Ab initio calculations of phonon spectra in ATiO3 perovskite crystals (A = Ca, Sr, Ba, Ra, Cd, Zn, Mg, Ge, Sn, Pb)

First-principles calculations of phonon spectra based on the density functional theory are carried out for calcium, strontium, barium, radium, cadmium, zinc, magnesium, germanium, tin, and lead titanates with a perovskite structure. By analyzing unstable modes in the phonon spectrum, the possible types of lattice distortion are determined and the energies of the corresponding phases are calculated. From analyzing the phonon spectra, force constants, and eigenvectors of TO phonons, a conclusion is drawn concerning the nature of ferroelectric phenomena in the crystals studied. It is shown that the main factors determining the possible appearance of off-center atoms in the A position are the geometric size and electronic configuration of these atoms.