their free ion value, whereas titaniums possess only 67% of their free ion charge. The eigenvector calculations of the lowest optic mode of E-symmetry correspond to the prediction by Last, whereas in BaTiO₃ the computed eigenvectors confirm the description of the soft mode due to Slater. The parameters obtained, have been utilized to compute elastic and piezoelectric properties of PbTiO₃. The calculations of the zone centre phonons near T_c reveal that the small anharmonic forces could lead to the observed frequency changes.