The vibrational modes of BaTiO₃ and PbTiO₃ in different crystalline phases have been investigated by means of density functional theory pseudopotential method. No evidences of low-temperature phase transition were found for PbTiO₃, while the tetragonal-orthogonal and orthorhombic-rhombohedral phase transitions were present for BaTiO₃. The variety of vibration frequency with tetragonal strain shows that the soft mode frequency increases with the tetragonal strain increasing followed by the transition of unstable soft mode to stable vibrational mode at a certain critical point. The tetragonal phase of PbTiO₃ is very stable owing to its large tetragonal strain, and relatively small tetragonal stain of BaTiO₃ is an important reason for its low-temperature phase transition.

Key words: ferroelectric phase transition, vibration frequency, tetragonal strain, PbTiO₃, BaTiO₃