Vibrational Self-Consistent Field Method Applied to the Ferroelectric Phase Transitions of Barium Titanate

Barium titanate is the prototypical ferroelectric ceramic, but the nature of the transitions between the various ferroelectric phases and the cubic non-ferroelectric phase is still under significant debate in the literature, with several different models proposed, such as the displacive and order-disorder models. The work presented here uses a vibrational self-consistent field method to obtain the anharmonic vibrational wavefunction of the system, and uses this to obtain a fully first-principles description of the phase transitions of this material for the first time. Our results are in qualitatitive agreement with the order-disorder description of phase transitions in barium titanate, with eight equal regions of nuclear probability density at high temperature, which gives way to a lower symmetry configuration at lower temperatures. To obtain a full quantitative picture of these phase transitions, further effects must be included, and potential ways of approaching this will be discussed.