| We have undertaken the first ever fully first-principles simulations of ferroelectric crystals at finite temperature with an aim to understand the nature of their phase transitions. In particular, we have studied the different aspects of phase transitions in two protypical ferroelectrics - PbTiO3 and KH2PO4.; In PbTiO3, we have successfully reproduced the temperature-driven transition from a tetragonal to a cubic phase by using constant-pressure Car-Parrinello molecular dynamics. By defining suitable order parameters in terms of atomic displacements, we are able to monitor the approach of the cubic phase. Using a quasi-harmonic analysis, with the inclusion of a temperature dependent volume and the average thermal atomic displacements as the most basic effects of anharmonicity, we are also able to recover the softening of ferroelectric modes as well as other features seen in experiments. These observations confirm the predominantly displacive nature of the transition, while our simulations also indicate a possible build-up of disorder near the transition temperature.; We have also studied the isotope effects in the ferroelectric transition in KH2PO4 by quantifying the temperature and mass dependence of the extent of delocalization of the hydrogens. Using a recently developed ab initio Open Path-integral Molecular Dynamics scheme we have calculated both the real and momentum-space distribution of the hydrogens in both protonated and deuterated KDP above and below their respective transition temperatures. We find that the two crystals not only involve different transition mechanisms but also the fluctuations above the transition temperature are of a qualitatively different nature. |
