Ti off-center displacements and the oxygen isotope-induced phase transition in SrTi O3

SrTi O3 (STO) displays a huge isotope effect. Replacing O16 with O18 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 ST O16 and ST O18, and their interaction with each other. Replacing O16 with O18 increases the Ti O3 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 O18 concentration dependence of the dielectric constant, and the O18 concentration and pressure dependence of the phase transition temperature.