The role of mechanical boundary conditions in the soft mode dynamics of PbTiO3

The role of different mechanical boundary conditions in the soft mode dynamics of ferroelectric PbTiO3 is systematically investigated using first-principles-based simulations and analytical model. The change in the soft mode dynamics due to hydrostatic pressure, uniaxial and biaxial stresses and biaxial strains is studied in a wide temperature range. Our computations predict: (i) the existence of Curie-Weiss laws that relate the soft mode frequency to the stress or strain; (ii) a non-trivial temperature evolution of the associated Curie-Weiss constants; (iii) a qualitative difference between the soft mode response to stresses/strains and hydrostatic pressure. The latter finding implies that the Curie-Weiss pressure law commonly used for residual stress estimation may not apply for the cases of uniaxial and biaxial stresses and strains. On the other hand, our systematic study offers a way to eliminate this difficulty through the establishment of Curie-Weiss stress and strain laws. Implications of our predictions for some available experimental data are discussed.