First-principles study of tetragonal PbTiO3: Phonon and thermal expansion

Tetragonal PbTiO3 is a ferroelectric material and is reported to exhibit an unusual negative thermal expansion (NTE) behavior from room temperature to Curie temperature in experimental measurements. Since thermal expansion is closely associated with the anharmonicity of the lattice vibrations, the role of phonon in NTE is necessary to be given a detailed investigation. The vibrational properties indicate that: despite the NTE behavior in experiments, the contribution from overall phonons to thermal expansion is positive. Moreover, different phonon modes have different effects. Acoustic phonons promote larger volume expansion. In contrast, optical phonons lead to volume contraction. Due to the distinction of occupied phonon modes in different temperatures, this can be used to explain the normal thermal expansion below room temperature based on the related experiments.