First-principles investigation of ferroelectricity in perovskite compounds

We have used a first-principles ultra-soft-pseudopotential method in conjunction with an efficient preconditioned conjugate-gradient scheme to investigate the properties of a series of eight cubic perovskite compounds. The materials considered in this study are ${\mathrm{BaTiO}}_3$, ${\mathrm{SrTiO}}_3$, ${\mathrm{CaTiO}}_3$, ${\mathrm{KNbO}}_3$, ${\mathrm{NaNbO}}_3$ ${\mathrm{PbTiO}}_3$ , ${\mathrm{PbZrO}}_3$, and ${\mathrm{BaZrO}}_3$. We computed the total-energy surface for zone-center distortions correct to fourth order in the soft-mode displacement, including renormalizations due to strain coupling. Quantities calculated for each material include lattice constants, elastic constants, zone-center phonon frequencies, Grüneisen parameters, and band structures. Our calculations correctly predict the symmetry of the ground-state structures of all compounds whose observed low-temperature structure retains a primitive five-atom unit cell. The database of results we have generated shows a number of trends which can be understood using simple chemical ideas based on the sizes of ions, and the frustration inherent in the cubic perovskite structure.