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Lattice Dynamics of (001) PbTiO3 Thin Films in a Polarizable Ions Model

The results of the lattice dynamics calculation of PbTiO3 thin films in framework of Gordon-Kim model accounting for polarizability of ions are presented. Slab with two different terminations of surface is considered. The films under consideration with various thickness have ferroelectric modes in which vibrations of atoms are parallel to surface and instable polar modes were found in PbO-terminated slab with thickness of 3.95 Á. The dependence of some film's properties such as dielectric permittivities, dynamical charges, in-plane polarization, and frequencies of unstable ferroelectric modes on the film thickness is obtained from calculation.