Ti off-center displacements and the oxygen isotope-induced phase transition in SrTiO₃

SrTiO₃ (STO) displays a huge isotope effect. Replacing ¹⁶O with ¹⁸O changes the incipient ferroelectric crystal into a ferroelectric crystal with a transition temperature of 24.5 K. We present a model that takes into account the soft mode, the NMR observed spontaneous Ti off-center displacements present in both ST¹⁶O and ST¹⁸O, and their interaction with each other. Replacing ¹⁶O with ¹⁸O increases the TiO₃ reduced mass by 5.5%. This is the only effect taken into account, and it affects only the soft mode leaving the Ti off-center displacements and their interaction with the soft mode constant. We show that the model accounts quantitatively for the ferroelectric phase transition, the Raman and neutron scattering observed soft modes, the temperature and ¹⁸O concentration dependence of the dielectric constant, and the ¹⁸O concentration and pressure dependence of the phase transition temperature.